**2. Description of the Hall thruster**

This description of the Hall thruster is shown in **Figure 1**. The anode and cathode set up an axial electric field and magnetic coils create a radial magnetic field. First cathode starts producing a stream of electrons and these electrons are attracted by positive anode. When electrons are moving to anode, then at the channel exit they face of perpendicular electric and magnetic fields, these fields are more strong at channel exit. Due to these perpendicular fields, electrons trapped in an ExB drift and formed Hall current [1]. At this time Xenon gas is released from the anode, when neutral atom of gas reached at the channel exit, then electron collides with neutral atoms and ionized them. These ions are accelerated out of channel by electric field at the channel exit and this motion of ions imparts a reaction force on the thruster in reverse direction. The cathode is also used to neutral the ions charge so it produce a stream of electron to neutral the ions [1–10].

### **2.1 Stationary plasma thruster (SPT)**

The wall material of this type of thruster is dielectric like borosil (BN-SiO2), boron nitride (BN) and alumina. This type of material has low secondary electron emission coefficient with Xenon ion interaction. Most of SPT use Xenon as a propellant because of its higher mass (131.3amu), lower first ionization potential, less toxicity, ionization cross section of (�2.310�<sup>6</sup> cm2 ) and of its desirable thermodynamics properties [1, 10].

**Figure 1.** *Schematic diagram of a typical Hall plasma thruster.*

## **2.2 Thruster with anode layer (TAL)**

These types of thruster has metallic conducting walls and has narrow acceleration zone associated with the narrow electric field region near the anode. The ratio of channel width and channel depth in these thruster is 2:1. The conducting channel wall is negatively biased and it is a part of magnetic circuit so it prevent electron to move in direction of wall and repel them to ionization region and reduce electron power losses [1–10].

## **3. Components of a Hall thruster**

The main components of a Hall thruster are body, magnetic coils, discharge channel, anode and cathode. The body of the Hall thruster provides better shape of external magnetic field, so it is normally made up of iron (steel). In this thruster a single thick disk shape annular discharge channel exist on the front face. To create better shape of magnetic field two type of magnetic coils are situated in the thruster channel. The inner coil is made of single reel and located radially inward in the channel and the outer coil is made of multiple reels and located radially outward in the channel. The magnetic coils and iron body made a magnetic circuit. The magnetic iron body of the thruster is separated from thruster discharge channel by walls and the material of these walls is metal or ceramic. The material of the anode is normally stainless steel, which avoids magnetic interaction and supply hardiness [1–10]. To set up an axial electric field in discharge channel of thruster a cathode is required and this cathode is normally hollow cathode with lanthanum hexaboride or barium oxide. The cathode completes the discharge circuit and work like an electron source. This description of the Hall thruster provides knowledge about the structure of thruster.

## **4. Hall current and thrust**

As discussed earlier, there is an azimuthal electron drift in a Hall thruster channel, which is normal to both the applied electric field and generates a Hall current [1, 10]. Because of the collisions of the electrons with neutrals, electrons, ions and potential fluctuations in the plasma, generate the axial electron current density. The azimuthal E X B drift is given by

$$
\nu\_d = \frac{\overrightarrow{E} \times \overrightarrow{B}}{B^2} \approx \frac{E\_r}{B\_x} \tag{5}
$$

The Hall current may be approximated by integrating the magnitude of *Er=Bz* along the acceleration region and multiplying the result by the electron charge density and width. In mathematically, it can be read as

$$I\_H \approx e n\_\epsilon \int\_0^L \frac{E\_r}{B\_x} d\infty \approx \frac{e \omega n\_\epsilon V\_d}{B} \tag{6}$$

Here, *w* is the channel width and *Vd* is the voltage at cathode.

*Numerical Investigations of Electromagnetic Oscillations and Turbulences in Hall… DOI: http://dx.doi.org/10.5772/intechopen.99883*
