**7. Magnetic field profiles and erosion problems**

Magnetic field is an important parameter, which affect the performance and operation of Hall thruster. The erosion on the channel walls and on the electrodes can be minimized by accelerated beam of ions to a narrower beam width and by use of appropriate profile of magnetic field. The radial magnetic field causes the erosions of the walls, so new topology of magnetic field 'lens' is proposed by Morozov [69]. By using magnetic shielding technique, the discharge chamber erosion rate can be reduced by orders of magnitude [70]. Morozov and Lebedev proposed a magnetic field lens to focus the plasma beam [71]. Morozov et al. have designed a lens-type magnetic field with a zero magnetic point to make the plume divergence half angle only 10° in SPT-ATON Hall thruster [72]. Hofer et al. showed that the performance of the Hall thruster can be enhanced by reducing the divergence of the plume that could damage the solar panels and other parts of the satellite [73]. Hofer et al. used magnetic field to control the unmagnetized ion beam that formed in Hall thruster. By controlling ion beam the wall erosion was reduced to 2–3 order by ion bombardment [74]. Huang et al. studied the effect of background pressure on performance and plume of NASA's High Voltage Hall Accelerator Hall thruster [75]. Their result shows that discharge current and thrust are increases with pressure and ion beam current, ion energy per charge, plum divergence decreases with increasing background pressure.

Liu et al. studied the effect of azimuthally electron drift on sheath profile and anomalous erosion in thrusters. Their results show that azimuthally electron drift induce sheath oscillations and it can produce an asymmetric sheath structure. To simulate the azimuthally erosion evolution, an erosion modal is used and it has been concluded that the azimuthally asymmetric ion sputtering is responsible for an asymmetric erosion profile [76]. Kim studied the ionization processes and ion dynamics in the accelerating channel to determine the stationary plasma thrusters performance levels [54]. Choueiri theoretically studied the difference between stationary plasma thruster and thruster with anode layer by measuring the temperature of secondary electron emission from the walls of thruster [77]. Hong et al. studied the effect of wall grooves on Hall thruster discharge to improve the performance of Hall thruster. If wall grooves are present in ionization region it increases near wall conductivity and decrease electron transient time, thrust and efficiency [78]. Ding et al. studied the discharge current and stability in graphite walls and BN-SiO2 walls for magnetic shielded and unshielded thruster. Their result shows that magnetic shielded thruster does not show change in stability and discharge current but 25% discharge current increases in unshielded thruster [79]. Experimental results and PIC simulation show that oblique channel's specific impulse, anode efficiency, thrust, propellant utilization and ionization in plume region is improved 20% rather than the straight channel thruster [80]. Olano et al. studied the effect of magnetic field configuration on thruster performance and plasma discharge by proposing three types of configurations: (A) nominal, (B) orthogonal magnetic field and (C) high magnetic field [80, 81]. Garrigues et al. did PIC simulations and shows that in a Hall thruster electric discharge produce due to wall-plasma interaction and wall of thruster channel is reduced due to interaction with ions [82]. The electrostatic and magnetic probes are used to investigate the electromagnetic fluctuations and coherent magnetohydrodynamic azimuthal modes in thruster [68].
