**Spacecraft Propulsion**

[20] Lee W, Bang H, Leeghim H. Cooperative localization between small UAVs using a combination of heterogeneous sensors. Aerospace Science and Technology. 2013;27(1):

[21] Cui P, Yu Z, Zhu S, Ai G. Real-time navigation for Mars final approach using X-ray pulsars. In: AIAA Guidance, Navigation, and Control Conference and Exhibit; 19–22

August; Boston, MA; 2013. p. AIAA 2013-5204

105-111

144 Space Flight

**Chapter 8**

**Provisional chapter**

**Long-Life Technology for Space Flight Hall Thrusters**

The vastly improved durability of spacecrafts, coupled with the simultaneous continuous development of thrusters for high power output, has created a strong demand for Hall thrusters (HT) with long service lives. However, erosion of the discharge channel walls by high-energy ions is the most impactful and visible process that limits the lifetime of the thruster. This process is very sensitive to the operation mode of the thruster and the corresponding power density. We hereby present the results of our investigation on the factors that limit the lifetime of Hall thrusters, and three proven techniques for improving longevity of use including magnetic shielding (MS), wall-less technology, and aft-

The development of space propulsion technology is the cornerstone of development in the aerospace industry. With the rapid development of a wide range of satellite and spacecraft technologies, the demand for space transportation systems is on the rise. Electric propulsion technology is widely used in spacecrafts due to its high specific impulse, compact structure, low propellant consumption, and other advantages. The Hall thruster is currently one of the

Hall thrusters (HT), also called stationary plasma thrusters (SPT), were invented in the 1960s, and an early model was first used to transport a Russian satellite (METEOR-18) on December 29, 1971 [2]. The number of SPTs used for scientific and commercial space missions in the United States, Russia, Europe, and Japan is on the rise. The United States involved some of the original work on Hall Thruster in the early and mid-1960s [3–6]. However, interest in that particular accelerator was considerably less than that in ion

**Keywords:** Hall thruster, long life, magnetic shield, wall-less, aft-magnetic

most widely used electric propulsion technologies at a global level [1].

**Long-Life Technology for Space Flight Hall Thrusters**

DOI: 10.5772/intechopen.73043

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Yongjie Ding, Liqiu Wei, Hong Li and Daren Yu

Yongjie Ding, Liqiu Wei, Hong Li and Daren Yu

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73043

magnetic fields with large gradient.

**Abstract**

**1. Introduction**

**Provisional chapter**

## **Long-Life Technology for Space Flight Hall Thrusters**

**Long-Life Technology for Space Flight Hall Thrusters**

DOI: 10.5772/intechopen.73043

Yongjie Ding, Liqiu Wei, Hong Li and Daren Yu Yongjie Ding, Liqiu Wei, Hong Li and Daren Yu Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73043

#### **Abstract**

The vastly improved durability of spacecrafts, coupled with the simultaneous continuous development of thrusters for high power output, has created a strong demand for Hall thrusters (HT) with long service lives. However, erosion of the discharge channel walls by high-energy ions is the most impactful and visible process that limits the lifetime of the thruster. This process is very sensitive to the operation mode of the thruster and the corresponding power density. We hereby present the results of our investigation on the factors that limit the lifetime of Hall thrusters, and three proven techniques for improving longevity of use including magnetic shielding (MS), wall-less technology, and aftmagnetic fields with large gradient.

**Keywords:** Hall thruster, long life, magnetic shield, wall-less, aft-magnetic

**1. Introduction**

The development of space propulsion technology is the cornerstone of development in the aerospace industry. With the rapid development of a wide range of satellite and spacecraft technologies, the demand for space transportation systems is on the rise. Electric propulsion technology is widely used in spacecrafts due to its high specific impulse, compact structure, low propellant consumption, and other advantages. The Hall thruster is currently one of the most widely used electric propulsion technologies at a global level [1].

Hall thrusters (HT), also called stationary plasma thrusters (SPT), were invented in the 1960s, and an early model was first used to transport a Russian satellite (METEOR-18) on December 29, 1971 [2]. The number of SPTs used for scientific and commercial space missions in the United States, Russia, Europe, and Japan is on the rise. The United States involved some of the original work on Hall Thruster in the early and mid-1960s [3–6]. However, interest in that particular accelerator was considerably less than that in ion

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

thrusters. Russia has played a dominant role in the development of SPTs until relatively recently, when the USA, Europe, and Japan began to develop a strong interest in SPTs in the early 1990s. This resurgence of interest has generated a strong recovery in related research and development.

**2. Long-life limitations of space flight Hall thrusters**

**Figure 2.** Channel geometry of a PPS 1350-GQM thruster after 4200 h of operation.

Improvements in the operational lifetime of spacecrafts, and the continuous development of high-power thrusters, have resulted in an increasing demand for Hall thrusters with a long service life. There are several physical processes that limit the lifetime and reliability of Hall thrusters. These include [8] erosion of the cathode and magnetic system elements by the accelerated primary and secondary ions and the erosion of cathode's thermoemitter by ions which are accelerated in the near-cathode potential drop in the hollow cathode discharge plasma. Additional processes include oxidization of the getter, contaminated Xe gas flowing through the cathode, evaporation of the thermoemitter and heater materials. Finally, suboptimal temperatures under operation conditions, degradation of insulating and structural element materials, operation in space under increased temperature and radiation factor's impact, mechanical deformation and cracking of the heater, cathode and accelerator materials, due to the thermal shocks which occur when the thruster is started, can all have undesired effects. The erosion of the discharge channel walls by high-energy ions is the most impactful and notable factor which limits the thruster's lifetime. This process is most sensitive to the thruster's operation mode and the corresponding power density [9, 10]. **Figure 2** shows photographs of the channel geometry of a PPS 1350-GQM thruster after 4200 h of operation. The interaction between the plasma and the wall causes power deposition on the channel wall and other structure components. The magnetic field topology leads directly to the large particle flux

Long-Life Technology for Space Flight Hall Thrusters http://dx.doi.org/10.5772/intechopen.73043 149

**Figure 1** shows a schematic of a common Hall thruster. The basic process of operation begins with the release of electrons from a cathode, which enter a chamber and are subjected to a circumferential Hall drift movement by an orthogonal, axial electric field, and a magnetic field that acts primarily in the radial direction. Neutral atoms that are injected through an anode/gas distributor collide with the electrons in the closed drift and are ionized. Although the magnetic field is strong enough to lock the electrons in a circumferential drift within the discharge channel, its intensity is not sufficiently strong to affect the ions, which are accelerated by the axial electric field. An axial electron flux equal to that of the ion reaches the anode due to the cross-field mobility that often exceeds classical values. The cathode can provide the same electron flux to neutralize the exhausted ions. Therefore, quasi-neutrality is maintained throughout the discharge channel and the plume, and there is consequently no space-charge limitation on the acceleration. Therefore, the thrust density of SPTs is relatively high, compared to that of conventional electrostatic propulsion devices [7].

At present, commercial spacecrafts require thrusters that are capable of trouble-free operation for over 8000 h; however, conventional HTs have a relatively short operational lifetime. Thus, the development of long-life technology for Hall thrusters is significant.

**Figure 1.** Schematic of a Hall thruster.

## **2. Long-life limitations of space flight Hall thrusters**

thrusters. Russia has played a dominant role in the development of SPTs until relatively recently, when the USA, Europe, and Japan began to develop a strong interest in SPTs in the early 1990s. This resurgence of interest has generated a strong recovery in related

**Figure 1** shows a schematic of a common Hall thruster. The basic process of operation begins with the release of electrons from a cathode, which enter a chamber and are subjected to a circumferential Hall drift movement by an orthogonal, axial electric field, and a magnetic field that acts primarily in the radial direction. Neutral atoms that are injected through an anode/gas distributor collide with the electrons in the closed drift and are ionized. Although the magnetic field is strong enough to lock the electrons in a circumferential drift within the discharge channel, its intensity is not sufficiently strong to affect the ions, which are accelerated by the axial electric field. An axial electron flux equal to that of the ion reaches the anode due to the cross-field mobility that often exceeds classical values. The cathode can provide the same electron flux to neutralize the exhausted ions. Therefore, quasi-neutrality is maintained throughout the discharge channel and the plume, and there is consequently no space-charge limitation on the acceleration. Therefore, the thrust density of SPTs is relatively high, compared to that of conventional electrostatic propulsion

At present, commercial spacecrafts require thrusters that are capable of trouble-free operation for over 8000 h; however, conventional HTs have a relatively short operational lifetime. Thus,

the development of long-life technology for Hall thrusters is significant.

research and development.

148 Space Flight

devices [7].

**Figure 1.** Schematic of a Hall thruster.

Improvements in the operational lifetime of spacecrafts, and the continuous development of high-power thrusters, have resulted in an increasing demand for Hall thrusters with a long service life. There are several physical processes that limit the lifetime and reliability of Hall thrusters. These include [8] erosion of the cathode and magnetic system elements by the accelerated primary and secondary ions and the erosion of cathode's thermoemitter by ions which are accelerated in the near-cathode potential drop in the hollow cathode discharge plasma. Additional processes include oxidization of the getter, contaminated Xe gas flowing through the cathode, evaporation of the thermoemitter and heater materials. Finally, suboptimal temperatures under operation conditions, degradation of insulating and structural element materials, operation in space under increased temperature and radiation factor's impact, mechanical deformation and cracking of the heater, cathode and accelerator materials, due to the thermal shocks which occur when the thruster is started, can all have undesired effects.

The erosion of the discharge channel walls by high-energy ions is the most impactful and notable factor which limits the thruster's lifetime. This process is most sensitive to the thruster's operation mode and the corresponding power density [9, 10]. **Figure 2** shows photographs of the channel geometry of a PPS 1350-GQM thruster after 4200 h of operation. The interaction between the plasma and the wall causes power deposition on the channel wall and other structure components. The magnetic field topology leads directly to the large particle flux

**Figure 2.** Channel geometry of a PPS 1350-GQM thruster after 4200 h of operation.

with high energy, which is also directed toward the channel walls. In the discharge channel, the atoms undergo diffusion movement before ionization, which results in a radial motion component. The ions that are generated via the ionization process acquire the initial velocity of the atom and a radial velocity component. This results in an acceleration of the ion beam along the radial direction. In addition, the sheath and the presheath structures which are formed by the interaction of the plasma and channel walls also generate a radial electric field, which leads to radial ion divergence. Due to the influence of various physical factors mentioned above, the ion beam will diverge in the channel. In the acceleration zone, a portion of the high-energy ions will not be able to directly exit the channel. Instead, the wall material is sputtered and bombarded. When the bombardment energy is greater than the binding energy of the atoms in the wall, the wall material is sputtered and the geometrical morphology of the channel wall is altered [11, 12].

Long-term ion bombardment of the channel wall causes erosion, and the resulting change in the channel's geometry alters the optimum working condition of the thruster, which results in a decline in performance; more importantly, the breakdown of the channel's ceramic causes the magnetic pole to be exposed to the plasma, which would affect this field. Eventually, the performance of the Hall thruster is significantly affected, resulting in eventual failure. The end of the lifetime of a Hall thruster is generally accepted as the point of time when the channel is completely eroded by ion bombardment, and the magnetic pole is exposed to the plasma.

#### **3. Magnetic shielding technology**

During the years 2007 and 2009, Aerojet and Lockheed Martin Space Systems Company demonstrated the extension of the working hours of the qualification model (BPT-4000 4.5 kW HT) over 10,400 h. Most significantly, no measurable erosion of the insulator ring was observed from 5600 h to 10,400 h, which indicated that the thruster had achieved a "zero" erosion configuration [13, 14]. These improvements are the result of the topological structure of the magnetic field near the erosion surface. Jet Propulsion Laboratory (JPL) describes this process as "magnetic shielding (MS)." **Figure 3** shows the design principles involved in a magnetically shielded (MS) configuration, compared to an unshielded (US) configuration. In the US configuration, the magnetic lines near the channel's exit are almost perpendicular to the channel walls; however, the magnetic field lines of the MS configuration extend to the acceleration region deep within the channel and are arranged close to the ceramic walls without intersecting it. This is called the "grazing line," which effectively inhibits cavity wall erosion by high-energy ions.

The electron number density (*ne*) in HTs is so low that collisions between electrons and gases have little influence on the *E × B* drift (where *E* and *B* denote the electric and magnetic fields, respectively) or Hall drift, and an important current, the Hall current, is produced in a circumferential direction. The electron parameter, Ω*<sup>e</sup>* ≡ *ω*ce /*υ<sup>e</sup>* ≫ 1, where *ω*ceis the electron gyro-frequency and *υ<sup>e</sup>* is the total collision frequency. Thus, electron temperature (*Te*) stays nearly constant along the magnetic field lines.

$$\nabla\_{\parallel} T\_e \approx \mathbf{0} \tag{1}$$

Furthermore, the momentum equation of electrons can be simplified as

two important properties of the force lines in HTs [15], that is, *Te* ≈ *Te*<sup>0</sup>

, *φ*<sup>0</sup>

tial, then they are not able to effectively control the near-wall electric field.

along a magnetic field lines, where *Te*<sup>0</sup>

decreased by 2–3 orders [19].

*E*// ≈ −*Te* ∇// ln*ne* (2)

**Figure 3.** Schematics of the different structure of HTs (top) the potential (*φ*) and the electron temperature (*Te*) distribution along the center line. From left to right are traditional configuration, US configuration, and MS configuration, respectively.

and the resistive contribution to the electric field is negligibly small. Eqs. (1) and (2) contribute to

As shown in **Figure 3**, the MS configuration can be obtained by optimizing the magnetic field to realize a higher potential *φ* and a lower Te near the cavity surface. The parameter Te has its lowest value when the electrons are closet to the discharge voltage Vd, such that the kinetic energy of the injected ions and the sheath energy are reduced to values near or below the sputtering yield threshold. In addition, if the magnetic field is designed to appropriately match with the geometry of the discharge channel, the generated self-consistent electric field will be larger, and the field direction will be approximately perpendicular to the channel.

Therefore, the main principle when designing MS HTs is to recognize that the pressure of the electrons (yielding *Te* × In (ne) in Eq. (2)) is such that the electric field E is no longer orthogonal to the magnetic field, which can be clearly observed in **Figure 3**. Hence, if the magnetic field lines with convex curvature toward the anode [16] near the channel walls are not equipoten-

These aforementioned ideas are consistent and provide some interesting insight into the theoretical development of magnetic shielding technology. The design of the H6MS Hall thruster in particular is based on this technological innovation [17, 18]. **Figure 4** (left) shows a photograph of the H6MS Hall thruster and its physical condition after operating continuously for 15 h. JPL demonstrated, using both numerical simulations and experiments, that the ion beam produced in a US HT can be controlled effectively, and the erosion rate on the walls is

, and *ne*<sup>0</sup>

and *φ* ≈ *φ*<sup>0</sup> + *Te*<sup>0</sup> ln(*ne*

Long-Life Technology for Space Flight Hall Thrusters http://dx.doi.org/10.5772/intechopen.73043

denote integration constants.

