**6.7 Oscillations and instabilities in Hall thrusters**

There are numerous types of oscillation found in thrusters which propagates in azimuthally and axially direction ranging from a few kHz to tens of MHz [1, 10]. These oscillations may reduce the specific impulse and the efficiency of a Hall thruster. These disturbances can also limit the operating life of a Hall thruster and therefore, suppression of this oscillation has become an essential task for Hall thrusters. These fluctuations are responsible for electron transport across magnetic field lines, performance and ionization of propellant [27–30]. The magnitude of these oscillations strongly depend on the magnetic field, location of the cathodes, the discharge voltage and the mass flow rate.

Low frequency oscillation, frequently referred to as the breathing mode, is intimately tied to the details of propellant ionization and eventual ion acceleration and manifests itself as a strong 10–30 kHz oscillation in the thruster discharge current. Breathing mode models suggest the presence of a propagating ionization front traversing the channel of the thrusters [31]. Benítez and Ahedo investigated the axial-azimuthal instabilities in the global discharge region of a Hall-thruster to identify dominant mode (develops in the near plume at 1–5 MHz) and subdominant mode (develops near the anode100–300 kHz) [32]. Lafleur *et al*. studied transport effects of the electron drift instability in Hall-effect Thrusters [33]. Fan *et al*. studied the effects of the peak magnetic field position on Hall thruster discharge characteristics [34]. Sekine *et al*. investigated the spatially and temporally resolved ion flow measurements inside the plasma source of an inductive radio frequency plasma thruster [35]. Puerta *et al*. generalized non-ideal treatment and growth rates analysis of drift waves instabilities in a collisions-free magnetized dusty plasma [36]. The electrostatic dispersion relation for an unbounded homogeneous plasma in the presence of unmagnetized ions, magnetized electrons and an applied magnetic field has been solved numerically by Mikellides and Ortega in the near-plume of a magnetically shielded Hall thruster [37]. Tomilin and Ivan Khmelevskoi studied the influence of kinetic effects on dispersion properties of high-frequency perturbations in Hall thruster plasmas [38]. Marcovati *et al*. reported the dynamic behavior of gradient-driven drift waves in a strongly magnetron discharge in multi ion plasma [39]. Litvak and Fisch [40] investigated resistive instabilities in a Hall plasma and found that plasma perturbations in the acceleration channel are unstable in the presence of collisions. Fernandez *et al*. [41] did simulations for resistive instabilities. Marusov et al. [42] modeled the stability of gradient-drift waves in a Hall-type plasma using two-fluid ideal magnetohydrodynamics. Ducrocq et al. [43] studied high-frequency electron drift instability, where they derived threedimensional dispersion relation for a model of a crossed electric and magnetic field configuration existing in the Hall thruster. Litvak and Fisch [44] have analyzed gradient driven Rayleigh type instabilities in a Hall thruster using two fluid

hydrodynamic equations. Kapulkin and Guelman [45] investigated low frequency instability in near anode region of a Hall thruster, where they obtained that the instability can be responsible for the enhanced transfer of the electrons between the ionization region and the anode. Choueiri [46] has quantitatively discussed the nature of oscillations in the 1 kHz–60 MHz frequency range observed during operation of Hall thrusters. Various plasma parameters measured inside the accelerating channel of a typical Hall thruster were used to evaluate the various stability criteria and dispersion relations of oscillations [46].

At small amplitudes, the oscillations can be considered a part of normal operation with no significant effect on operation. At large amplitudes, the oscillations can severely and adversely affect operation. The details of these oscillation are given in **Table 1**.

Lakhin *et al.* have developed the effects of finite electron temperature on gradient drift instabilities in partially magnetized plasmas in the frequency range *ωBi* ≪ *ω* ≪ *ωBe* driven by the equilibrium current perpendicular to the magnetic field [56]. Romadanov *et al.* [57] studied the structure of nonlocal gradient-drift instabilities in Hall E B discharge plasma. Koshkarov *et al.* calculated the linear and nonlinear nonlocal instability of axial lower-hybrid modes in plasma under the influence of ion flow rate [58]. Smolyakov *et al.* have used fluid theory and performed the simulations of instabilities, turbulent transport and coherent structures in magnetized plasmas [59]. Singh and Malik [60, 61] investigated that temperature of the ion and drift velocity profiles of the electron modifies the conditions


**Table 1.**

*Types and frequency range of oscillations in Hall thrusters.*

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

for Rayleigh type instability under the effects of thermal motions of ions and plasma resistivity induces resistive instabilities (electrostatic and electromagnetic) [62–65] associated with azimuthal and axial directions. Yadav et al. presented the model for relativistic electron-beam assisted growth of oscillating two-stream instability [66]. Aria and Malik [67] have investigated the propagating modes, instabilities and plasma sheath formed on the outer surface of a spacecraft. The detailed physical picture of the processes in the thruster is very complex. It includes a whole series of phenomena, such as stabilization of the flow in cross-fields. Becatti et al. investigated the properties of plasma oscillations in the exterior region of a high-current hollow cathode [68].
