Resistive MHD modes in hollow cathodes external plasma

Abstract

A significant number of plasma instabilities occur in the region just outside of hollow cathodes, depending on the injected gas flow, the current level and the application of an external magnetic field. In particular, the presence of an axial magnetic field induces a helical mode, affecting all the plasma parameters and the total current transported by the plasma. To explore the onset and behavior of this helical mode, the fluctuations in the plasma parameters in the current-carrying plume outside of a hollow cathode discharge have been investigated. The hollow cathode was operated at a current of 25 A, and at variable levels of propellant flow rate and applied magnetic fields. Electromagnetic probes were used to measure the electromagnetic fluctuations, and correlation analysis between each of the probe signals provided spatial-temporal characterization of the generated waves. Time-averaged plasma parameters, such as plasma potential and ion energy distribution function, were also collected in the near-cathode plume region by means of scanning emissive probe and retarding potential analyzer. The results show that the helical mode exists in the cathode plume at sufficiently high applied magnetic field, and is characterized by the presence of a finite electromagnetic component in the axial direction, detectable at discharge currents $\geq$ 25 A. A theoretical analysis of this mode reveals that one possible explanation is consistent with the hypotheses of resistive magnetohydrodynamics, which predicts the presence of helical modes in the forms of resistive kink. The analysis has been carried out by linear perturbation of the resistive MHD equations, from which it is possible to obtain the dispersion relation of the mode and find the $k-\omega$ unstable branch associated with the instability. These findings provided the basis for more detailed investigation of resistive MHD modes and their effect in the plume of hollow cathodes developed for electric propulsion application.

Hollow cathode discharge instability onset in electric thrusters

“…The two Langmuir probes are 180°apart azimuthally, and so the collected ion current is about 180°out of phase consistent with a rotating m = 1 mode. This is characteristic of helical MHD kink modes identified by Becatti 31 because the potential structure in the near field is a "trough" in the plasma potential, 31 so as the kink pushes the plume column off axis it drives lower potential regions at the emissive probe. The kink also pushes the higher plasma density along the axis sideways, causing the ion saturation current measured by the Langmuir probe positioned next to the emissive probe to show a density spike.…”

“…m = 1 rotational mode in the cathode plume of a Hall thruster and attributed it to electrostatic anti-drift wave oscillations. Becatti 30,31 showed that these oscillations can be electromagnetic, attributing them to rotating MHD kink instabilities 30 and later showed 31 that resistive MHD modes could exist at these lower currents (25-50 A) and correlated their amplitude with the generation of energetic ions incident on the keeper face. As shown later, the measurements described here support the MHD kink modes interpretation for the rotational instability.…”

Electromagnetic particle-in-cell simulation on self-induced magnetic field by hollow cathode discharge

“…Plokhikh et al [6] and Beiting et al [7] studied the microwave radiation generated by the hollow cathode, and found the radiation frequency ranges from 500 to 800 MHz when working alone, and the radiation power decreases as the thruster starts working, and the radiation frequency moves to 1 GHz. Recent studies have also shown that the high-current cathode plume oscillation and instabilities can be strongly affected by the self-induced magnetic field [8]. Therefore, to better understand the physics of hollow cathodes and the reasons for the associated instabilities and oscillations, the EM effects of hollow cathodes must be well studied.…”

Ionization instability and turbulence in the plume of sub-ampere hollow cathodes with applied magnetic field

“…It was previously shown for high-current cathodes, operating in excess of 1 A [13], that the existence of an axial magnetic field led to the emergence of drift instability due to gradients in plasma density transverse to B and magnetohydrodynamic (MHD) kinks and helical modes, as the current exceeds a certain threshold. These electrostatic and resistive MHD rotating structures have been studied with high-current cathodes in both standalone mode [5,6,12] and when coupled with kW-class Hall thrusters [14,15]. These instabilities can be observed in the discharge current spectra with their distinctive increased power density at similar frequency range as the longitudinal ionization instability [16], i.e.…”

“…In order to replicate the magnetic field topology and strength during cathode standalone testing with external anodes, magnetic field generators are employed. The magnetic field is produced by magnetic coils placed usually behind or around the anode [5,6] or around the cathode and/or the plume [7][8][9][10][11][12]. It was observed that an applied axial magnetic field did not change only the morphology of the plume, suggesting electron magnetization and changes in ionization [9,10], but also affected the discharge stability and the main oscillatory phenomena in the plume [5,10,11].…”