/*ne*0)

151

**Figure 3.** Schematics of the different structure of HTs (top) the potential (*φ*) and the electron temperature (*Te*) distribution along the center line. From left to right are traditional configuration, US configuration, and MS configuration, respectively.

Furthermore, the momentum equation of electrons can be simplified as

with high energy, which is also directed toward the channel walls. In the discharge channel, the atoms undergo diffusion movement before ionization, which results in a radial motion component. The ions that are generated via the ionization process acquire the initial velocity of the atom and a radial velocity component. This results in an acceleration of the ion beam along the radial direction. In addition, the sheath and the presheath structures which are formed by the interaction of the plasma and channel walls also generate a radial electric field, which leads to radial ion divergence. Due to the influence of various physical factors mentioned above, the ion beam will diverge in the channel. In the acceleration zone, a portion of the high-energy ions will not be able to directly exit the channel. Instead, the wall material is sputtered and bombarded. When the bombardment energy is greater than the binding energy of the atoms in the wall, the wall material is sputtered and the geometrical morphology of the

Long-term ion bombardment of the channel wall causes erosion, and the resulting change in the channel's geometry alters the optimum working condition of the thruster, which results in a decline in performance; more importantly, the breakdown of the channel's ceramic causes the magnetic pole to be exposed to the plasma, which would affect this field. Eventually, the performance of the Hall thruster is significantly affected, resulting in eventual failure. The end of the lifetime of a Hall thruster is generally accepted as the point of time when the channel is completely eroded by ion bombardment, and the magnetic pole is exposed to the plasma.

During the years 2007 and 2009, Aerojet and Lockheed Martin Space Systems Company demonstrated the extension of the working hours of the qualification model (BPT-4000 4.5 kW HT) over 10,400 h. Most significantly, no measurable erosion of the insulator ring was observed from 5600 h to 10,400 h, which indicated that the thruster had achieved a "zero" erosion configuration [13, 14]. These improvements are the result of the topological structure of the magnetic field near the erosion surface. Jet Propulsion Laboratory (JPL) describes this process as "magnetic shielding (MS)." **Figure 3** shows the design principles involved in a magnetically shielded (MS) configuration, compared to an unshielded (US) configuration. In the US configuration, the magnetic lines near the channel's exit are almost perpendicular to the channel walls; however, the magnetic field lines of the MS configuration extend to the acceleration region deep within the channel and are arranged close to the ceramic walls without intersecting it. This is called the

"grazing line," which effectively inhibits cavity wall erosion by high-energy ions.

The electron number density (*ne*) in HTs is so low that collisions between electrons and gases have little influence on the *E × B* drift (where *E* and *B* denote the electric and magnetic fields, respectively) or Hall drift, and an important current, the Hall current, is produced in a circumferential direction. The electron parameter, Ω*<sup>e</sup>* ≡ *ω*ce /*υ<sup>e</sup>* ≫ 1, where *ω*ceis the electron

∇// *Te* ≈ 0 (1)

is the total collision frequency. Thus, electron temperature (*Te*) stays

channel wall is altered [11, 12].

150 Space Flight

**3. Magnetic shielding technology**

gyro-frequency and *υ<sup>e</sup>*

nearly constant along the magnetic field lines.

$$E\_{\parallel} \approx -T\_e \nabla\_{\parallel \parallel} \ln n\_e \tag{2}$$

and the resistive contribution to the electric field is negligibly small. Eqs. (1) and (2) contribute to two important properties of the force lines in HTs [15], that is, *Te* ≈ *Te*<sup>0</sup> and *φ* ≈ *φ*<sup>0</sup> + *Te*<sup>0</sup> ln(*ne* /*ne*0) along a magnetic field lines, where *Te*<sup>0</sup> , *φ*<sup>0</sup> , and *ne*<sup>0</sup> denote integration constants.

As shown in **Figure 3**, the MS configuration can be obtained by optimizing the magnetic field to realize a higher potential *φ* and a lower Te near the cavity surface. The parameter Te has its lowest value when the electrons are closet to the discharge voltage Vd, such that the kinetic energy of the injected ions and the sheath energy are reduced to values near or below the sputtering yield threshold. In addition, if the magnetic field is designed to appropriately match with the geometry of the discharge channel, the generated self-consistent electric field will be larger, and the field direction will be approximately perpendicular to the channel.

Therefore, the main principle when designing MS HTs is to recognize that the pressure of the electrons (yielding *Te* × In (ne) in Eq. (2)) is such that the electric field E is no longer orthogonal to the magnetic field, which can be clearly observed in **Figure 3**. Hence, if the magnetic field lines with convex curvature toward the anode [16] near the channel walls are not equipotential, then they are not able to effectively control the near-wall electric field.

These aforementioned ideas are consistent and provide some interesting insight into the theoretical development of magnetic shielding technology. The design of the H6MS Hall thruster in particular is based on this technological innovation [17, 18]. **Figure 4** (left) shows a photograph of the H6MS Hall thruster and its physical condition after operating continuously for 15 h. JPL demonstrated, using both numerical simulations and experiments, that the ion beam produced in a US HT can be controlled effectively, and the erosion rate on the walls is decreased by 2–3 orders [19].

**Figure 5** depicts the standard configuration of a conventional Hall thruster and a wall-less Hall thruster. The anode/gas distributor is usually positioned at the bottom of the discharge channel. The cathode is located on the outside of the channel and is the source of electrons for discharge balancing and neutralization of the ion beam in the plume area. A radial directed magnetic field with a bell-shaped intensity distribution along the center line is generally by coils or permanent magnets. As shown in **Figure 5**, the peak value of the magnetic field intensity is typically located near the discharge channel outlet. The ceramic channel constrains the propellant and thus maintains a higher atom density for subsequent ionization processes. The easiest way to move the ionization and the acceleration regions out of the discharge channel is to place the anode directly at the channel outlet plane, which is shown in **Figure 5**. This requires that the shape and size of the channel, as well as the magnetic field topology and discharge channel geometry, are unchanged. The proposed idea is the simplest way to transform

Long-Life Technology for Space Flight Hall Thrusters http://dx.doi.org/10.5772/intechopen.73043 153

**Figure 6** depicts images of a low-power ion source working with Xenon propellant in the standard 200 W-class Hall thruster and WL configuration with a ring anode. The discharge voltage is 200 V, and the propellant mass flow rate (MFR) is 1 mg/s. The photograph with bright light near the channel exit (right) indicates that the discharge region was pushed outside the ceramic channel, as expected in the WL configuration. A distinct difference between the two methods is that the boundary of the ion beam with WL configuration is less distinct, which means that the divergence angle of the plume region in a wall-less configuration is much larger. The discharge current is also higher for WL compared to the standard configuration. Therefore, the thruster's performance will diminish and the erosion of external parts, such as the pole pieces, will be increased with time. Moreover, a large beam divergence means that the plasma from thrusters will have a negative effect on the

Hall thrusters into WL-HTs.

spacecraft elements [23].

**Figure 5.** Configurations of a standard Hall thruster and wall-less Hall thruster.

**Figure 4.** H6MS Hall thruster before (left) and after (right) 15 h of testing. The ceramic walls were covered with a carbon film which was back-sputtered from the vacuum device's inner wall.

In addition, JPL also applied a magnetic shielding technique to a miniature Hall thruster. This investigation, which was performed with the cooperation of the University of California, led to the development of a magnetically shielded miniature HT (MaSMi HT), which was operated with a 275 V discharge voltage and a 325 W discharge power [20]. In Europe, CNRS (France) also realized a magnetic shielding technique for Hall thrusters which operated at a discharge power of 1.5 kW (200 W–PPS-flex and ISCT200-MS Hall thruster) [9, 21].

#### **4. Wall-less technology**

The relatively short lifetime of HTs due to plasma-surface interactions inside the discharge chamber is another drawback of conventional Hall thrusters. The underlying cause of this problem is channel wall erosion caused by the bombardment of high-energy electrons and ions. It is known that the choice of material of the channel wall influences the properties of the plasma discharge dynamics, which consequently influences the performance and the lifetime of the thruster. The plasma properties in a Hall thruster are also influenced by the secondary electron emission of the wall material.

Wall-less Hall thruster (WL-HT) was proposed to reduce the interaction between plasma and Hall thruster's channel walls. The objective is to limit the plasma-wall interaction by moving the ionization and acceleration regions to the exterior of the discharge channel. Such an unusual configuration was first proposed by Kapulkin et al. of Russia, during the 1990s. The concept was then proposed based on the idea of a Hall thruster, with an external electric field. Nevertheless, the assumption that limitations of the ion current are linked to the plasma instabilities led researchers to transition from a standard one-stage structure to a two-stage structure. However, the concept of a two-stage structure is less attractive because of its complicated design and operation. The concept of moving the electric field to the exterior of the channel was also investigated in Russia at TsNIIMASH, for thrusters with anode layer (TAL) in the late 1990s and early 2000s. The researchers demonstrated the possibility of stable operation at a high voltage with a high efficiency [22].

**Figure 5** depicts the standard configuration of a conventional Hall thruster and a wall-less Hall thruster. The anode/gas distributor is usually positioned at the bottom of the discharge channel. The cathode is located on the outside of the channel and is the source of electrons for discharge balancing and neutralization of the ion beam in the plume area. A radial directed magnetic field with a bell-shaped intensity distribution along the center line is generally by coils or permanent magnets. As shown in **Figure 5**, the peak value of the magnetic field intensity is typically located near the discharge channel outlet. The ceramic channel constrains the propellant and thus maintains a higher atom density for subsequent ionization processes. The easiest way to move the ionization and the acceleration regions out of the discharge channel is to place the anode directly at the channel outlet plane, which is shown in **Figure 5**. This requires that the shape and size of the channel, as well as the magnetic field topology and discharge channel geometry, are unchanged. The proposed idea is the simplest way to transform Hall thrusters into WL-HTs.

**Figure 6** depicts images of a low-power ion source working with Xenon propellant in the standard 200 W-class Hall thruster and WL configuration with a ring anode. The discharge voltage is 200 V, and the propellant mass flow rate (MFR) is 1 mg/s. The photograph with bright light near the channel exit (right) indicates that the discharge region was pushed outside the ceramic channel, as expected in the WL configuration. A distinct difference between the two methods is that the boundary of the ion beam with WL configuration is less distinct, which means that the divergence angle of the plume region in a wall-less configuration is much larger. The discharge current is also higher for WL compared to the standard configuration. Therefore, the thruster's performance will diminish and the erosion of external parts, such as the pole pieces, will be increased with time. Moreover, a large beam divergence means that the plasma from thrusters will have a negative effect on the spacecraft elements [23].

**Figure 5.** Configurations of a standard Hall thruster and wall-less Hall thruster.

In addition, JPL also applied a magnetic shielding technique to a miniature Hall thruster. This investigation, which was performed with the cooperation of the University of California, led to the development of a magnetically shielded miniature HT (MaSMi HT), which was operated with a 275 V discharge voltage and a 325 W discharge power [20]. In Europe, CNRS (France) also realized a magnetic shielding technique for Hall thrusters which operated at a

**Figure 4.** H6MS Hall thruster before (left) and after (right) 15 h of testing. The ceramic walls were covered with a carbon

The relatively short lifetime of HTs due to plasma-surface interactions inside the discharge chamber is another drawback of conventional Hall thrusters. The underlying cause of this problem is channel wall erosion caused by the bombardment of high-energy electrons and ions. It is known that the choice of material of the channel wall influences the properties of the plasma discharge dynamics, which consequently influences the performance and the lifetime of the thruster. The plasma properties in a Hall thruster are also influenced by the secondary

Wall-less Hall thruster (WL-HT) was proposed to reduce the interaction between plasma and Hall thruster's channel walls. The objective is to limit the plasma-wall interaction by moving the ionization and acceleration regions to the exterior of the discharge channel. Such an unusual configuration was first proposed by Kapulkin et al. of Russia, during the 1990s. The concept was then proposed based on the idea of a Hall thruster, with an external electric field. Nevertheless, the assumption that limitations of the ion current are linked to the plasma instabilities led researchers to transition from a standard one-stage structure to a two-stage structure. However, the concept of a two-stage structure is less attractive because of its complicated design and operation. The concept of moving the electric field to the exterior of the channel was also investigated in Russia at TsNIIMASH, for thrusters with anode layer (TAL) in the late 1990s and early 2000s. The researchers demonstrated the possibility of stable operation at a high voltage with a high efficiency [22].

discharge power of 1.5 kW (200 W–PPS-flex and ISCT200-MS Hall thruster) [9, 21].

**4. Wall-less technology**

152 Space Flight

film which was back-sputtered from the vacuum device's inner wall.

electron emission of the wall material.

curved anode located at the exit is shaped so that it does not intersect with the field lines, which ensures that the magnetic field can trap electrons and effectively produce thrust. This type of optimization may appear similar to the MS Hall thruster, but the most striking difference is that it is not necessary for the field lines in the WL magnetic configuration to extend deep into the cavity to capture electrons. Therefore, it is quite easy to generate the required

Long-Life Technology for Space Flight Hall Thrusters http://dx.doi.org/10.5772/intechopen.73043 155

Based on the 1.5-kW PPS-Flex HT, some experiments have also been performed. As expected, the discharge current is significantly reduced by the adjustment of the magnetic topology, and the positioning of the anode in parallel. In order to improve the utilization of propellant and achieve a satisfactory specific impulse, thrust level, and anode efficiency, the thruster was operated with a voltage of 500 V. However, the current magnetic does not allow the generation of WL topology with a peak magnetic field value above 90 G. This significantly impacts the operation at high voltage, and further optimization is necessary to reduce discharge current oscillations and increase the thruster efficiency. An improved Hall thruster based on PPS-Flex, which is capable of forming a stronger magnetic field intensity, is currently under development. The influence of the ceramic channel length of the thruster is an important factor that requires further study. It is possible that the channel length may be reduced as ionization takes place near the channel outlet plane. However, it should also be kept sufficiently

Another proposed WL prototype was also based on the structure of the PPI thruster. To facilitate more effective and uniform distribution of the xenon gas, a 3-mm-thick gridded anode which covers the channel exit was designed, as shown in **Figure 4**. In order to limit the plasma diffusion in the discharge channel, the width of the anode was decreased. The gridded anode has a transparency of 68% with a 3-mm-diameter hole. Apart from the anode design, the sec-

**Figure 8.** Photograph of the second wall-less thruster prototype with a gridded anode at the exit plane.

magnetic circuit.

long to ensure the homogenization of neutral gas.

ond prototype is almost identical to the first one (**Figure 8**).

**Figure 6.** Photographs of the low-power PPI Hall thruster operating at the voltage of 200 V and a MFR of 1 mg/s in standard (left) and WLHT (right) configurations.

