Magnetic moment conservation and nonadiabatic behavior of electrons in axisymmetric inhomogeneous magnetic fields

Partially magnetized plasma discharges in $E\times B$ configurations are versatile tools, with applications ranging from Hall-effect thrusters for space propulsion to high-power impulse magnetron sputtering (HiPIMS) for thin-film deposition. Their magnetic fields are typically described in cylindrical coordinates \((r,\theta,z)\), with field lines in the \(r\)–\(z\) plane [1]. Electrons confined in the race-track region are considered magnetized, with their magnetic moment serving as an indicator of the degree of confinement; if the magnetic moment is conserved along the trajectory, the electron remains magnetized. However, various processes can disrupt this conservation, including collisions, electric field interactions, and resonant particle motion [2,3].

If the magnetic moment of an electron is not conserved, a diffusion in velocity space can be associated with this nonadiabatic behavior [4]. This work investigates the dynamics of the electron magnetic moment $\mu$ in these configurations with an axisymmetric magnetic field, examining their nonadiabatic behavior and its impact on electron energization under such conditions.

[1] R. P. Brinkmann et al. 2020 Phys. Plasmas; 27 (5): 053504.

[2] R. J. Hastie et al. 1969 IAEA pp. p. 389–401

[3] C. D. Stephens et al. 2017 Phys. Plasmas; 24 (10): 102517.

[4] I. B. Bernstein Phys. Fluids 19, 1546–1550 (1976)