**5.2 Thruster with anode layer**

generated inside the discharge channel along the axial direction of the device [3]. In addition, these kind of devices have implication in partially ionized plasmas (tokamaks), in ionosphere (base of the solar photosphere), in protoplanetary discs, circum nuclear discs in active galactic nuclei and neutron stars. Hall thruster has high thrust resolution, it is being used for the adjustment of the location of the

The first issue is that the divergence angle of these devices is about 60°, which relatively large and cause problem related to erosion of the channel walls and outer surfaces of the thruster. The erosion of the walls decreases the lifetime of the device. This channel usually has a length of the order of centimeters. In addition, densities in the channel are typically in the range between 10<sup>17</sup> and 10<sup>18</sup> m<sup>3</sup> for the plasma, and 1018 and 10<sup>20</sup> m<sup>3</sup> for the neutral gas [4]. The plasma in a Hall thruster does not stay uniform and an inhomogeneous plasma immersed in the external electric and magnetic fields is not in the thermodynamically equilibrium state, this deviation in general is a source of plasma instabilities. The amplitudes of the waves and instabilities are attributed by the density scale lengths of plasma and magnetic field and other parameters. These waves/oscillation and instabilities may affect the efficiency of the device, hence forth research on studies on oscillation/instabilities always

Two types of Hall thrusters have been developed: a thruster with closed electron drift and extended acceleration zone or stationary plasma thruster and a thruster

In **Table 1**, typical values of some of the pertinent properties are listed at the

Such thrusters have a wall made up of dielectric of boron nitride or silicon carbide and extended channel compared to its width. The role of the wall is that the collisions of the electrons and ions with the wall generate low energy secondary electrons. These secondary electrons keep tending the electron temperature low in the discharge plasma. By reducing the discharge electron energy, a smooth and continuous variation in plasma potential between the anode and the cathode is

**Property Value Property Value** Inner diameter 60 mm Neutral velocity 300 m/s Outer diameter 100 mm Electron temperature 5–10 eV Plasma density <sup>10</sup>17/m3 Ion temperature <sup>1</sup>–5 eV Neutral density <sup>10</sup>18/m3 Neutral temperature 0.9 eV Ion velocity 104 m/s Debye length <sup>10</sup><sup>5</sup> <sup>m</sup>

with a very short acceleration channel or thruster with anode layer.

**5.1 Dielectric wall thruster or stationary plasma thruster**

satellite onboard.

**4. Spacecraft issues**

*Selected Topics in Plasma Physics*

attracted the investigators.

thruster exit for the SPT-100.

**5. Types of Hall plasma thruster**

Collision mean free 1 m

*Typical plasma parameters for Hall Thrusters.*

**Table 1.**

**26**

Thruster with anode layer also developed in Russia has a narrow acceleration zone associated with the narrow electric field region near the anode. This geometry considerably shortens the electric field region in the channel, where the ion acceleration occurs. However, this configuration does not change the basic ion generation or acceleration method. The channel wall made up of conductor, which is usually also a part of the magnetic circuit, is biased negatively (usually cathode potential) to repel electrons in the ionization region and to reduce electron-power losses. This reduces the loss caused by the ion and electron collisions with the walls. Since the walls are conductive, a constant potential (same as that of the cathode) is observed along the entire wall. Very high electron temperatures, i.e. more than 50 eV, are typically observed in such thrusters [1].

## **6. Review of status of current research and development in the subject**

The range of the oscillations lies from few kHz to MHz in the acceleration channel of the thrusters and has been given in **Table 2**. Rayleigh-Taylor (RT) instability takes place when a lighter fluid supports a heavy fluid. The plasma in the Hall thruster possesses Rayleigh-Taylor instability, resistive instability, transit time instability, electromagnetic instability and sheath instabilities [5–11]. These systems are rampant with plasma instabilities and fluctuations, many of which are responsible for performance, driving electron transport across magnetic field lines and contributing to propellant ionization. Over the last decade several studies have been carried out with HET to characterize the low frequency azimuthal and axial oscillations and optimizing magnetic field profile for a wide range of operating conditions for better efficiency and performance. Singh and Malik [10, 11], investigated that temperature of the ion and drift velocity profiles of the electron modifies the conditions for Rayleigh type instability under the effects of thermal motions of ions.

The plasma resistivity induces resistive instabilities (electrostatic and electromagnetic) [6–9] associated with azimuthal and axial directions. High-frequency (1–10 MHz) instabilities have been studied in the Hall-effect thruster [6–9], where it was found that these instabilities have the highest level near the thruster exit plane. These oscillations in the Hall thruster determine the efficiency of the system and may affect the divergence of the ion beam and electron transport across the


**Table 2.** *Range and classification of oscillations in a Hall Thrusters.* magnetic field. Smolyakov et al. reported that sheath instabilities has a vital role in anomalous transport phenomena in Hall plasma thruster [12, 13].