**Figure 7** displays the interaction between the annular anode and the B-field lines. The magnetic circuit of the original WL-HT prototype, as shown in **Figure 7** (left), is based on the classical Hall thruster design. By shifting the anode from the bottom, to the channel outlet without any other changes, the magnetic field lines are roughly perpendicular to the ceramic wall and intersect with the anode located near the cavity outlet. This results in a decline in the efficiency of the electron confinement. Moreover, a large number of high-energy electrons emitted from the cathode will be trapped along the magnetic field lines and eventually arrive at the anode. Therefore, the electron current is relatively large, and the propellant utilization is low [24].

To solve the problem of excessive energy losses of the electrons at the anode, some optimized prototypes were proposed. The first optimization approach involves rotating the anode by 90 degrees to restore the magnetic barrier, while maintaining the topology of the magnetic field. However, this design does not perform satisfactorily due to two limitations. The first is that a large component of the magnetic field lines near the channel exit does not contribute to the trapping of electrons and the production of thrust. The other is that the ionization and acceleration region are too short for effective electron-atom collision. **Figure 7** (right) portrays a generally satisfactory design. The magnetic field lines are injected axially, and the peak of the magnetic field intensity is pushed downstream at the channel exit. The

**Figure 7.** Schematics of original (left) and optimized (right) WL-HT prototype.

curved anode located at the exit is shaped so that it does not intersect with the field lines, which ensures that the magnetic field can trap electrons and effectively produce thrust. This type of optimization may appear similar to the MS Hall thruster, but the most striking difference is that it is not necessary for the field lines in the WL magnetic configuration to extend deep into the cavity to capture electrons. Therefore, it is quite easy to generate the required magnetic circuit.

Based on the 1.5-kW PPS-Flex HT, some experiments have also been performed. As expected, the discharge current is significantly reduced by the adjustment of the magnetic topology, and the positioning of the anode in parallel. In order to improve the utilization of propellant and achieve a satisfactory specific impulse, thrust level, and anode efficiency, the thruster was operated with a voltage of 500 V. However, the current magnetic does not allow the generation of WL topology with a peak magnetic field value above 90 G. This significantly impacts the operation at high voltage, and further optimization is necessary to reduce discharge current oscillations and increase the thruster efficiency. An improved Hall thruster based on PPS-Flex, which is capable of forming a stronger magnetic field intensity, is currently under development. The influence of the ceramic channel length of the thruster is an important factor that requires further study. It is possible that the channel length may be reduced as ionization takes place near the channel outlet plane. However, it should also be kept sufficiently long to ensure the homogenization of neutral gas.

**Figure 7** displays the interaction between the annular anode and the B-field lines. The magnetic circuit of the original WL-HT prototype, as shown in **Figure 7** (left), is based on the classical Hall thruster design. By shifting the anode from the bottom, to the channel outlet without any other changes, the magnetic field lines are roughly perpendicular to the ceramic wall and intersect with the anode located near the cavity outlet. This results in a decline in the efficiency of the electron confinement. Moreover, a large number of high-energy electrons emitted from the cathode will be trapped along the magnetic field lines and eventually arrive at the anode. Therefore, the electron current is relatively large, and the propellant utilization

**Figure 6.** Photographs of the low-power PPI Hall thruster operating at the voltage of 200 V and a MFR of 1 mg/s in

To solve the problem of excessive energy losses of the electrons at the anode, some optimized prototypes were proposed. The first optimization approach involves rotating the anode by 90 degrees to restore the magnetic barrier, while maintaining the topology of the magnetic field. However, this design does not perform satisfactorily due to two limitations. The first is that a large component of the magnetic field lines near the channel exit does not contribute to the trapping of electrons and the production of thrust. The other is that the ionization and acceleration region are too short for effective electron-atom collision. **Figure 7** (right) portrays a generally satisfactory design. The magnetic field lines are injected axially, and the peak of the magnetic field intensity is pushed downstream at the channel exit. The

**Figure 7.** Schematics of original (left) and optimized (right) WL-HT prototype.

is low [24].

154 Space Flight

standard (left) and WLHT (right) configurations.

Another proposed WL prototype was also based on the structure of the PPI thruster. To facilitate more effective and uniform distribution of the xenon gas, a 3-mm-thick gridded anode which covers the channel exit was designed, as shown in **Figure 4**. In order to limit the plasma diffusion in the discharge channel, the width of the anode was decreased. The gridded anode has a transparency of 68% with a 3-mm-diameter hole. Apart from the anode design, the second prototype is almost identical to the first one (**Figure 8**).

**Figure 8.** Photograph of the second wall-less thruster prototype with a gridded anode at the exit plane.

**Figure 9.** (Left) Photograph of the low-power PPI Hall thruster in standard configuration firing with Xe at 200 V and 1 mg/s. (Right) Photograph of the second prototype of WL-HT with a gridded anode firing with Xe under same conditions.

**Figure 9** shows two plume region photographs of the PPI thruster operating with a Xe propellant; the left photograph shows the thruster in a standard configuration, and the right one is the wall-less Hall thruster with a gridded anode. The discharge voltage is 200 V, and the MFR is 1 mg/s. Compared to the anode ring, the discharge area of the Hall thruster with the gridded anode is repositioned outside the discharge channel, which is indicated by the bright light in front of the outlet. The ion beam boundaries of the WL Hall thruster are also less defined in this prototype, which implies that there is a degradation in performance.

Hall thrusters in WL configuration generally experience significant benefit in integration, lifetime, operating envelope, and propellant options. Since the acceleration zone is outside the discharge channel, the channel wall can be substantially shortened, thus reducing the mass and improving the economy of volume. The interaction between the plasma and the walls is also significantly reduced. Therefore, the impact of the channel material on the thrusters' performance is reduced. More importantly, it is presumably possible for the thruster to operate at a higher voltage and with an extended lifetime. In addition, the reduction of the plasma-wall interaction can lead to higher electron temperatures and positive points, which should result in efficient ionization of the propellants such as krypton and argon.

An approach to push down the magnetic field and the channel can be adjusted accordingly and can achieve plasma discharge without wall loss. The result of calculations based on simulation has confirmed that the abovementioned approach causes acceleration processes to occur outside the channel, but ionization occurs in the channel. The temperature of the walls remains relatively low, since the resulting power deposition on this structure is minimal. This is because the wall is only bombarded with low-energy ions and electrons. Therefore, the channel erosion is effectively reduced, and the operational life of the thruster is extended. In addition, the overall efficiency of the system is improved because additional coil power is not consumed.

Long-Life Technology for Space Flight Hall Thrusters http://dx.doi.org/10.5772/intechopen.73043 157

**Figure 10.** Magnetic structure and configuration.

Based on this research, Harbin Institute of Technology designed a 200-W Hall thruster with two permanent magnet rings, to facilitate an in-depth investigation of the effects of the aftmagnetic field with a large gradient, on discharge properties and device performance. This thruster has five noteworthy features. First, the magnetic field is only excited by an inner and an outer permanent magnetic ring. Second, the gas distributor and the anode are made of nonmagnetic stainless steel, while the other metal structures of the thruster are made of titanium. Therefore, the other parts of the entire thruster are nonmagnetic, and a magnetic screen is not necessary. Third, the anode's front end-face is at the internal magnetic separatrix position, and it has a hollow structure. Compared to the traditional Hall thrusters, the distance from the channel outlet to the zero-magnetic region is shorter, which implies that the magnetic field gradient is larger than that of traditional Hall thrusters. Fourth, by using various sets of ceramic rings, the channel length can be easily changed while keeping the width of the channel fixed. Finally, 50% of the thruster's shell components are hollow. To effectively reduce the discharge channel temperature, they are directly exposed. References [27, 28] highlight the visual preliminarily evidence, which confirms the feasibility of the proposed thrusters. The thruster is able

#### **5. Aft-magnetic field with large gradient technology**

To address the problems associated with power losses, and the low lifetime associated with the high surface-to-volume ratio of low power Hall thrusters, Harbin Institute of Technology proposed an aft-magnetic field with large gradient technique. In this approach, the maximum magnetic field strength is located on the outside of the channel with a large gradient. Harbin Institute of Technology developed a Hall thruster using a focused magnetic field of low power, which was excited using only two permanent magnet rings, such that the maximum magnetic field strength is outside the channel (Brexit/Brmax = 0.75 can be achieved). The magnetic field gradient in this configuration is much larger than that of a conventional Hall thruster, which can achieve a value of 20 G/mm [25, 26]. **Figure 10** shows the magnetic structure and configuration of the aft-magnetic field setup.

**Figure 10.** Magnetic structure and configuration.

**Figure 9** shows two plume region photographs of the PPI thruster operating with a Xe propellant; the left photograph shows the thruster in a standard configuration, and the right one is the wall-less Hall thruster with a gridded anode. The discharge voltage is 200 V, and the MFR is 1 mg/s. Compared to the anode ring, the discharge area of the Hall thruster with the gridded anode is repositioned outside the discharge channel, which is indicated by the bright light in front of the outlet. The ion beam boundaries of the WL Hall thruster are also less

**Figure 9.** (Left) Photograph of the low-power PPI Hall thruster in standard configuration firing with Xe at 200 V and 1 mg/s. (Right) Photograph of the second prototype of WL-HT with a gridded anode firing with Xe under same conditions.

Hall thrusters in WL configuration generally experience significant benefit in integration, lifetime, operating envelope, and propellant options. Since the acceleration zone is outside the discharge channel, the channel wall can be substantially shortened, thus reducing the mass and improving the economy of volume. The interaction between the plasma and the walls is also significantly reduced. Therefore, the impact of the channel material on the thrusters' performance is reduced. More importantly, it is presumably possible for the thruster to operate at a higher voltage and with an extended lifetime. In addition, the reduction of the plasma-wall interaction can lead to higher electron temperatures and positive points, which should result

To address the problems associated with power losses, and the low lifetime associated with the high surface-to-volume ratio of low power Hall thrusters, Harbin Institute of Technology proposed an aft-magnetic field with large gradient technique. In this approach, the maximum magnetic field strength is located on the outside of the channel with a large gradient. Harbin Institute of Technology developed a Hall thruster using a focused magnetic field of low power, which was excited using only two permanent magnet rings, such that the maximum magnetic field strength is outside the channel (Brexit/Brmax = 0.75 can be achieved). The magnetic field gradient in this configuration is much larger than that of a conventional Hall thruster, which can achieve a value of 20 G/mm [25, 26]. **Figure 10** shows the magnetic

defined in this prototype, which implies that there is a degradation in performance.

in efficient ionization of the propellants such as krypton and argon.

156 Space Flight

**5. Aft-magnetic field with large gradient technology**

structure and configuration of the aft-magnetic field setup.

An approach to push down the magnetic field and the channel can be adjusted accordingly and can achieve plasma discharge without wall loss. The result of calculations based on simulation has confirmed that the abovementioned approach causes acceleration processes to occur outside the channel, but ionization occurs in the channel. The temperature of the walls remains relatively low, since the resulting power deposition on this structure is minimal. This is because the wall is only bombarded with low-energy ions and electrons. Therefore, the channel erosion is effectively reduced, and the operational life of the thruster is extended. In addition, the overall efficiency of the system is improved because additional coil power is not consumed.

Based on this research, Harbin Institute of Technology designed a 200-W Hall thruster with two permanent magnet rings, to facilitate an in-depth investigation of the effects of the aftmagnetic field with a large gradient, on discharge properties and device performance. This thruster has five noteworthy features. First, the magnetic field is only excited by an inner and an outer permanent magnetic ring. Second, the gas distributor and the anode are made of nonmagnetic stainless steel, while the other metal structures of the thruster are made of titanium. Therefore, the other parts of the entire thruster are nonmagnetic, and a magnetic screen is not necessary. Third, the anode's front end-face is at the internal magnetic separatrix position, and it has a hollow structure. Compared to the traditional Hall thrusters, the distance from the channel outlet to the zero-magnetic region is shorter, which implies that the magnetic field gradient is larger than that of traditional Hall thrusters. Fourth, by using various sets of ceramic rings, the channel length can be easily changed while keeping the width of the channel fixed. Finally, 50% of the thruster's shell components are hollow. To effectively reduce the discharge channel temperature, they are directly exposed. References [27, 28] highlight the visual preliminarily evidence, which confirms the feasibility of the proposed thrusters. The thruster is able to discharge with lower wall energy loss and eliminate wall erosion both in a straight channel and in an oblique arrangement (Brexit/Brmax = 0.75). The maximum anode efficiency is 29.1% (straight channel) and 34.2% (oblique channel) with a discharge power of 200 W. When the channel is enlarged to Brexit/Brmax = 0.9, the anode efficiency can be improved to 42% [27]. **Figure 11** depicts photographs of the ceramic channel after a discharge with Brexit/Brmax = 0.75. It is observed that there is a 1-mm-long area, which is slightly yellow, in the outlet area of the inner ceramic wall. A black deposition is also observed, which almost completely covers the entire outer ceramic wall. Neither of these observations indicate that the whiteness of the ceramic bottom is caused by a bombardment of high-energy ions. It can therefore be concluded that there are very few high-energy ions which bombard the wall and cause erosion. The resulting ions are mainly low-energy ions [26].

Due to the large gradient of the magnetic field, matching the magnetic field to the anode's position is very important, which when carried out to a very large extent determines the performance of the thruster. Simulation and experimental results demonstrate that when the anode is placed between the outer and inner magnetic separatrices, both the efficiency and the thrust are at a maximum. The significant energy losses on the walls result in a low efficiency and thrust, despite the high degree of ionization, when the anode is placed at the inner magnetic separatrix. Thus, the performance of the thruster is at its lowest when the anode is at the outer magnetic separatrix, because of the lower ionization level and larger divergence angle of the

Long-Life Technology for Space Flight Hall Thrusters http://dx.doi.org/10.5772/intechopen.73043 159

A hollow indented anode is proposed to increase the neutral gas density in the discharge channel, so that the performance of the thruster can be improved. The experimental results to date indicate that this structure can effectively improve the performance (in terms of anode efficiency, ionization rate, propellant utilization, and thrust) compared to the hollow straight anode, under similar operating conditions. Simulation results indicate that the neutral gas density can be effectively increased by the utilization of an indented anode in a discharge channel and on the centerline of the channel. Furthermore, the ionization rate in the channel and the preionization in the anode can also be increased. Therefore, the hollow indented anode can be considered as an important design concept for improving the thruster's performance [30].

As acceleration occurs in the plume area and ionization occurs in the channel, the simulation and experimental results indicate that the maximum electron temperature can be found in the plume zone, while the electron temperature in the channel is relatively low. The secondary electron emission yield of the channel material will have a small but measurable effect on the thruster's performance. This assertion was experimentally verified. It was confirmed that materials with low sputtering yield could be used to further increase the life of the low-power thrusters while discharging through a channel with walls of titanium and graphite. **Figure 12** shows a picture of the 200-W prototype Hall thruster and plume discharge with titanium wall material [31].

