Kinetic features and non-stationary electron trapping in paraxial magnetic nozzles

Abstract

The paraxial expansion of a collisionless plasma jet into vacuum, guided by a magnetic nozzle, is studied with an Eulerian and non-stationary Vlasov-Poisson solver. Parametric analyses varying the magnetic field expansion rate, the size of the simulation box, and the electrostatic potential fall are presented. After choosing the potential fall leading to a zero net current beam, the steady states of the simulations exhibit a quasi-neutral region followed by a downstream sheath. The latter, an unavoidable consequence of the finite size of the computational domain, does not affect the quasi-neutral region if the box size is chosen appropriately. The steady state presents a strong decay of the perpendicular temperature of the electrons, whose profile versus the inverse of the magnetic field does not depend on the expansion rate within the quasi-neutral region. As a consequence, the electron distribution function is highly anisotropic downstream. The simulations revealed that the ions reach a higher velocity during the transient than in the steady state and their distribution functions are not far from mono-energetic. The density percentage of the population of electrons trapped during the transient, which is computed self-consistently by the code, is up to 25% of the total electron density in the quasi-neutral region. It is demonstrated that the exact amount depends on the history of the system and the steady state is not unique. Nevertheless, the amount of trapped electrons is smaller than the one assumed heuristically by kinetic stationary theories.

Macroscopic and parametric study of a kinetic plasma expansion in a paraxial magnetic nozzle

“…This fact must be taken in to account when comparing convergent-divergent MN models with divergence-only MN models such as those of Refs. [31,34]. In particular, the comparison of the present model with the convergent-only MN of Ref.…”

“…Several works on kinetic models consider the plasma expansion in a divergent MN only, placing the plasma source at the throat M (or nearby) [31,36]. This configuration makes full sense when plasma processes on the convergent MN are dominated by phenomena different from magnetic guiding, such as plasma production and heating or interaction with chamber walls.…”

“…Each subplot depicts the different terms of the momentum, the total energy, and the perpendicular energy equations for ions and electrons along the nozzle, thus illustrating on the dominant terms in each equation and nozzle region. Concerning plots 6(c)-(d), equation (31) has been used and the constant on its right-hand side has been included into the potential energy term. This is not possible in plots 6(e)-(f) for the flows of perpendicular energy, but units have been set in order that the right-side constant in equation ( 30) is equal to 1.…”

Three dimensional fluid-kinetic model of a magnetically guided plasma jet

“…Incidentally, this model is fully analogous to that of an unmagnetized plasma plume [41]. A posterior time-dependent kinetic paraxial model has demonstrated the formation of trapped populations in the transient period of formation of the MN [32]. This paper attempts to continue these previous modeling efforts by establishing a consis-tent 3D stationary fluid-kinetic model of the MN, which takes advantage when possible of fluid equations and relies on the moments of the collisionless VDF when necessary.…”

“…One of them is the total electric potential fall along the MN, which is set by the full expansion of the plasma beam, closely related to the thruster specific impulse and determinant in the interaction between the plasma and the spacecraft wet surfaces. The total potential fall depends again on the electron thermodynamics and also on the ratio of bulk electron current extracted from the plasma source to the thermal electron flux [31,32]. A second one is the plasma detachment from the MN [33], and thus the effective plume divergence angle.…”