### **7. Ion stream speed study for electrostatic thruster**

Let us consider a Hall thruster having potential difference between anode and virtual cathode is Φ Volt and ions density (mass) *n* (*M*). The mass flow of propel-

lant of ions of mass *<sup>M</sup>* through an area *<sup>A</sup>* is given by *<sup>m</sup>*\_ *<sup>p</sup>* <sup>¼</sup> *nMAU*! *ex*.

The thrust is also constant as

$$T = \dot{m}\_p \overrightarrow{U}\_{\text{ex}},\tag{8}$$

Substituting the value of mass flow rate, the thrust per unit area

$$\frac{T}{A} = \left(nM\vec{U}\_{\text{ex}}\right)\vec{U}\_{\text{ex}} = \frac{J\_i}{q}M\vec{U}\_{\text{ex}}\tag{9}$$

where *Ji* the current density of ions.

From the definition of work energy theorem, that the kinetic energy of each ion should equal to the work done in moving the charge across a potential drop. That is

$$\frac{1}{2}\overrightarrow{\mathbf{M}\overrightarrow{U}}\_{\text{cc}}^{2} = q\Phi \tag{10}$$

Or

$$
\overrightarrow{U}\_{\text{ex}} = I\_{\text{pp}} \mathbf{g} = \sqrt{\frac{2q\Phi}{M}} \tag{11}
$$

**Author details**

Sukhmander Singh

**29**

Plasma Waves and Electric Propulsion Laboratory, Department of Physics,

© 2020 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,

Central University of Rajasthan, Ajmer, Kishangarh, India

*Hall Thruster: An Electric Propulsion through Plasmas DOI: http://dx.doi.org/10.5772/intechopen.91622*

provided the original work is properly cited.

\*Address all correspondence to: sukhmandersingh@curaj.ac.in

Thus the specific impulse or exhaust velocity of the ions depends on the potential drop developed across the anode and cathode and to the mass of the ion.

### **8. Conclusions**

The *E* ! � *B* ! configurations of fields are used to confine electrons, increasing the electron residence time and allowing ionization and plasma sustainment. The magnetron sputtering used in material science for ion implantation is also based on the same *E* ! � *B* ! drift. The primary concern of the study to enhance the lifetime and performance of the Hall thruster by studying the instabilities that takes place in the channel and optimization of profile of the magnetic field which is the main parameter in respect to the erosion of the channel walls.

### **Acknowledgements**

The University Grants Commission (UGC), New Delhi, India is thankfully acknowledged for providing the startup Grant (No. F. 30-356/2017/BSR).

*Hall Thruster: An Electric Propulsion through Plasmas DOI: http://dx.doi.org/10.5772/intechopen.91622*

magnetic field. Smolyakov et al. reported that sheath instabilities has a vital role in

Let us consider a Hall thruster having potential difference between anode and virtual cathode is Φ Volt and ions density (mass) *n* (*M*). The mass flow of propel-

> *T* ¼ *m*\_ *pU* !

*ex* � �

*U* ! *ex* <sup>¼</sup> *Ji q MU*!

From the definition of work energy theorem, that the kinetic energy of each ion should equal to the work done in moving the charge across a potential drop. That is

> ffiffiffiffiffiffiffiffiffi 2*q*Φ *M*

configurations of fields are used to confine electrons, increasing the

drift. The primary concern of the study to enhance the lifetime and

r

*ex*.

*ex* (9)

(11)

*ex*, (8)

*ex* ¼ *q*Φ (10)

anomalous transport phenomena in Hall plasma thruster [12, 13].

lant of ions of mass *<sup>M</sup>* through an area *<sup>A</sup>* is given by *<sup>m</sup>*\_ *<sup>p</sup>* <sup>¼</sup> *nMAU*!

Substituting the value of mass flow rate, the thrust per unit area

1 2 *MU*!<sup>2</sup>

*U* !

eter in respect to the erosion of the channel walls.

*ex* ¼ *Ispg* ¼

tial drop developed across the anode and cathode and to the mass of the ion.

Thus the specific impulse or exhaust velocity of the ions depends on the poten-

electron residence time and allowing ionization and plasma sustainment. The magnetron sputtering used in material science for ion implantation is also based on the

performance of the Hall thruster by studying the instabilities that takes place in the channel and optimization of profile of the magnetic field which is the main param-

The University Grants Commission (UGC), New Delhi, India is thankfully

acknowledged for providing the startup Grant (No. F. 30-356/2017/BSR).

*<sup>A</sup>* <sup>¼</sup> *nMU*!

**7. Ion stream speed study for electrostatic thruster**

*T*

The thrust is also constant as

*Selected Topics in Plasma Physics*

where *Ji* the current density of ions.

Or

**8. Conclusions**

**Acknowledgements**

The *E* ! � *B* !

same *E* ! � *B* !

**28**