Two additional low-power Hall thrusters were designed by Harbin Institute of Technology, with power ratings of 10–20 W and 50–100 W. The maximum anode efficiency was about 30%,

**Figure 12.** 200 W Hall thruster discharge with titanium wall material (a) prototype of the Hall thruster and (b) picture

of discharge plume.

plume, as the ionization zone is shifted toward the plume region [24].

In order to extend the life and improve the performance of low-power Hall thrusters, Harbin Institute of Technology has done further research on anode design [29–31] and channel wall material analysis [32].

Unlike conventional Hall thrusters, the peak of the magnetic field strength is outside the discharge channel, for Hall thrusters which adopt an aft-magnetic field with a large gradient and double peak. Therefore, the distance from the channel outlet to the zero magnetic field region is relatively short. However, if the thruster adopts a traditional anode configuration and anode location, it will experience a drop in its performance, as this configuration may cause an inadequate homogenization of neutral gas. Hence, a comparative study was performed for a U-shaped hollow anode with the front end-face and the flat plate anodes in the zero magnetic field region, with the first magnetic peak (corresponding to the rear and front end-faces of the U-shaped anode, respectively). The research shows that under the same operating conditions, the highest overall performance is achieved for thrusters with a hollow anode. For an anode positioned at the magnetic peak, its ionization rate is at a maximum. However, most of the ionized ions produced bombarded the walls, resulting in energy loss and reduced performance. For an anode in the zero magnetic field region, the voltage and propellant utilization are lower than those of the hollow anode. Thus, although the maximum ionization rate is higher than that of the hollow anode, the wall power loss is slightly smaller. In addition, due to its shorter ionization region and relatively shorter channel, it also has a poor overall performance compared to that of the hollow anode [28].

**Figure 11.** Ceramics rings after discharge.

Due to the large gradient of the magnetic field, matching the magnetic field to the anode's position is very important, which when carried out to a very large extent determines the performance of the thruster. Simulation and experimental results demonstrate that when the anode is placed between the outer and inner magnetic separatrices, both the efficiency and the thrust are at a maximum. The significant energy losses on the walls result in a low efficiency and thrust, despite the high degree of ionization, when the anode is placed at the inner magnetic separatrix. Thus, the performance of the thruster is at its lowest when the anode is at the outer magnetic separatrix, because of the lower ionization level and larger divergence angle of the plume, as the ionization zone is shifted toward the plume region [24].

to discharge with lower wall energy loss and eliminate wall erosion both in a straight channel and in an oblique arrangement (Brexit/Brmax = 0.75). The maximum anode efficiency is 29.1% (straight channel) and 34.2% (oblique channel) with a discharge power of 200 W. When the channel is enlarged to Brexit/Brmax = 0.9, the anode efficiency can be improved to 42% [27]. **Figure 11** depicts photographs of the ceramic channel after a discharge with Brexit/Brmax = 0.75. It is observed that there is a 1-mm-long area, which is slightly yellow, in the outlet area of the inner ceramic wall. A black deposition is also observed, which almost completely covers the entire outer ceramic wall. Neither of these observations indicate that the whiteness of the ceramic bottom is caused by a bombardment of high-energy ions. It can therefore be concluded that there are very few high-energy ions which bombard the wall and cause erosion.

In order to extend the life and improve the performance of low-power Hall thrusters, Harbin Institute of Technology has done further research on anode design [29–31] and channel wall

Unlike conventional Hall thrusters, the peak of the magnetic field strength is outside the discharge channel, for Hall thrusters which adopt an aft-magnetic field with a large gradient and double peak. Therefore, the distance from the channel outlet to the zero magnetic field region is relatively short. However, if the thruster adopts a traditional anode configuration and anode location, it will experience a drop in its performance, as this configuration may cause an inadequate homogenization of neutral gas. Hence, a comparative study was performed for a U-shaped hollow anode with the front end-face and the flat plate anodes in the zero magnetic field region, with the first magnetic peak (corresponding to the rear and front end-faces of the U-shaped anode, respectively). The research shows that under the same operating conditions, the highest overall performance is achieved for thrusters with a hollow anode. For an anode positioned at the magnetic peak, its ionization rate is at a maximum. However, most of the ionized ions produced bombarded the walls, resulting in energy loss and reduced performance. For an anode in the zero magnetic field region, the voltage and propellant utilization are lower than those of the hollow anode. Thus, although the maximum ionization rate is higher than that of the hollow anode, the wall power loss is slightly smaller. In addition, due to its shorter ionization region and relatively shorter channel, it also has a

poor overall performance compared to that of the hollow anode [28].

The resulting ions are mainly low-energy ions [26].

material analysis [32].

158 Space Flight

**Figure 11.** Ceramics rings after discharge.

A hollow indented anode is proposed to increase the neutral gas density in the discharge channel, so that the performance of the thruster can be improved. The experimental results to date indicate that this structure can effectively improve the performance (in terms of anode efficiency, ionization rate, propellant utilization, and thrust) compared to the hollow straight anode, under similar operating conditions. Simulation results indicate that the neutral gas density can be effectively increased by the utilization of an indented anode in a discharge channel and on the centerline of the channel. Furthermore, the ionization rate in the channel and the preionization in the anode can also be increased. Therefore, the hollow indented anode can be considered as an important design concept for improving the thruster's performance [30].

As acceleration occurs in the plume area and ionization occurs in the channel, the simulation and experimental results indicate that the maximum electron temperature can be found in the plume zone, while the electron temperature in the channel is relatively low. The secondary electron emission yield of the channel material will have a small but measurable effect on the thruster's performance. This assertion was experimentally verified. It was confirmed that materials with low sputtering yield could be used to further increase the life of the low-power thrusters while discharging through a channel with walls of titanium and graphite. **Figure 12** shows a picture of the 200-W prototype Hall thruster and plume discharge with titanium wall material [31].

Two additional low-power Hall thrusters were designed by Harbin Institute of Technology, with power ratings of 10–20 W and 50–100 W. The maximum anode efficiency was about 30%,

**Figure 12.** 200 W Hall thruster discharge with titanium wall material (a) prototype of the Hall thruster and (b) picture of discharge plume.

when the design was based on an aft-magnetic field with large gradient technique. Highpower thrusters which operate at 1.35 and 5 kW have been designed and tested at the Harbin Institute of Technology using the aft-magnetic field with large gradient technique. The maximum efficiency attained was 65%. Therefore, the aft-magnetic field with large gradient technique can be widely used in Hall thrusters to achieve different power outputs.

**Author details**

People's Republic of China

Harbin, People's Republic of China

\*, Liqiu Wei2

, Hong Li1

\*Address all correspondence to: dingyongjie@hit.edu.cn

2017;**121**(1):011101. DOI: 10.1063/1.4972269

Society, Series II. June 1962;**7**:414

1426. DOI: 10.1063/1.1354644

U.S.A. AIAA; 1997. p. 2789

DOI: 10.1109/tps.2014.2331180

Harbin Institute of Technology; 2010

Physics Reports. 2003;**29**(3):235-250. DOI: 10.1134/1.1561119

and experiment. Bulletin of the American Physical Society. 1962;**7**:441

and Daren Yu1

Long-Life Technology for Space Flight Hall Thrusters http://dx.doi.org/10.5772/intechopen.73043 161

1 School of Energy Science and Engineering, Harbin Institute of Technology, Harbin,

2 Academy of Fundamental an Interdisciplinary Science, Harbin Institute of Technology,

[1] Boeuf JP. Tutorial: Physics and modeling of Hall thrusters. Journal of Applied Physics.

[2] Morozov AI. The conceptual development of stationary plasma thrusters. Plasma

[3] Lary E, Meyerand R, Salz F. Ion acceleration in a gyro-dominated neutral plasma: Theory

[4] Seikel GR, Reshotko E. Hall current ion accelerator. Bulletin of the American Physical

[5] Banas CM, Brown CO, Pinsley EA. Hall-current accelerator utilizing surface contact ionization. Journal of Spacecraft & Rockets. 1971;**1**(5):525-531. DOI: 10.2514/3.27692

[6] Janes GS, Lowder RS. Anomalous electron diffusion and ion acceleration in a low-density plasma. The Physics of Fluids. 1966;**9**(6):1115-1123. DOI: 10.1063/1.1761810

[7] Choueiri EY. Plasma oscillations in Hall thrusters. Physics of Plasmas. 2001;**8**(4):1411-

[8] Clauss C, Day M, Kim V, et al. Preliminary study of possibility to ensure large enough lifetime of SPT operating under increased powers. In: Proceedings of the 33rd AIAA/ ASME/SAE/ASEE Joint Propulsion Conference and Exhibit; 11-14 July 1997; Seattle, WA,

[9] Mazouffre S, Vaudolon J, Largeau G, et al. Visual evidence of magnetic shielding with the PPS-flex Hall thruster. IEEE Transactions on Plasma Science. 2014;**42**(10):2668-2669.

[10] Mikellides IG, Katz I, Hofer RR, et al. Magnetic shielding of a laboratory Hall thruster. I.Theory and validation. Journal of Applied Physics. 2014;**115**(4):203. DOI: 10.1063/1.4862313

[11] Cai N. Influence of magnetic lens on wall erosion of Hall effect thruster [thesis]. Harbin:

Yongjie Ding1

**References**

#### **6. Outstanding problems**

The purpose of the MS technology is to facilitate the equipotentialization of the near-wall magnetic field lines. The topology of these lines reaches deeply into the near anode region and eliminates the influence on the potential originating from electron pressure. On the basis of the isothermal principle of magnetic field lines, E// is negligibly small. Meanwhile, the induced E⊥ prevents ion bombardment of the ceramic walls, which significantly reduces channel erosion. Nevertheless, there are still two primary problems that need to be addressed: (1) the large excitation power consumption and the relatively low thruster efficiency. As a result, an additional component for heat dissipation is required, especially for low-power HTs; (2) Ioannis et al. [33–35] first discovered that the pole erosion of the magnetic shield of Hall thrusters is a by-product of magnetic shielding. Although the erosion rate is small, it will affect the lifetime of thrusters over long periods of time.

The wall-less technology involves moving the anode to the channel exit, which entirely shifts the ionization and acceleration region to the outside of the channel defined by the wall-less Hall thrusters. The ionization of neutrals occurs in the plume region, where the neutrals spread radially without the control of the channel wall, thus resulting in a larger plume divergence (55°–62°). Thus, the performance of this device is relatively lower.

The aft-magnetic field with large gradient technique causes the maximum magnetic field strength to be generated on the outside of the channel with a large gradient. Primary ionization can be maintained inside the channel, and the primary acceleration can be directed toward the plume region, which can maintain a high level of propellant utilization while decreasing the energy, flux of electrons, and the ions that bombard the ceramic channel wall. In the future, the channel and the magnetic field should be the two main considerations while attempting to optimize the discharge performance of HTs. In addition, the coupling of the cathode with the thrusters should be studied.

#### **Acknowledgements**

The authors want to gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 51777045 and 51477035).

#### **Conflict of interest**

This chapter has no conflicts of interest.

#### **Author details**

when the design was based on an aft-magnetic field with large gradient technique. Highpower thrusters which operate at 1.35 and 5 kW have been designed and tested at the Harbin Institute of Technology using the aft-magnetic field with large gradient technique. The maximum efficiency attained was 65%. Therefore, the aft-magnetic field with large gradient tech-

The purpose of the MS technology is to facilitate the equipotentialization of the near-wall magnetic field lines. The topology of these lines reaches deeply into the near anode region and eliminates the influence on the potential originating from electron pressure. On the basis of the isothermal principle of magnetic field lines, E// is negligibly small. Meanwhile, the induced E⊥ prevents ion bombardment of the ceramic walls, which significantly reduces channel erosion. Nevertheless, there are still two primary problems that need to be addressed: (1) the large excitation power consumption and the relatively low thruster efficiency. As a result, an additional component for heat dissipation is required, especially for low-power HTs; (2) Ioannis et al. [33–35] first discovered that the pole erosion of the magnetic shield of Hall thrusters is a by-product of magnetic shielding. Although the erosion rate is small, it will affect the lifetime of thrusters over long periods of time. The wall-less technology involves moving the anode to the channel exit, which entirely shifts the ionization and acceleration region to the outside of the channel defined by the wall-less Hall thrusters. The ionization of neutrals occurs in the plume region, where the neutrals spread radially without the control of the channel wall, thus resulting in a larger plume diver-

The aft-magnetic field with large gradient technique causes the maximum magnetic field strength to be generated on the outside of the channel with a large gradient. Primary ionization can be maintained inside the channel, and the primary acceleration can be directed toward the plume region, which can maintain a high level of propellant utilization while decreasing the energy, flux of electrons, and the ions that bombard the ceramic channel wall. In the future, the channel and the magnetic field should be the two main considerations while attempting to optimize the discharge performance of HTs. In addition, the coupling of the

The authors want to gratefully acknowledge the financial support from the National Natural

nique can be widely used in Hall thrusters to achieve different power outputs.

gence (55°–62°). Thus, the performance of this device is relatively lower.

Science Foundation of China (Grant Nos. 51777045 and 51477035).

cathode with the thrusters should be studied.

**Acknowledgements**

**Conflict of interest**

This chapter has no conflicts of interest.

**6. Outstanding problems**

160 Space Flight

Yongjie Ding1 \*, Liqiu Wei2 , Hong Li1 and Daren Yu1

\*Address all correspondence to: dingyongjie@hit.edu.cn

1 School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, People's Republic of China

2 Academy of Fundamental an Interdisciplinary Science, Harbin Institute of Technology, Harbin, People's Republic of China

#### **References**


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[26] Ding Y, Peng W, Sun H, et al. Performance characteristics of no-wall-losses Hall thruster. European Physical Journal Special Topics. 2017;**226**(13):2945-2953. DOI: 10.1140/epjst/

[27] Ding Y, Peng W, Sun H, et al. Visual evidence of suppressing the ion and electron energy loss on the wall in Hall thrusters. Japanese Journal of Applied Physics. 2017;**56**(3):038001.

[28] Ding Y, Peng W, Sun H, et al. Effect of oblique channel on discharge characteristics of 200-W Hall thruster. Physics of Plasmas. 2017;**24**:023507. DOI: 10.1063/1.4976104

[29] Ding Y, Sun H, Li P, et al. Application of hollow anodes in a Hall thruster with doublepeak magnetic fields. Journal of Physics D Applied Physics. 2017;**50**(33):335201. DOI:

[30] Ding Y, Sun H, Li P, et al. Influence of hollow anode position on the performance of a Hall-effect thruster with double-peak magnetic field. Vacuum. 2017;**143**:251-261. DOI:

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[32] Ding Y, Sun H, Peng W, et al. Experimental test of 200 W Hall thruster with titanium wall. Japanese Journal of Applied Physics. 2017;**56**(5):050312. DOI: 10.7567/jjap.56.050312

[33] Mikellides IG, Lopez Ortega A, Jorns B. Assessment of pole erosion in a magnetically shielded Hall thruster. In: Proceedings of the 50th AIAA/ASME/SAE/ASEE Joint

[34] Goebel DM, Jorns B, Hofer RR, Mikellides I G, Katz I. Pole-piece interactions with the plasma in a magnetically shielded Hall thruster. In: Proceedings of the 50th AIAA/ ASME/SAE/ASEE Joint Propulsion Conference; 28-30 July 2014; Cleveland. AIAA; 2014.

