7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Numerical Analysis of the Gradient Drift Instability and its Control
in Hall Thruster Plasmas
Rei Kawashima1, Kimiya Komurasaki2
1
Department of Electrical Engineering, Shibaura Institute of Technology,2
Department of Aeronautics and Astronautics, The University of Tokyoe-mail: reik@shibaura-it.ac.jp
Hall thruster is an electric propulsion system which has
an E×B configuration with the axial electric field andradial magnetic field. Owing to the magnetic
confinement of electrons, the Hall thrusters enableefficient ionization of propellant gas and ion extraction.
Although the Hall thrusters have attained high thrust
efficiency exceeding 60%, further improvement of thethruster efficiency is desired. One of the issues limiting
the thruster efficiency is related to the anomalous
electron transport. The anomalous electron transport is
the well-known issue in the E×B discharge plasmas.
Despite the long history of research, the physics behind
the anomalous electron transport is not fully understood.
According to recent findings, it is hypothesized thatplasma oscillations that develop in the azimuthal (E×B)
direction cause the electron transport enhancement.
The objective of this study is to numerically model theplasma instabilities that affect the cross-field electrontransport, and to find an approach to mitigating the
instabilities. The authors have reproduced 10 kHz-orderrotating spoke (RS) [1] and 100 kHz-order gradient drift
instability (GDI) [2]. The effects of these instabilities on
the cross-field electron transport are discussed.
An axial-azimuthal two-dimensional model was built
for the Hall thruster discharge. The hybrid particle-fluid
model with the quasineutral assumption was used. In thisstudy, the axial distributions of ionization source term
and magnetic flux density were assumed. 100 μs
simulation was performed to attain the converged
discharge current and plasma states.
Figure 1(a) shows the axial-azimuthal distribution of
the plasma density. At the upstream region of x < 12 mm,
Coherent wave structure moving in the azimuthal
direction (+E×B direction) was observed. This structureis the RS, and its characteristics are consistent withexperimental data. Figure 1(b) shows the axial electron
velocity distribution. At the downstream region of x > 12mm, plasma instabilities with vortex like structures are
induced. Through comparisons between the simulation
results and the linear theory of the GDI, the simulated
plasma instability is identified as the GDI.
The RS and GDI affects the cross-field electrontransport in the Hall thruster discharge channel. The
electron mobility under a magnetic field is described by
the classical diffusion theory based on theelectron-neutral atom collisions. Figure 2 presents theeffective electron mobility distribution along thedischarge channel. A significant enhancement of thecross-field electron transport is observed, especially inthe downstream region of x > 12 mm. In this region, theelectrons move across magnetic fields due to the GDI,
rather than the electron-neutral collisions.

In the conference, the operating parameters affecting
the GDI and the enhanced electron transport are
discussed. We further propose controlling method for theplasma instabilities that use artificial disturbances, suchas the inhomogeneous propellant gas injection [3] andazimuthally nonuniform magnetic field [4].

Figure 1 x-y (axial-azimuthal) distribution of (a)plasma density and (b) x- (axial) electron velocity.

Figure 2
Effective electron mobility distribution
compared with the classical (collisional) mobility.
References[1] Kawashima and Komurasaki, Phys. Plasmas 28(2021) 063502.
[2] Kawashima et al., Plasma Sources Sci. Technol. 27(2018) 035010.
[3] Bak et al., Phys. Plasmas 26 (2019) 073505.
[4] Bak et al., J. Appl. Phys. 131 (2022) 0302.