**7. Literature review**

Various phenomena have been investigated theoretically, numerically (PIC simulation) and experimentally in Hall thrusters. The physical phenomena currently studied in Hall thrusters are the plasma oscillations of different frequency ranges, propagation and neutralization of the ion beam, electron transport, plasma interaction with a dielectric wall and the plasma sheath. Some of them are discussed below.

#### **7.1 Studies on lifetime**

Low frequency oscillation and performance are modified strongly, when the magnetic field configuration is changed. The smaller curvature of the magnetic field configuration suppresses the amplitude of low frequency oscillation and enhances the performance of Hall thruster. There have been many studies on the lifetime of the Hall thrusters, including endurance test and erosion measurements, which

limits the lifetime of the Hall thruster. The erosion depends on wall material, operating condition, channel geometry, magnetic field design and anode configuration. Garrigues et al. [21] have given an emphasis on the thrusters lifetime and reported that configuration with a zero magnetic field and a smaller region with large magnetic field tend to decrease wall erosion and low frequency current oscillations. Dorf et al. [22] reported that thruster operation is more stable with the coated anode. Barral and Miedzik [23] investigated the role of inductor-capacitor and resistor-inductor-capacitor networks in the stabilization of the plasma discharge. Tahara et al. [24] have studied the effects of channel wall material on Hall thruster performance. Ahedo and Escobar [25] have studied the influence of design and operation parameters on Hall thruster performances.

### **7.2 Studies on plasma plume**

The structure of the plasma plume exhaust from the thruster is of great interest since its huge exhaust-beam divergence may cause communication interference of satellites and electrostatic charging problems. Askhabov *et al*. [26] found that the plasma jet has a half angle of 45° and the electron temperature monotonically decays along the jet and drops by an order of magnitude at 10 m. The plasma potential was found to be substantially increased with the distance from the thruster exit. This is an important result in view of the effective acceleration potential drop [27]. Fruchtman theoretically [28] shown that the control of the electricfield profile in the Hall thruster through the positioning of an additional electrode along the channel is to enhance the efficiency. Keidar and Boyd [29] have studied the effect of the magnetic field on the plasma plume of a Hall thruster.

#### **7.3 Studies on oscillations and instabilities**

The plasma density, external electric and magnetic fields in a Hall thruster are in inhomogeneous form and are not in the thermodynamically equilibrium state. These deviations act as a source of plasma instabilities. These oscillations and instabilities in the Hall thruster may affect the divergence of the ion beam and electron transport across the magnetic field which control the productivity of the system. Choueiri [11] has qualitatively discussed the nature of oscillations in 1 kHz– 60 MHz frequency range that have been observed during operation of Hall thrusters. The typical range of oscillations have been recognized in Hall thrusters, such as 10–20 kHz discharge oscillations, 5–25 kHz rotating spokes (due to ionization process), 20–60 kHz azimuthal modes (due to drift type instability associated with gradient of density and magnetic field), 70–500 kHz transient time (ion residence time in the channel), 0.5–5 MHz azimuthal wave and high frequency oscillations (**Table 1**). The above waves regulate the efficacy of the thruster. The real frequency, growth rate and amplitude of the oscillations depend on geometry, magnetic field profile, mass flow rate and discharge voltage. Ducrocq *et al*. [30] have studied high-frequency electron drift instability and derived threedimensional dispersion relation. Keidar [31] has modeled plasma dynamics and ionization of the propellant gas within the anode holes. Barral and Makowski [32] have analyzed transit-time instability in Hall thruster. Kapulkin and Guelman [33] have investigated low frequency instability in near anode region of a Hall thruster. Lazurenko *et al*. [34] have reviewed high-frequency instabilities and anomalous electron transport in Hall thrusters. Researchers have investigated resistive instabilities in a Hall thruster and found that the plasma perturbations in the acceleration channel are unstable in the presence of collisions [13, 15, 17, 35–40]. Fernandez

et al. [41] did simulations for the growth of resistive instabilities in *E* ! � *B* ! plasma discharge. The plasma resistivity induces resistive instabilities (electrostatic and electromagnetic) [13, 15, 17] associated with azimuthal and axial directions and it was depicted that these instabilities have the highest level near the thruster exit plane. Smolyakov *et al.* reported that sheath instabilities has a vital role in anomalous transport phenomena in Hall plasma thruster [41]. Plasma sheath plays an important role to control the mobility of electrons inside a plasma channel [42–44].