[35] Jorns B, Dodson CA, Anderson JR, Goebel DM, Hofer RR, Sekerak MJ, et al. Mechanisms for pole piece erosion in a 6-kW magnetically-shielded Hall thruster. In: Proceedings of the 52nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference; 25-27 July 2016; Salt

Astronautica. 2017;**139**:521-527. DOI: 10.1016/j.actaastro.2017.08.001

Propulsion Conference; 28-30 July 2014. Cleveland AIAA; 2014. p. 3897

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e2016-60247-y

DOI: 10.7567/jjap.56.038001

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[12] Dumazert P, Marchandise F, Jolivet L, Estublier D, Cornu N. PPS-1350-G qualification status. In: Proceedings of the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference;

[13] De Grys K, Mathers A, Welander B, Khayms V. Demonstration of 10,400 hours of operation on 4.5 kW qualification model Hall Thruster. In: Proceedings of the 46th AIAA/ASME/ SAE/ASEE Joint Propulsion Conference; 25-28 July 2010; Nashville. AIAA; 2010. p. 6698 [14] Mikellides I, Katz I, Hofer R, Goebel D, de Grys K, Mathers A. Magnetic shielding of the acceleration channel walls in a long-life Hall thruster. In: Proceedings of the 46th AIAA/ ASME/SAE/ASEE Joint Propulsion Conference; 25-28 July 2010; Nashville. AIAA; 2010.

[15] Morozov AI, Esipchuk YV, Tilinin GN, Trofimov AV, Sharov YA, Shchepkin GY. Plasma accelerator with closed electron drift and extended acceleration zone soviet physics:

[16] Morozov AI, Savelyev VV. Fundamentals of stationary plasma thruster theory. Reviews

[17] Mikellides I, Katz I, Hofer R. Design of a laboratory Hall thruster with magnetically shielded channel walls, Phase I: Numerical simulations. In: Proceedings of the 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference; 31 July–03 August 2011; San

[18] Hofer R, Goebel D, Mikellides I, Katz I. Design of a laboratory Hall thruster with magnetically shielded channel walls, Phase II: Experiments. In: Proceedings of the 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference; 30 July–01 August 2012; Atlanta.

[19] Mikellides IG, Katz I, Hofer RR, et al. Magnetic shielding of walls from the unmagnetized ion beam in a Hall thruster. Applied Physics Letters. 2013;**102**(2):4906-4911. DOI:

[20] Conversano R, Goebel D, Hofer R, Matlock T, Wirz R. Magnetically shielded miniature Hall thruster: Development and initial testing. In: Proceedings of 33rd International Electric Propulsion Conference (IEPC); October 2013; Washington, IEPC-2013-201 [21] Grimaud L, Vaudolon J, Mazouffre S, Boniface C. Design and characterization of a 200W Hall thruster in "magnetic shielding" configuration. In: Proceedings of the 52nd AIAA/ ASME/SAE/ASEE Joint Propulsion Conference; 25-27 July 2016; Salt Lake City. AIAA;

[22] Mazouffre S, Tsikata S, Vaudolon J. Development and experimental characterization of a wall-less Hall thruster. Journal of Applied Physics. 2014;**116**:243302. DOI: 10.1063/

[23] Mazouffre S, Tsikata S, Vaudolon J. Development and characterization of a wall-less Hall thruster. In: Proceedings of the 50th AIAA/ASME/SAE/ASEE Joint Propulsion

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1.4904965


**Chapter 9**

Provisional chapter

**Low-Thrust Control Strategies for Earth-to-Mars**

DOI: 10.5772/intechopen.73041

Low-Thrust Control Strategies for Earth-to-Mars

Recent advances in electric propulsion systems have demonstrated that these engines have the potential to be used for long-duration travels, with applications such as cargo and human transportation for interplanetary voyages. The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) is an example of this type of engine, possessing the ability to operate at a wide range of specific impulse levels. This chapter presents the results of a study comparing three different thrust control strategies for Earth-Mars trajectories, using the VASIMR engine at a power of 150 kW. These are constant thrust trajectories, trajectories with coasting periods, and trajectories with variable specific impulse, resulting in variable thrust. To achieve this, an optimization tool was created using spherical coordinates to model the dynamics of the spacecraft, optimal control theory to setup the optimization problem, and a differential evolution algorithm to minimize the cost function. A novel approach to model variable specific impulse and coast-arcs in the trajectories for spherical coordinates is presented as well. The optimization tool was utilized to find optimal trajectories from Earth to Mars orbit, and it was concluded that using variable thrust reduces propellant consumption for a variety of

Keywords: low-thrust trajectories, high power electric propulsion, global optimization

The National Aeronautics and Space Administration (NASA) announced in 2015 its partnership with commercial industry to develop 12 key technologies that will allow space and human exploration to deep-space destinations, such as the Moon and Mars [1]. The Next Space Technologies for Exploration Partnerships (NextSTEP) include concepts in advanced

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

**Trajectories**

Trajectories

Abstract

1. Introduction

Marco Gómez Jenkins and Jose Antonio Castro Nieto

Marco Gómez Jenkins and Jose Antonio Castro Nieto

http://dx.doi.org/10.5772/intechopen.73041

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

trajectories, when compared to the other two methods.

Provisional chapter

#### **Low-Thrust Control Strategies for Earth-to-Mars Trajectories** Low-Thrust Control Strategies for Earth-to-Mars Trajectories

DOI: 10.5772/intechopen.73041

Marco Gómez Jenkins and Jose Antonio Castro Nieto Marco Gómez Jenkins and

Additional information is available at the end of the chapter Jose Antonio Castro Nieto

http://dx.doi.org/10.5772/intechopen.73041 Additional information is available at the end of the chapter

#### Abstract

Recent advances in electric propulsion systems have demonstrated that these engines have the potential to be used for long-duration travels, with applications such as cargo and human transportation for interplanetary voyages. The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) is an example of this type of engine, possessing the ability to operate at a wide range of specific impulse levels. This chapter presents the results of a study comparing three different thrust control strategies for Earth-Mars trajectories, using the VASIMR engine at a power of 150 kW. These are constant thrust trajectories, trajectories with coasting periods, and trajectories with variable specific impulse, resulting in variable thrust. To achieve this, an optimization tool was created using spherical coordinates to model the dynamics of the spacecraft, optimal control theory to setup the optimization problem, and a differential evolution algorithm to minimize the cost function. A novel approach to model variable specific impulse and coast-arcs in the trajectories for spherical coordinates is presented as well. The optimization tool was utilized to find optimal trajectories from Earth to Mars orbit, and it was concluded that using variable thrust reduces propellant consumption for a variety of trajectories, when compared to the other two methods.

Keywords: low-thrust trajectories, high power electric propulsion, global optimization

#### 1. Introduction

The National Aeronautics and Space Administration (NASA) announced in 2015 its partnership with commercial industry to develop 12 key technologies that will allow space and human exploration to deep-space destinations, such as the Moon and Mars [1]. The Next Space Technologies for Exploration Partnerships (NextSTEP) include concepts in advanced

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

propulsion, habitation, and small satellites. Among these, three companies developing high power electric propulsion systems were selected to develop engines in the 50–300 kW range, with high specific impulse (2000–5000 s) and efficiency (greater than 60%). The purpose of the development of these engines is to obtain propulsion systems that can operate continuously for long periods, to enable deep space transportation using highly efficient propulsion.

2. Variable Specific Impulse Magnetoplasma Rocket

of approximately 6 N at an specific impulse of 5000 s.

Figure 1. VASIMR operating principles.

The VASIMR is an electric thruster of the electromagnetic kind. It uses magnetic fields to guide plasma through an exhaust, producing thrust in the process. The concept was created by Dr. Franklin Chang Díaz during his time as a graduate student at the Massachusetts Institute of Technology (MIT) and has been developed since the late 1970s [2]. During the 1990s, development of the engine took place in the Advanced Space Propulsion Laboratory (ASPL) at NASA's Johnson Space Center. The experimental engine tested at the laboratory operated at 10 kW and was later upgraded to a 50 kW version producing 0.5 N of thrust. Ad Astra Rocket Company was then created as a spin-off of the NASA laboratory and the engine has seen a significant development in technology during the company's lifespan. The most recent version of the engine (VX-200 or VASIMR eXperimental 200) runs at 200 kW and produces a maximum thrust

Low-Thrust Control Strategies for Earth-to-Mars Trajectories

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167

Currently, researchers are improving the engine to operate at steady state. In 2015, Ad Astra Rocket Company was awarded a 3-year, \$9 million contract from NASA to develop the maturity of the VX-200 engine [6]. Specifically, by the end of the contract, company must demonstrate that the engine is able to operate at a power level of 100 kW for 100 h. Ad Astra is currently on schedule with this goal, and has successfully completed a NASA review after its second year of contract. Currently, the engine has operated for a total 10 h and there have been considerable changes to the vacuum chamber where the VX-200 operates. These modifications are necessary, so the engine can handle the thermal load produced by the engine. After demonstrating successful steady-state operations, a flight version of the engine called the

Figure 1 presents a schematic of the VASIMR and its operating principles. The propellant (in gaseous form) enters the first stage of the engine and is converted to plasma by a helicon radio frequency (RF) generator. This was established in nuclear fusion experiments and consists of ionizing the gas. The plasma is guided forward using a magnetic field created by superconducting magnets. It then advances to the second stage where it is energized using ion cyclotron resonance heating (ICRH). The high-energy plasma is then exhausted using a magnetic nozzle, creating thrust. One unique feature of this engine is a technique

VASIMR Flight 200 (VF-200) is planned to be constructed and tested in space.

The selected companies for NextSTEP are:


Although all three companies are working on electric propulsion systems, these engines operate under different principles. Ad Astra Rocket Company's Variable Specific Impulse Magnetoplasma Rocket (VASIMR) uses radio waves to ionize and energize a propellant, converting it to a plasma state, and a magnetic field to guide and expel the plasma, producing thrust [2]. Aerojet Rocketdyne is working on a high power Hall thruster, which uses electrons trapped in a magnetic field to ionize propellant and accelerate the propellant to produce thrust, while neutralizing the plume to avoid the spacecraft from acquiring a charge [3]. The electrodeless Lorentz force (ELF) thruster developed by MSNW LLC, is a pulsed propulsion system that generates a high density and magnetized plasmoid, known as a field reversed configuration (FRC), using radio waves to produce a rotating magnetic field (RMF) [4]. These FRC sources are pulsed devices where the plasmoid evolves from neutral gas injection and ionization, to plasmoid growth and acceleration, and finally to plasmoid ejection.

If the parameters specified by NASA for engine performance are reached, these propulsions systems could be powered by solar energy for interplanetary flight. These type of systems are called solar electric propulsion (SEP) and would require approximately 10 times less propellant to operate than the typical chemical propellant that are currently operating [5]. Furthermore, SEP systems with thrust control could provide even more propellant savings compared to continuous thrust system. The main motivation of this study is to test whether this thrust strategy is indeed more efficient in terms of propellant consumed for interplanetary travel.

This chapter aims to find the optimal low thrust control strategy for transfers from Earth to Mars using three different thrust control strategies: (1) constant thrust trajectories, (2) trajectories with coasting periods, and (3) trajectories with variable specific impulse, resulting in variable thrust. To achieve this goal, an optimization tool was created to compute the optimal trajectory, given a fixed time of flight, for each thrust control strategy. The optimal trajectory was selected based on propellant consumption for each transfer. The engine used for the study is the VASIMR, given its ability to operate at a wide range of specific impulse values, and therefore thrust levels. Section 2 presents a description of this engine, while Section 3 presents the optimization tool created for this study. The results of the analysis are presented in Section 4, leading to the conclusions presented in Section 5.

### 2. Variable Specific Impulse Magnetoplasma Rocket

propulsion, habitation, and small satellites. Among these, three companies developing high power electric propulsion systems were selected to develop engines in the 50–300 kW range, with high specific impulse (2000–5000 s) and efficiency (greater than 60%). The purpose of the development of these engines is to obtain propulsion systems that can operate continuously

Although all three companies are working on electric propulsion systems, these engines operate under different principles. Ad Astra Rocket Company's Variable Specific Impulse Magnetoplasma Rocket (VASIMR) uses radio waves to ionize and energize a propellant, converting it to a plasma state, and a magnetic field to guide and expel the plasma, producing thrust [2]. Aerojet Rocketdyne is working on a high power Hall thruster, which uses electrons trapped in a magnetic field to ionize propellant and accelerate the propellant to produce thrust, while neutralizing the plume to avoid the spacecraft from acquiring a charge [3]. The electrodeless Lorentz force (ELF) thruster developed by MSNW LLC, is a pulsed propulsion system that generates a high density and magnetized plasmoid, known as a field reversed configuration (FRC), using radio waves to produce a rotating magnetic field (RMF) [4]. These FRC sources are pulsed devices where the plasmoid evolves from neutral gas injection and

ionization, to plasmoid growth and acceleration, and finally to plasmoid ejection.

If the parameters specified by NASA for engine performance are reached, these propulsions systems could be powered by solar energy for interplanetary flight. These type of systems are called solar electric propulsion (SEP) and would require approximately 10 times less propellant to operate than the typical chemical propellant that are currently operating [5]. Furthermore, SEP systems with thrust control could provide even more propellant savings compared to continuous thrust system. The main motivation of this study is to test whether this thrust strategy is indeed more efficient in terms of propellant consumed for interplanetary travel.

This chapter aims to find the optimal low thrust control strategy for transfers from Earth to Mars using three different thrust control strategies: (1) constant thrust trajectories, (2) trajectories with coasting periods, and (3) trajectories with variable specific impulse, resulting in variable thrust. To achieve this goal, an optimization tool was created to compute the optimal trajectory, given a fixed time of flight, for each thrust control strategy. The optimal trajectory was selected based on propellant consumption for each transfer. The engine used for the study is the VASIMR, given its ability to operate at a wide range of specific impulse values, and therefore thrust levels. Section 2 presents a description of this engine, while Section 3 presents the optimization tool created for this study. The results of the analysis are presented in Section

for long periods, to enable deep space transportation using highly efficient propulsion.

The selected companies for NextSTEP are:

166 Space Flight

• MSNW LLC of Redmond, Washington

• Ad Astra Rocket Company of Webster, Texas

• Aerojet Rocketdyne Inc. of Redmond, Washington

4, leading to the conclusions presented in Section 5.

