Hall Thruster: An Electric Propulsion through Plasmas

*Sukhmander Singh*

### **Abstract**

The chapter discussed the technological application of plasma physics in space science. The plasma technology is using laser-plasma fusion, inertial fusion, Terahertz wave generation and welding of metals. In this chapter, the application of plasma physics in the field of electric propulsion and types has been discussed. These devices have much higher exhaust velocities, longer life time, high thrust density than chemical propulsion devices and useful for space missions with regard to the spacecraft station keeping, rephrasing and orbit topping applications. The mathematical relation has been derived to obtain the performance parameters of the propulsion devices.

**Keywords:** electric propulsion, Hall thruster, impulse, exhaust velocity

### **1. Overview of propulsion devices and rocket equation**

Electric propulsion (EP) devices use electric power to produce thrust. These devices have much higher exhaust velocities than chemical propulsion devices. Therefore, EP devices require much less propellant mass than chemical systems for a given space task. Here first we have overview of different thrusters and their basic mechanism based on type of propellant used to get the thrust.

The motion of any propulsion devices is given by Newton's 3rd Law of action and equal, opposite reaction which forms the basis for the motivation for the study of electric propulsion. The rocket equation states that a device can accelerate to a desired final velocity by reaction against an expelled propellant stream [1].

Consider a rocket of mass *m*, which expels an infinitely small unit of fuel *dm* at an exhaust velocity *U* ! *ex*. The exhaust velocity *U* ! *ex* is almost constant and it is a fixed property of the propellant [2]. Conservation of linear momentum requires that the spacecraft experience a small change in velocity *dυ* !, such that

$$m\frac{d\overrightarrow{v}}{dt} + \overrightarrow{U}\_{\text{ex}}\frac{dm}{dt} = 0\tag{1}$$

Integrating by setting appropriate limits in mass and velocity yields

$$\int\_{v\_i}^{v\_f} \frac{d\overrightarrow{v}}{\overrightarrow{U}\_{\infty}} + \overrightarrow{U}\_{\infty} \int\_{m\_i}^{m\_f} \frac{dm}{m} = \mathbf{0} \tag{2}$$

After simplification, we get

$$\ln\left(\frac{m\_f}{m\_i}\right) = -\frac{\nu\_f - \nu\_i}{\vec{U}\_{\infty}} = -\frac{\Delta\vec{\nu}}{\vec{U}\_{\infty}}\tag{3}$$

**2.2 Electromagnetic thrusters**

**2.3 Electrostatic thrusters**

**3. Hall thruster operation**

**Figure 1.**

**25**

*Schematic diagram of a typical Hall plasma thruster.*

eration by electromagnetic force to generate thrust.

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

field at the exit side of the thruster to produce thrust.

In electromagnetic thrusters an inert gas is used as a propellant and it is ionized by heating to produce plasma. Then these ionized gas (charged particles) are accel-

In electrostatic thrusters only ions are accelerated by applying direct electric

Hall effect thrusters (HETs) were originally developed in United States and Russia about 60 years ago, and the first working devices were reported in U.S. in the early 1960s. Now a days, most of the countries using the Hall thruster technology in their space mission. Unlike chemicals and electric rockets, the propulsive thrust in a Hall thruster is achieved by an ionized inert gas (Xenon) which has high atomic number and low ionization potential. For this Xenon is mostly used. In a Hall thruster, the propellant is ionized and then accelerated by electrostatic forces. **Figure 1** shows the internal parts of a plasma Hall thruster. Generally, the discharge channel is cylindrical shape made up with metallic material. The magnetic field of the order of 150 Gauss is applied to produce closed drift of electrons inside the channel. The applied magnetic field which is strong enough so that the electrons get magnetized, i.e. they are able to gyrate within the discharge channel, but the ions remain unaffected due to their Larmor radius much larger than the dimension of the thruster. Thus the electrons remain effectively trapped in azimuthally *E*

drifts around the annular channel and slowly diffuse towards the anode. This azimuthal drift current of the electrons is referred to as the Hall current. The propellant enters from the left side of the channel via anode and gets ionized through hollow cathode of the device. The electric field of strength �1000 V/m gets

! � *B* !

The above rocket equation provides the relationship between the mission velocity and the mass of propellant *mp* ¼ *mi* � *mf* required for a given mission. It is clear that a higher *dυ* ! demands more propellant. Unfortunately, the mass ratio cannot be increased so much to avoid payloads problems in space mission, therefore for a given mass fraction, the exhaust velocity *U* ! *ex* of the propellant needs to be the order of *dυ* ! and the higher the propellant exit velocity, the less propellant mass is required.

### **2. Thrust, impulse and efficiency**

The performance of thrusters is usually characterized by a number of parameters. A first quantity relevant to thruster performance is the thrust *T*, which is the total force undergone by the rocket. The specific impulse is used to compare the efficiencies of different type of propulsion systems [2]. The performance parameter is the specific impulse *Isp*, defined below

$$I\_{sp} = \frac{T}{\dot{m}\_p \text{g}} \tag{4}$$

Here *m*\_ *<sup>p</sup>* is the mass flow rate and *g* is the acceleration due to gravity. The specific impulse has the dimension of time and is a measure for the effective lifetime of the thruster, when lifting its own propellant from the earth's surface.

For the case of a constant mass flow rate the thrust is also constant as

$$T = \dot{m}\_p \overrightarrow{U}\_{\text{ex}},\tag{5}$$

and the specific impulse simplifies to

$$I\_{\mathcal{P}} = \frac{\vec{U}\_{\text{ex}}}{\mathcal{g}} \tag{6}$$

Finally, the rocket equation turned into

$$\frac{m\_f}{m\_i} = e^{\frac{-\Delta \vec{v}}{k^{I\_p}}} \tag{7}$$

The rocket equation is equally applicable to all type of propulsion systems. Therefore high specific impulse related to better efficiency for a propellant. Based on the acceleration of gases for propulsion, electrical thrusters have been classified into three main categories.

#### **2.1 Electrothermal thrusters**

In electrothermal thrusters, the hot gas is expanded through a nozzle without ionizing it. When it is being passed through a thin nozzle, the thermal energy of gas gets converted into kinetic energy and produce a thrust.
