Electron cooling and finite potential drop in a magnetized plasma expansion

Abstract

The steady, collisionless, slender flow of a magnetized plasma into a surrounding vacuum is considered. The ion component is modeled as mono-energetic, while electrons are assumed Maxwellian upstream. The magnetic field has a convergent-divergent geometry, and attention is restricted to its paraxial region, so that 2D and drift effects are ignored. By using the conservation of energy and magnetic moment of particles and the quasi-neutrality condition, the ambipolar electric field and the distribution functions of both species are calculated self-consistently, paying attention to the existence of effective potential barriers associated to magnetic mirroring. The solution is used to find the total potential drop for a set of upstream conditions, plus the axial evolution of various moments of interest (density, temperatures, and heat fluxes). The results illuminate the behavior of magnetic nozzles, plasma jets, and other configurations of interest, showing, in particular, in the divergent plasma the collisionless cooling of electrons, and the generation of collisionless electron heat fluxes. V C 2015 AIP Publishing LLC.

Thermodynamics of a magnetically expanding plasma with isothermally behaving confined electrons

“…The electrons responsible for the adiabatic expansion produce spatial changes in the slope of the downward 1D eepfs along the axial direction, relating γ e closer to 5/3 near the nozzle throat. In comparison to the adiabatic electrons, the newly observed electrons measured by the back probe, which cannot be explained by adiabatic cooling, can be classified into groups of free and confined electrons according to their energy and magnetic moment values [27]. For electrons, the local maximum magnetic moment μ e,m (z, E e ) with total energy E e can be expressed as follows: μ e,m (z, E e )=(E e +ef(z))/B z , where the axial variation of the plasma potential f(z) is calculated using the average knee of measured I-V characteristics with front and back probe.…”

“…The polytropic exponent γ e in the equation describes the exchange of heat between a magnetically expanding plasma and the system, and various kinetic modeling approaches have been established to explore the physical meaning of MN devices by relating the thermodynamic model to the MN phenomena, e.g. plasma detachment, plume divergence efficiency, and thruster gain [26][27][28][29][30][31].…”

“…Theoretically, kinetic approaches to the motion of electron and ion in the MN system divide the electrons into several groups according to their magnetic moment and total energy with a given plasma potential and magnetic field structure in the MN [27]. The model assumed the conservation of the adiabatic invariants of the electrons in a decreasing plasma potential that eventually tended to asymptotic values with non-isothermal cases as bounded plasma in magnetically diverging structure.…”

Collisionless electron cooling in unmagnetized plasma thruster plumes

“…Luckily, the plasma plumes of electric thrusters (in particular, their far-region) present several advantageous characteristics, such as axisymmetry and moderate divergence, that can be exploited to set up a nearlyanalytical kinetic model. In a previous study, 40,41 a steady-state 1D-2V kinetic model based on the conservation of energy and the quasi-conservation of the magnetic moment of each electron in a strong convergentdivergent magnetic field (i.e., a magnetic nozzle 42,43 ), which improved on a previous non-stationary model by Arefiev and Breizman, 44 was established and used to compute the evolution of electron temperature in the collisionless plasma and derive simple closure relations that can be used to inform fluid electron models. The success of that model for a similar, related problem encourages us to follow a similar approach for the case of interest here (an unmagnetized plasma plume).…”

“…In the absence of a better criterion at present, and following the choice taken in Ref. 40,41, it can be assumed that after sufficiently long periods of time these regions are populated by the same distribution function as the plasma source electrons (or, alternatively a fixed fraction density of it to study the effect of these regions being only partially filled).…”