The VASIMR is an electric thruster of the electromagnetic kind. It uses magnetic fields to guide plasma through an exhaust, producing thrust in the process. The concept was created by Dr. Franklin Chang Díaz during his time as a graduate student at the Massachusetts Institute of Technology (MIT) and has been developed since the late 1970s [2]. During the 1990s, development of the engine took place in the Advanced Space Propulsion Laboratory (ASPL) at NASA's Johnson Space Center. The experimental engine tested at the laboratory operated at 10 kW and was later upgraded to a 50 kW version producing 0.5 N of thrust. Ad Astra Rocket Company was then created as a spin-off of the NASA laboratory and the engine has seen a significant development in technology during the company's lifespan. The most recent version of the engine (VX-200 or VASIMR eXperimental 200) runs at 200 kW and produces a maximum thrust of approximately 6 N at an specific impulse of 5000 s.

Currently, researchers are improving the engine to operate at steady state. In 2015, Ad Astra Rocket Company was awarded a 3-year, \$9 million contract from NASA to develop the maturity of the VX-200 engine [6]. Specifically, by the end of the contract, company must demonstrate that the engine is able to operate at a power level of 100 kW for 100 h. Ad Astra is currently on schedule with this goal, and has successfully completed a NASA review after its second year of contract. Currently, the engine has operated for a total 10 h and there have been considerable changes to the vacuum chamber where the VX-200 operates. These modifications are necessary, so the engine can handle the thermal load produced by the engine. After demonstrating successful steady-state operations, a flight version of the engine called the VASIMR Flight 200 (VF-200) is planned to be constructed and tested in space.

Figure 1 presents a schematic of the VASIMR and its operating principles. The propellant (in gaseous form) enters the first stage of the engine and is converted to plasma by a helicon radio frequency (RF) generator. This was established in nuclear fusion experiments and consists of ionizing the gas. The plasma is guided forward using a magnetic field created by superconducting magnets. It then advances to the second stage where it is energized using ion cyclotron resonance heating (ICRH). The high-energy plasma is then exhausted using a magnetic nozzle, creating thrust. One unique feature of this engine is a technique

Figure 1. VASIMR operating principles.

called constant power throttling (CPW) [2]. This means that the engine can vary its thrust and specific impulse using constant power settings. The throttling is possible by controlling the amount of power that goes to each stage: if more power is directed to the first stage, more plasma is created generating more thrust, but at a lower specific impulse. If more power is directed to the second stage, less plasma is created but it will have a higher exhaust velocity (higher specific impulse), since it gets a greater energy boost from the ICRH. This variation in thrust and specific impulse is a great advantage since the engine can fit many mission profiles due to its flexibility. Additionally, the VASIMR can be scaled up in power (theoretically to MW capability), enabling crewed interplanetary flights using electric propulsion [7].

consumed, time of flight, and the offsets. These are defined as the difference between the target state and the final simulated state. If the results meet the mission requirements, then the user will process them further by creating plots and analyzing which trajectory is best based on

Spherical coordinates were the preferred method of modeling for this project since it has been successfully used for first-order mission analysis of interplanetary trajectories, resulting in an efficient computation time [10]. The position of the spacecraft in the two-dimensional Euclidean space is defined by the radius vector and the angle θ. The x–y coordinate system is centered at the main body (Sun for interplanetary trajectories). At the center of the satellite, there is another coordinate system defined, consisting of the radial axis and the θ axis. The velocity vector, originated at its center of mass, defines the velocity of the spacecraft. Another vector that starts at the same position is the thrust vector. The angle between the θ axis and the thrust vector is called the pitch angle (α). It is one of the control parameters in the optimization problem (further explained in the following chapter). The radial and tangential acceleration

> ar,T <sup>¼</sup> <sup>T</sup> m

<sup>a</sup>θ,T <sup>¼</sup> <sup>T</sup> m

from one orbit to the other. Therefore, the final state X is defined as:

This is essential to compute the future state. They are defined as [11]:

where m is the mass of the spacecraft. The state can then be defined using four parameters: r, θ, vr, and vθ, where the last two parameters are the radial and tangential velocity, respectively. The mass of the spacecraft must be included as well, since it is using propellant to transfer

X ¼ r; θ; vr ½ � ; vθ; m

Once the state parameters were selected, the following step is to define their rate of change.

θ r<sup>2</sup> þ

<sup>m</sup>\_ ¼ � <sup>2</sup>η<sup>P</sup>

T m

<sup>v</sup>\_<sup>r</sup> <sup>¼</sup> <sup>μ</sup> � rv<sup>2</sup>

<sup>v</sup>\_<sup>θ</sup> <sup>¼</sup> vrv<sup>θ</sup> r þ T m

sin ∝ (1)

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cos α (2)

<sup>T</sup> (3)

r\_ ¼ vr (4)

<sup>θ</sup>\_ <sup>¼</sup> <sup>v</sup><sup>θ</sup> (5)

sin α (6)

cos α (7)

<sup>g</sup>0Isp <sup>2</sup> (8)

mission needs.

3.2. Propagation

components due to thrust are defined as:

#### 3. VASITOS

A low-thrust spacecraft trajectory optimization tool, called the Variable Specific Impulse Trajectory Optimization Software (VASITOS), was created to analyze the optimal thrust strategy. This section presents the software environment in which it was created, the propagation scheme used to model the dynamics of the spacecraft, and the global optimization algorithm incorporated to compute optimal low-thrust trajectories.

#### 3.1. Software environment

The software environment in which VASITOS was developed consists of two sections: Spyder and PyGMO. The former was used to model the propagation of the orbit, while the latter was used for optimization. Spyder is an integrated development environment (IDE) that combines various open source packages written in Python [8]. These include some for scientific computing (NumPy and SciPy) and other for plotting (Matplotlib). It offers several advantages over other programs for scientific computing, mainly that it is an open source and that it is written in Python, a language, which is quite intuitive.

The Parallel Global Multiobjective Optimizer (PaGMO) is an optimization toolbox created by the Advanced Concepts Team at the European Space Agency (ESA) to solve complex optimization problems [9]. It is available for C++ and Python (the Python version is called PyGMO). The software features the generalized island model (GIM), which allows parallel computing in order to reduce computation time. PyGMO includes several optimization algorithms and global optimization problems, such as the genetic algorithm (GA), differential evolution (DE), particle swarm optimization (PSO), and adaptive simulated annealing (ASA), among others. The parallel computing scheme was implemented in the software and optimization simulations were performed in a Lenovo U410 with an Intel Core i5. This has multithreading, which means the operating system can identify up to four CPUs. Therefore, four islands were included in the parallel computing scheme.

To operate VASITOS, the user will input the initial and target orbit into the tool, along with the thruster specifications. VASITOS will run simulations until the end condition specified for the optimization algorithm is met. For example, for GA and DE, one must define the number of generations required in the simulation. The output will be the optimal path, propellant mass consumed, time of flight, and the offsets. These are defined as the difference between the target state and the final simulated state. If the results meet the mission requirements, then the user will process them further by creating plots and analyzing which trajectory is best based on mission needs.

#### 3.2. Propagation

called constant power throttling (CPW) [2]. This means that the engine can vary its thrust and specific impulse using constant power settings. The throttling is possible by controlling the amount of power that goes to each stage: if more power is directed to the first stage, more plasma is created generating more thrust, but at a lower specific impulse. If more power is directed to the second stage, less plasma is created but it will have a higher exhaust velocity (higher specific impulse), since it gets a greater energy boost from the ICRH. This variation in thrust and specific impulse is a great advantage since the engine can fit many mission profiles due to its flexibility. Additionally, the VASIMR can be scaled up in power (theoretically to MW

A low-thrust spacecraft trajectory optimization tool, called the Variable Specific Impulse Trajectory Optimization Software (VASITOS), was created to analyze the optimal thrust strategy. This section presents the software environment in which it was created, the propagation scheme used to model the dynamics of the spacecraft, and the global optimization algorithm

The software environment in which VASITOS was developed consists of two sections: Spyder and PyGMO. The former was used to model the propagation of the orbit, while the latter was used for optimization. Spyder is an integrated development environment (IDE) that combines various open source packages written in Python [8]. These include some for scientific computing (NumPy and SciPy) and other for plotting (Matplotlib). It offers several advantages over other programs for scientific computing, mainly that it is an open source and that it is written

The Parallel Global Multiobjective Optimizer (PaGMO) is an optimization toolbox created by the Advanced Concepts Team at the European Space Agency (ESA) to solve complex optimization problems [9]. It is available for C++ and Python (the Python version is called PyGMO). The software features the generalized island model (GIM), which allows parallel computing in order to reduce computation time. PyGMO includes several optimization algorithms and global optimization problems, such as the genetic algorithm (GA), differential evolution (DE), particle swarm optimization (PSO), and adaptive simulated annealing (ASA), among others. The parallel computing scheme was implemented in the software and optimization simulations were performed in a Lenovo U410 with an Intel Core i5. This has multithreading, which means the operating system can identify up to four CPUs. Therefore, four islands were

To operate VASITOS, the user will input the initial and target orbit into the tool, along with the thruster specifications. VASITOS will run simulations until the end condition specified for the optimization algorithm is met. For example, for GA and DE, one must define the number of generations required in the simulation. The output will be the optimal path, propellant mass

capability), enabling crewed interplanetary flights using electric propulsion [7].

incorporated to compute optimal low-thrust trajectories.

in Python, a language, which is quite intuitive.

included in the parallel computing scheme.

3. VASITOS

168 Space Flight

3.1. Software environment

Spherical coordinates were the preferred method of modeling for this project since it has been successfully used for first-order mission analysis of interplanetary trajectories, resulting in an efficient computation time [10]. The position of the spacecraft in the two-dimensional Euclidean space is defined by the radius vector and the angle θ. The x–y coordinate system is centered at the main body (Sun for interplanetary trajectories). At the center of the satellite, there is another coordinate system defined, consisting of the radial axis and the θ axis. The velocity vector, originated at its center of mass, defines the velocity of the spacecraft. Another vector that starts at the same position is the thrust vector. The angle between the θ axis and the thrust vector is called the pitch angle (α). It is one of the control parameters in the optimization problem (further explained in the following chapter). The radial and tangential acceleration components due to thrust are defined as:

$$a\_{r,T} = \frac{T}{m} \sin \infty \tag{1}$$

$$a\_{\theta,T} = \frac{T}{m} \cos \alpha \tag{2}$$

where m is the mass of the spacecraft. The state can then be defined using four parameters: r, θ, vr, and vθ, where the last two parameters are the radial and tangential velocity, respectively. The mass of the spacecraft must be included as well, since it is using propellant to transfer from one orbit to the other. Therefore, the final state X is defined as:

$$\mathbf{X} = \begin{bmatrix} r, \theta, \upsilon\_r, \upsilon\_\theta, m \end{bmatrix}^T \tag{3}$$

Once the state parameters were selected, the following step is to define their rate of change. This is essential to compute the future state. They are defined as [11]:

$$
\dot{r} = \upsilon\_r \tag{4}
$$

$$
\dot{\theta} = v\_{\theta} \tag{5}
$$

$$
\dot{\upsilon}\_r = \frac{\mu - r\upsilon\_\theta^2}{r^2} + \frac{T}{m}\sin\alpha\tag{6}
$$

$$
\dot{\upsilon}\_{\theta} = \frac{\upsilon\_{r}\upsilon\_{\theta}}{r} + \frac{T}{m}\cos\alpha \tag{7}
$$

$$\dot{m} = -\frac{2\eta P}{\left(g\_0 I\_{sp}\right)^2} \tag{8}$$

where μ is the gravitational parameter of the central body and T is the thrust of the low-thrust system. Most variables in equation m\_ are engine specifications: η is its efficiency, P is the power, and Isp is the specific impulse. The parameter g<sup>0</sup> is the standard acceleration due to gravity. The thrust magnitude is defined as:

$$T = \frac{2\eta P}{g\_0 I\_{sp}}\tag{9}$$

<sup>λ</sup>\_ <sup>θ</sup> <sup>¼</sup> <sup>0</sup> (13)

Low-Thrust Control Strategies for Earth-to-Mars Trajectories

<sup>r</sup> (14)

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<sup>r</sup> (15)

<sup>q</sup> (16)

<sup>δ</sup><sup>u</sup> <sup>¼</sup> <sup>0</sup> (17)

δα <sup>¼</sup> <sup>0</sup> (18)

¼ 0 (19)

<sup>q</sup> (20)

<sup>q</sup> (21)

<sup>q</sup> (22)

(23)

<sup>λ</sup>\_ vr ¼ �λ<sup>r</sup> <sup>þ</sup>

<sup>v</sup><sup>θ</sup> <sup>¼</sup> �2vθλvr <sup>þ</sup> vrλ<sup>v</sup><sup>θ</sup>

λ<sup>m</sup>

δH

δH

δH δIsp

sin <sup>∝</sup> ¼ � <sup>λ</sup>vr ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ2 vr <sup>þ</sup> <sup>λ</sup><sup>2</sup> vθ

cos <sup>∝</sup> ¼ � <sup>λ</sup><sup>v</sup><sup>θ</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ2 vr <sup>þ</sup> <sup>λ</sup><sup>2</sup> vθ

> Isp <sup>¼</sup> <sup>2</sup>mλ<sup>m</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ2 vr <sup>þ</sup> <sup>λ</sup><sup>2</sup> vθ

The angle of attack is divided into sine and cosine to ensure the right sign (+/�). It is important to use the atan2 function when computing the magnitude and direction of this angle. The

> <sup>T</sup><sup>∗</sup> <sup>¼</sup> <sup>2</sup>η<sup>P</sup> g0I ∗ sp

sp defines the optimal thrust <sup>T</sup>\* in the following fashion:

where u is the control parameter. Since we have two control parameters, the resulting equa-

Computing the costates is of the utmost importance in optimal control theory since the control parameters depend on them. For this study, there are two of them: the thrust direction and the thrust magnitude. The former is defined as the angle of attack α. The latter is inversely proportional to the specific impulse, meaning that if we control the specific impulse, we control the thrust magnitude. To obtain the profile of both control parameters, we need to use

λvr þ λ<sup>v</sup><sup>θ</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ2 vr <sup>þ</sup> <sup>λ</sup><sup>2</sup> vθ

λ\_

Pontryagin's Minimum Principle, which is expressed mathematically as:

By solving these two equations, we obtain the following control laws:

tions are:

optimal specific impulse I

∗

<sup>λ</sup>\_ <sup>m</sup> <sup>¼</sup> <sup>T</sup> m vθλ<sup>v</sup><sup>θ</sup>

The equation shows that the thrust magnitude and specific impulse are inversely proportional, meaning that if one is increased, then the other is decreased. For this study, it is assumed that the engine efficiency and power are constant, so the specific impulse is an independent variable while the thrust is the dependent one. This will be important when selecting the former variable as a control parameter. Once the initial state of the system is defined, it can be combined with this system of equations to compute the state of the spacecraft at future times using an integrator.

#### 3.3. Optimization

The rates of change of the state parameters are essential to form the Hamiltonian. In the context of optimal control theory, the Hamiltonian does not possess any physical meaning; it is a parameter derived from calculus of variation, which aids in finding the optimal trajectory. In a recent study, optimal control theory was applied to a spherical system, which only considered the radius, radial velocity, and tangential velocity [12]. Additionally, the only control parameter defined was the pitch angle. This chapter expands on previous work by including the position θ of the spacecraft within the trajectory and the mass of the vehicle. Furthermore, it includes the specific impulse as a control parameter. For the system defined in Section 3.2, the Hamiltonian is expressed mathematically as:

$$H = \lambda\_r \frac{dr}{dt} + \lambda\_\theta \frac{d\theta}{dt} + \lambda\_{v\_r} \frac{dv\_r}{dt} + \lambda\_{v\_\theta} \frac{dv\_\theta}{dt} + \lambda\_m \frac{dm}{dt} \tag{10}$$

where λ's are the costates of each parameter that makes up the state. These costates represent the cost of changing one parameter relative to another. For example, if one simulates a transfer, where the change in radius is much greater than the change in angle θ, then the costates of the radius and radial velocity will be greater in magnitude than the ones associated with θ. The rate of change of the costates over time can be obtained by using the following property derived from optimal control theory:

$$
\dot{\lambda}\_i = -\frac{\delta H}{\delta \dot{\mathbf{i}}} \tag{11}
$$

This results in the following expressions:

$$
\dot{\lambda}\_r = \frac{v\_\theta^2 \lambda\_{v\_r} - v\_r v\_\theta \lambda\_{v\_0}}{r^2} - \frac{2\mu \lambda\_{v\_r}}{r^3} \tag{12}
$$

Low-Thrust Control Strategies for Earth-to-Mars Trajectories http://dx.doi.org/10.5772/intechopen.73041 171

$$
\dot{\lambda}\_{\theta} = 0 \tag{13}
$$

$$
\dot{\lambda}\_{v\_r} = -\lambda\_r + \frac{v\_\theta \lambda\_{v\_\theta}}{r} \tag{14}
$$

$$
\dot{\lambda}\_{v\_0} = \frac{-\mathfrak{D}v\_\theta \lambda\_{v\_r} + v\_r \lambda\_{v\_0}}{r} \tag{15}
$$

$$\dot{\lambda}\_m = \frac{T}{m} \frac{\lambda\_{v\_r} + \lambda\_{v\_0}}{\lambda\_m \sqrt{\lambda\_{v\_r}^2 + \lambda\_{v\_0}^2}} \tag{16}$$

Computing the costates is of the utmost importance in optimal control theory since the control parameters depend on them. For this study, there are two of them: the thrust direction and the thrust magnitude. The former is defined as the angle of attack α. The latter is inversely proportional to the specific impulse, meaning that if we control the specific impulse, we control the thrust magnitude. To obtain the profile of both control parameters, we need to use Pontryagin's Minimum Principle, which is expressed mathematically as:

$$\frac{\delta H}{\delta u} = 0\tag{17}$$

where u is the control parameter. Since we have two control parameters, the resulting equations are:

$$\frac{\delta H}{\delta \alpha} = 0\tag{18}$$

$$\frac{\delta H}{\delta I\_{sp}} = 0\tag{19}$$

By solving these two equations, we obtain the following control laws:

where μ is the gravitational parameter of the central body and T is the thrust of the low-thrust system. Most variables in equation m\_ are engine specifications: η is its efficiency, P is the power, and Isp is the specific impulse. The parameter g<sup>0</sup> is the standard acceleration due to

> <sup>T</sup> <sup>¼</sup> <sup>2</sup>η<sup>P</sup> g0Isp

The equation shows that the thrust magnitude and specific impulse are inversely proportional, meaning that if one is increased, then the other is decreased. For this study, it is assumed that the engine efficiency and power are constant, so the specific impulse is an independent variable while the thrust is the dependent one. This will be important when selecting the former variable as a control parameter. Once the initial state of the system is defined, it can be combined with this system of equations to compute the state of the spacecraft at future times

The rates of change of the state parameters are essential to form the Hamiltonian. In the context of optimal control theory, the Hamiltonian does not possess any physical meaning; it is a parameter derived from calculus of variation, which aids in finding the optimal trajectory. In a recent study, optimal control theory was applied to a spherical system, which only considered the radius, radial velocity, and tangential velocity [12]. Additionally, the only control parameter defined was the pitch angle. This chapter expands on previous work by including the position θ of the spacecraft within the trajectory and the mass of the vehicle. Furthermore, it includes the specific impulse as a control parameter. For the system defined in Section 3.2,

> dvr dt <sup>þ</sup> <sup>λ</sup><sup>v</sup><sup>θ</sup>

where λ's are the costates of each parameter that makes up the state. These costates represent the cost of changing one parameter relative to another. For example, if one simulates a transfer, where the change in radius is much greater than the change in angle θ, then the costates of the radius and radial velocity will be greater in magnitude than the ones associated with θ. The rate of change of the costates over time can be obtained by using the following property

<sup>λ</sup>\_ <sup>i</sup> ¼ � <sup>δ</sup><sup>H</sup>

<sup>θ</sup>λvr � vrvθλ<sup>v</sup><sup>θ</sup>

<sup>r</sup><sup>2</sup> � <sup>2</sup>μλvr

dv<sup>θ</sup> dt <sup>þ</sup> <sup>λ</sup><sup>m</sup> dm

<sup>δ</sup><sup>i</sup> (11)

<sup>r</sup><sup>3</sup> (12)

dt (10)

(9)

gravity. The thrust magnitude is defined as:

the Hamiltonian is expressed mathematically as:

derived from optimal control theory:

This results in the following expressions:

H ¼ λ<sup>r</sup>

dr dt <sup>þ</sup> λθ

> λ\_ <sup>r</sup> <sup>¼</sup> <sup>v</sup><sup>2</sup>

dθ dt <sup>þ</sup> <sup>λ</sup>vr

using an integrator.

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3.3. Optimization

$$\sin \infty = -\frac{\lambda\_{v\_r}}{\sqrt{\lambda\_{v\_r}^2 + \lambda\_{v\_\theta}^2}} \tag{20}$$

$$\cos\infty = -\frac{\lambda\_{v\_0}}{\sqrt{\lambda\_{v\_r}^2 + \lambda\_{v\_0}^2}}\tag{21}$$

$$I\_{sp} = \frac{2m\lambda\_m}{\sqrt{\lambda\_{v\_r}^2 + \lambda\_{v\_\theta}^2}}\tag{22}$$

The angle of attack is divided into sine and cosine to ensure the right sign (+/�). It is important to use the atan2 function when computing the magnitude and direction of this angle. The optimal specific impulse I ∗ sp defines the optimal thrust <sup>T</sup>\* in the following fashion:

$$T^\* = \frac{2\eta P}{g\_0 I\_{sp}^\*} \tag{23}$$

The value of the optimal specific impulse will depend on the boundaries defined by the engine specifications. This is expressed mathematically as:

$$\mathbf{I}\_{\rm sp,L} < \mathbf{I}\_{\rm sp}^\* < \mathbf{I}\_{\rm sp,U} \tag{24}$$

The first one consists of operating at a constant thrust throughout the trajectory, meaning that the engine is operating continuously. The second strategy consists of using "coast arcs," defined as periods where the engine is not producing thrust. Finally, variable thrust control will be tested given that the VASIMR has the ability to modify this parameter given that it

Each thrust strategy was considered for a transfer from Earth's orbit to Mars' orbit in a twodimensional heliocentric reference frame. Furthermore, it was assumed that the orbits of both planets are circular. The initial and final orbital parameters are displayed in Table 1. It can be observed that the final position in the target orbit is not specified, since the aim in these simulations is to reach the orbit, not the planet. The forces acting on the spacecraft are due to

Radius, <sup>r</sup> (km) 149.597 � <sup>10</sup><sup>6</sup> 227.937 � <sup>10</sup><sup>6</sup> Velocity, v (km/s) 29.785 24.130 Position, θ (deg) 0.0 —

Table 1. Initial (Earth) and target (Mars) orbits to test control strategies.

Figure 2. Transfer from Earth to Mars orbit using continuous thrust.

Initial orbit: Earth Target orbit: Mars

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features variable specific impulse.

4.1. Simulation parameters

where Isp,L and Isp,U are the lower and upper boundaries of the specific impulse, respectively. If the user wishes to introduce coast arcs (assuming that the specific impulse of the engine is constant), then the following bang-bang strategy is applied:

$$\text{if } I\_{sp} > I\_{sp}^\* \text{ then } T^\* = T \tag{25}$$

$$\text{else if } I\_{sp} < I\_{sp}^\* \text{ then } T^\* = 0 \tag{26}$$

Now, there are 10 equations for rate of change of the state and costate parameter (5 equations for states and 5 for costates). We also have the initial and final values for the states, which are defined by the users. The only thing we are missing is the initial values for the costates. These are called the design variables and are stored in the decision vector, which is defined as:

$$\mathcal{L} = \left[\lambda\_r(0), \lambda\_\theta(0), \lambda\_{v\_r}(0), \lambda\_{v\_\theta}(0), \lambda\_m(0)\right]^T \tag{27}$$

The goal of the optimization process is to find the decision vector that minimizes the following cost function:

$$J = W\_r \Delta r + W\_\theta \Delta \theta + W\_{v\_r} \Delta v\_r + W\_{v\_\theta} \Delta v\_\theta \tag{28}$$

where the Δ's are the offsets (defined as the absolute difference between the final simulated value and target value for selected state parameters) and the W's represent the weights assigned to each offset. The weights are selected by the user and are modified according to the mission needs. This optimization method is indirect since the function we are minimizing does not include the main parameter to minimize: the time of flight. By obtaining the optimal costate profiles and ensuring the final conditions are met, the time of flight is ensured to be minimized (which is why the method is called indirect). For this project, the optimal decision vector was obtained using a numerical method called differential evolution, which is part of the family of evolutionary algorithms. A detailed description of the algorithm can be found in [13].

#### 4. Thrust control strategies

Electric propulsion systems have considerable potential for interplanetary travel, but to analyze its feasibility, one has to consider not only the spacecraft's optimal path, but thrust strategy. Three strategies are considered in this study:


The first one consists of operating at a constant thrust throughout the trajectory, meaning that the engine is operating continuously. The second strategy consists of using "coast arcs," defined as periods where the engine is not producing thrust. Finally, variable thrust control will be tested given that the VASIMR has the ability to modify this parameter given that it features variable specific impulse.

#### 4.1. Simulation parameters

The value of the optimal specific impulse will depend on the boundaries defined by the engine

where Isp,L and Isp,U are the lower and upper boundaries of the specific impulse, respectively. If the user wishes to introduce coast arcs (assuming that the specific impulse of the engine is

∗

Now, there are 10 equations for rate of change of the state and costate parameter (5 equations for states and 5 for costates). We also have the initial and final values for the states, which are defined by the users. The only thing we are missing is the initial values for the costates. These are called the design variables and are stored in the decision vector, which is defined as:

The goal of the optimization process is to find the decision vector that minimizes the following

where the Δ's are the offsets (defined as the absolute difference between the final simulated value and target value for selected state parameters) and the W's represent the weights assigned to each offset. The weights are selected by the user and are modified according to the mission needs. This optimization method is indirect since the function we are minimizing does not include the main parameter to minimize: the time of flight. By obtaining the optimal costate profiles and ensuring the final conditions are met, the time of flight is ensured to be minimized (which is why the method is called indirect). For this project, the optimal decision vector was obtained using a numerical method called differential evolution, which is part of the family of

Electric propulsion systems have considerable potential for interplanetary travel, but to analyze its feasibility, one has to consider not only the spacecraft's optimal path, but thrust

evolutionary algorithms. A detailed description of the algorithm can be found in [13].

sp < Isp,<sup>U</sup> (24)

sp then T<sup>∗</sup> <sup>¼</sup> <sup>T</sup> (25)

sp then T<sup>∗</sup> <sup>¼</sup> <sup>0</sup> (26)

<sup>ξ</sup> <sup>¼</sup> <sup>λ</sup>rð Þ<sup>0</sup> ; λθð Þ<sup>0</sup> ; <sup>λ</sup>vr ð Þ<sup>0</sup> ; <sup>λ</sup><sup>v</sup><sup>θ</sup> ½ � ð Þ<sup>0</sup> ; <sup>λ</sup>mð Þ<sup>0</sup> <sup>T</sup> (27)

J ¼ WrΔr þ WθΔθ þ WvrΔvr þ WvθΔv<sup>θ</sup> (28)

Isp,<sup>L</sup> < I ∗

if Isp > I ∗

else if Isp < I

specifications. This is expressed mathematically as:

cost function:

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4. Thrust control strategies

• Continuous thrust

• Variable thrust

• Coasting

strategy. Three strategies are considered in this study:

constant), then the following bang-bang strategy is applied:

Each thrust strategy was considered for a transfer from Earth's orbit to Mars' orbit in a twodimensional heliocentric reference frame. Furthermore, it was assumed that the orbits of both planets are circular. The initial and final orbital parameters are displayed in Table 1. It can be observed that the final position in the target orbit is not specified, since the aim in these simulations is to reach the orbit, not the planet. The forces acting on the spacecraft are due to


Table 1. Initial (Earth) and target (Mars) orbits to test control strategies.

Figure 2. Transfer from Earth to Mars orbit using continuous thrust.

the Sun's gravity and the thrust produced by the engine. Third body perturbations from the planets on the spacecraft are not considered, nor the position of the planets on arrival and departure of the spacecraft.

4.2. Results

Table 2.

Figure 2 presents the results of a transfer from Earth to Mars orbit in a heliocentric reference frame in astronomical units (AU). The dashed inner circle represents Earth's orbit, while the dashed outer circle represents Mars' orbit. The curve represents the spacecraft's trajectory, while the arrows represents the thrust magnitude and direction. This last parameter demonstrates how the thrust direction was controlled to obtain the optimal trajectory. The spacecraft starts thrusting almost normal to the velocity vector and reverses direction at approximately mid-flight until reaching the final orbit. The thrust magnitude is not considered as a control parameter for this simulation since the thrust is assumed to be continuous. The final orbital trajectory results in a time of flight of 185.78 days and a propellant consumption of 1303 kg. The same transfer was computed for the coasting and variable thrust case. For both of these cases, the time of flight was set to 185.78 days, which was the optimal time for the continuous thrust case. The propellant consumed to achieve the transfer for each case is presented in

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Figure 4. Eccentricity profile for Earth-Mars trajectories using different thrust control methods. Top image displays the complete profile, while the bottom figure displays the profile at mid-flight (blue line = continuous thrust, green

line = coasting, and red line = variable thrust).

The spacecraft was assumed to have a wet mass of 4500 kg, with a propellant mass of 1500 kg, and a VASIMR engine with 150 W of power and 65% efficiency. The specific impulse ranges from 5000 to 30,000 s, which are the theoretical limits of the engine [14]. When operating at a constant specific impulse, it was assumed that the specific impulse is equal to the lower boundary. The step size defined in the simulation was 24 hours, while the integrator used for propagation was the fourth order Runge-Kutta method. The differential evolution algorithm was set to a population size of 20, running for 500 generations.


Table 2. Propellant consumption for Earth to Mars transfer for three different thrust strategies.

Figure 3. Semi-major axis profile for Earth-Mars trajectories using different thrust control methods. Top image displays the complete profile, while the bottom figure displays the profile at mid-flight (blue line = continuous thrust, green line = coasting, and red line = variable thrust).

#### 4.2. Results

the Sun's gravity and the thrust produced by the engine. Third body perturbations from the planets on the spacecraft are not considered, nor the position of the planets on arrival and

The spacecraft was assumed to have a wet mass of 4500 kg, with a propellant mass of 1500 kg, and a VASIMR engine with 150 W of power and 65% efficiency. The specific impulse ranges from 5000 to 30,000 s, which are the theoretical limits of the engine [14]. When operating at a constant specific impulse, it was assumed that the specific impulse is equal to the lower boundary. The step size defined in the simulation was 24 hours, while the integrator used for propagation was the fourth order Runge-Kutta method. The differential evolution algorithm

Figure 3. Semi-major axis profile for Earth-Mars trajectories using different thrust control methods. Top image displays the complete profile, while the bottom figure displays the profile at mid-flight (blue line = continuous thrust, green

was set to a population size of 20, running for 500 generations.

Continuous thrust Coasting Variable thrust

1303 kg 1267 kg 1267 kg

Table 2. Propellant consumption for Earth to Mars transfer for three different thrust strategies.

departure of the spacecraft.

174 Space Flight

line = coasting, and red line = variable thrust).

Figure 2 presents the results of a transfer from Earth to Mars orbit in a heliocentric reference frame in astronomical units (AU). The dashed inner circle represents Earth's orbit, while the dashed outer circle represents Mars' orbit. The curve represents the spacecraft's trajectory, while the arrows represents the thrust magnitude and direction. This last parameter demonstrates how the thrust direction was controlled to obtain the optimal trajectory. The spacecraft starts thrusting almost normal to the velocity vector and reverses direction at approximately mid-flight until reaching the final orbit. The thrust magnitude is not considered as a control parameter for this simulation since the thrust is assumed to be continuous. The final orbital trajectory results in a time of flight of 185.78 days and a propellant consumption of 1303 kg.

The same transfer was computed for the coasting and variable thrust case. For both of these cases, the time of flight was set to 185.78 days, which was the optimal time for the continuous thrust case. The propellant consumed to achieve the transfer for each case is presented in Table 2.

Figure 4. Eccentricity profile for Earth-Mars trajectories using different thrust control methods. Top image displays the complete profile, while the bottom figure displays the profile at mid-flight (blue line = continuous thrust, green line = coasting, and red line = variable thrust).

From Table 2, one can observe that using coasting and variable thrust results in a 2.7% reduction in propellant consumption relative to the continuous thrust strategy. To properly understand why this reduction occurs, one must analyze the in-plane orbital elements, as well as the thrust profile for each control method.

efficient compared to the constant thrust case, given that it requires less propellant. A similar phenomenon is observed when using variable thrust, where the thrust is lowered when

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Figure 4 explains why the spacecraft performs the rapid change in thrust direction. It is observed that the change in the eccentricity can be divided into two segments: the first one is a uniform increase while the second one is a uniform decrease. The change occurs at the halfway point, where the spacecraft performs the turn. The eccentricity profile is similar to the Hohmann transfer, considered an optimal transfer strategy for chemical rockets. In this type of transfer, the semi-major axis and eccentricity are increased instantly (modeled as an impulsive burn) when the spacecraft enters the transfer orbit and then the former is further

In Section 4.2, it was observed that using coasting or variable thrust resulted in a more efficient transfer than using continuous thrust. Another advantage when using these two control strategies is that the mission designer can vary the time of flight to transfer from the initial to the target orbit, to account for the position of the target planet when the spacecraft arrives at its orbit. By varying the time of flight for this transfer, one could also analyze which control strategy would be best for different flight periods. To achieve this goal, both coasting and variable thrust methods were tested for Earth to Mars transfers using fixed time of flights of 195, 205, and 215 days. The results for the propellant consumption for each case are presented

Figure 6. Propellant consumption for Earth to Mars transfers for different cases of time of flight using three thrust control

strategies (gray dot = continuous thrust, orange line/dot = coasting, and blue line/dot = variable thrust).

performing the change of direction (see Figure 5).

in Figure 6, along with the case presented in Section 4.2.

increased but the latter return to zero.

4.3. Variable time of flight

Figures 3 and 4 present the semi-major axis and eccentricity profile for the three thrust control methods, respectively. Additionally, Figure 5 presents the specific impulse for each case. With this figure, the thrust profile can be deduced, given that the specific impulse is inversely proportional to the thrust of the engine. Presenting the specific impulse was favorable to ensure that the engine is operating within its limits. For the coasting case, the specific impulse was set to infinity during periods when the spacecraft is required to coast as dictated by the control law, resulting in zero thrust.

From Figure 3, it can be observed that the overall trend in the semi-major axis is an increase throughout the trajectory, except at approximately the halfway point. Here, there exists a considerable decrease in this parameter because the spacecraft performs a radical change in thrust direction: nearly 180. With the use of a coast arc, the majority of the change of direction is performed without thrust (see Figure 5), meaning that there is a smaller change in the semimajor axis during this period, resulting in a lower loss of orbital energy. The strategy is more

Figure 5. Specific impulse profile for Earth-Mars trajectories using different thrust control methods at mid-flight (blue line = continuous thrust, green line = coasting, and red line = variable thrust).

efficient compared to the constant thrust case, given that it requires less propellant. A similar phenomenon is observed when using variable thrust, where the thrust is lowered when performing the change of direction (see Figure 5).

Figure 4 explains why the spacecraft performs the rapid change in thrust direction. It is observed that the change in the eccentricity can be divided into two segments: the first one is a uniform increase while the second one is a uniform decrease. The change occurs at the halfway point, where the spacecraft performs the turn. The eccentricity profile is similar to the Hohmann transfer, considered an optimal transfer strategy for chemical rockets. In this type of transfer, the semi-major axis and eccentricity are increased instantly (modeled as an impulsive burn) when the spacecraft enters the transfer orbit and then the former is further increased but the latter return to zero.

#### 4.3. Variable time of flight

From Table 2, one can observe that using coasting and variable thrust results in a 2.7% reduction in propellant consumption relative to the continuous thrust strategy. To properly understand why this reduction occurs, one must analyze the in-plane orbital elements, as well

Figures 3 and 4 present the semi-major axis and eccentricity profile for the three thrust control methods, respectively. Additionally, Figure 5 presents the specific impulse for each case. With this figure, the thrust profile can be deduced, given that the specific impulse is inversely proportional to the thrust of the engine. Presenting the specific impulse was favorable to ensure that the engine is operating within its limits. For the coasting case, the specific impulse was set to infinity during periods when the spacecraft is required to coast as dictated by the

From Figure 3, it can be observed that the overall trend in the semi-major axis is an increase throughout the trajectory, except at approximately the halfway point. Here, there exists a considerable decrease in this parameter because the spacecraft performs a radical change in thrust direction: nearly 180. With the use of a coast arc, the majority of the change of direction is performed without thrust (see Figure 5), meaning that there is a smaller change in the semimajor axis during this period, resulting in a lower loss of orbital energy. The strategy is more

Figure 5. Specific impulse profile for Earth-Mars trajectories using different thrust control methods at mid-flight (blue

line = continuous thrust, green line = coasting, and red line = variable thrust).

as the thrust profile for each control method.

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control law, resulting in zero thrust.

In Section 4.2, it was observed that using coasting or variable thrust resulted in a more efficient transfer than using continuous thrust. Another advantage when using these two control strategies is that the mission designer can vary the time of flight to transfer from the initial to the target orbit, to account for the position of the target planet when the spacecraft arrives at its orbit. By varying the time of flight for this transfer, one could also analyze which control strategy would be best for different flight periods. To achieve this goal, both coasting and variable thrust methods were tested for Earth to Mars transfers using fixed time of flights of 195, 205, and 215 days. The results for the propellant consumption for each case are presented in Figure 6, along with the case presented in Section 4.2.

Figure 6. Propellant consumption for Earth to Mars transfers for different cases of time of flight using three thrust control strategies (gray dot = continuous thrust, orange line/dot = coasting, and blue line/dot = variable thrust).

Figure 6 displays that as the time of flight increases, the variable thrust control strategy is more efficient than coasting in terms of propellant. To properly understand this phenomenon, the trajectory for both strategies was plotted for the case where time of flight was equal to 215 days. For this case, the propellant mass was reduced by 12% when using variable thrust compared to

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Figure 7 shows the trajectory in blue, with the red arrows representing the thrust magnitude and direction. The thrust direction profile is similar to what was computed in Section 4.2, with the main difference being that the trajectory is longer, since the time of flight defined is approximately 30 days greater. The thrust magnitude for the variable thrust control strategy is constant at the beginning, but decreases as the spacecraft starts to change direction. At midflight, this parameter reaches its minimum but then starts increasing until it reaches at maximum at the end of the trajectory. For the coasting strategy, it is observed that the thrust is constant until approximately a quarter of the time of flight, when the coasting period begins. The thrust resumes in the opposite direction when there is a quarter of the time of flight remaining. This can also be observed in Figure 8, where the profile of the specific impulse is plotted. It is seen that using variable specific impulse creates a more gradual change in the orbit, when compared to the coasting mechanism, resulting in a more efficient transfer with a lower propellant consumption. Additionally, it is observed that the engine operates at its highest specific impulse for approximately 35 days, demonstrating the importance of achiev-

Growing interest in high-power electric propulsion systems motivated the analysis of their performance when used to transfer from Earth to Mars orbits. VASITOS was created to study not only the optimal thrust direction, but the optimal thrust magnitude as well. Three thrust control laws were studied: continuous thrust, coasting, and variable thrust. By using a 150 kW thruster with a specific impulse of 5000 s and an efficiency of 0.65 on a 4500 kg spacecraft, it was computed that the optimal time of flight for the transfer using constant thrust was 185.78 days. Additionally, it was observed that there was a loss in orbital energy mid-way through the transfer. By using a variable specific impulse system (with boundaries of 5000– 30,000 s), the propellant consumption was reduced by 2.7% due to the system's ability to throttle down at the point where the energy loss occurred. The coasting strategy resulted in a 2.7% propellant reduction as well since the engine stopped thrusting at the point of energy loss. Further results include the comparison of the coasting and variable thrust strategies for fixed time of flights. As the time of flight was increased, it was observed that the propellant consumption of the former strategy was less than the latter. For example, for a fixed time of flight of 215 days, the propellant consumption of the variable thrust strategy was 12% less. From these simulations, it was concluded that the best thrust control law for Earth to Mars transfers was variable thrust, due to its ability to gradually change the orbit relative to the

ing these high levels of specific impulse for interplanetary orbits.

other methods studied, resulting in a lower propellant consumption.

coasting.

5. Conclusion

Figure 7. Transfer from Earth to Mars orbit using variable thrust (left) and coasting (right).

Figure 8. Specific impulse profile for Earth-Mars trajectories using different thrust control methods (blue line = variable thrust, and red line = coasting).

Figure 6 displays that as the time of flight increases, the variable thrust control strategy is more efficient than coasting in terms of propellant. To properly understand this phenomenon, the trajectory for both strategies was plotted for the case where time of flight was equal to 215 days. For this case, the propellant mass was reduced by 12% when using variable thrust compared to coasting.

Figure 7 shows the trajectory in blue, with the red arrows representing the thrust magnitude and direction. The thrust direction profile is similar to what was computed in Section 4.2, with the main difference being that the trajectory is longer, since the time of flight defined is approximately 30 days greater. The thrust magnitude for the variable thrust control strategy is constant at the beginning, but decreases as the spacecraft starts to change direction. At midflight, this parameter reaches its minimum but then starts increasing until it reaches at maximum at the end of the trajectory. For the coasting strategy, it is observed that the thrust is constant until approximately a quarter of the time of flight, when the coasting period begins. The thrust resumes in the opposite direction when there is a quarter of the time of flight remaining. This can also be observed in Figure 8, where the profile of the specific impulse is plotted. It is seen that using variable specific impulse creates a more gradual change in the orbit, when compared to the coasting mechanism, resulting in a more efficient transfer with a lower propellant consumption. Additionally, it is observed that the engine operates at its highest specific impulse for approximately 35 days, demonstrating the importance of achieving these high levels of specific impulse for interplanetary orbits.

#### 5. Conclusion

Figure 7. Transfer from Earth to Mars orbit using variable thrust (left) and coasting (right).

Figure 8. Specific impulse profile for Earth-Mars trajectories using different thrust control methods (blue line = variable

thrust, and red line = coasting).

178 Space Flight

Growing interest in high-power electric propulsion systems motivated the analysis of their performance when used to transfer from Earth to Mars orbits. VASITOS was created to study not only the optimal thrust direction, but the optimal thrust magnitude as well. Three thrust control laws were studied: continuous thrust, coasting, and variable thrust. By using a 150 kW thruster with a specific impulse of 5000 s and an efficiency of 0.65 on a 4500 kg spacecraft, it was computed that the optimal time of flight for the transfer using constant thrust was 185.78 days. Additionally, it was observed that there was a loss in orbital energy mid-way through the transfer. By using a variable specific impulse system (with boundaries of 5000– 30,000 s), the propellant consumption was reduced by 2.7% due to the system's ability to throttle down at the point where the energy loss occurred. The coasting strategy resulted in a 2.7% propellant reduction as well since the engine stopped thrusting at the point of energy loss. Further results include the comparison of the coasting and variable thrust strategies for fixed time of flights. As the time of flight was increased, it was observed that the propellant consumption of the former strategy was less than the latter. For example, for a fixed time of flight of 215 days, the propellant consumption of the variable thrust strategy was 12% less. From these simulations, it was concluded that the best thrust control law for Earth to Mars transfers was variable thrust, due to its ability to gradually change the orbit relative to the other methods studied, resulting in a lower propellant consumption.

#### Author details

Marco Gómez Jenkins<sup>1</sup> \* and Jose Antonio Castro Nieto<sup>2</sup>


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Author details

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Marco Gómez Jenkins<sup>1</sup>

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1 Space Systems Laboratory, Costa Rica Institute of Technology, Cartago, Costa Rica

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2 Ad Astra Rocket Company, Costa Rica

2012; Atlanta, Georgia, USA; 2012


**Section 5**

**Suborbital Flight**

**Section 5**
