Time-dependent kinetic analysis of trapped electrons in a magnetically expanding plasma

Abstract

A deep understanding of the kinetic properties of the electrons in a magnetic nozzle (MN), which is attracting attention as an acceleration stage for thrusters, is of great significance as it directly contributes to the development of the MN performance. In the sense that a conversion of the electron momentum to the ion kinetic energy determines the characteristics of the MN, fundamental research on the kinetic feature of a magnetically expanding plasma has focused on the spatial distribution of the electron properties and proposed directions to the desired application. Unlike the common perception of this importance, various research groups have proposed contradictory arguments based on their theoretical approaches regarding the ion beam acceleration from the viewpoint of heat flow of electrons. We point out that the main reason for the absence of a theoretical consensus for the nozzle efficiency improvements arises from the lack of the clear interpretation of the plasma properties by focusing only on the final state of the electrons. In this Letter, time-resolved measurement of the electron energy distributions has been performed to grasp a detailed series of expansion processes. It has been revealed that the effective potential well gradually formed by the self-generated electric field acts as a limiting factor in the motion of electrons; this effect attributes to the changes of the electron energy distribution represented as the accumulation of the trapped electrons. The accumulation over the entire region diminishes the degree of the cooling rate of a system and decreases the electric field in the downstream region initially generated by the adiabatic expansion. The present study emphasizes that the kinetic features of an MN are strongly affected by the non-stationary motion of the trapped electrons; thus, the temporal behavior of the trapped electrons must be considered for prediction and analysis of nozzle performances.

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

“…The adiabatic caseᾱ = 0 corresponds toγ = 5/3 and, as the relative heat flux increases,γ decreases. For instance, the intermediate value α = 7/2, extracted from figure 10(c), o yieldsγ ≈ 1.2, a value close to some experimental evidence [26][27][28][29]39]. Implementing the crude closure (37) in the energy equation (33) yields the known law between the electric potential fall and the polytropic coefficient, [34] e|φ…”

Plasma beam characterization along the magnetic nozzle of an ECR thruster

“…The 2D magnetic field topology may influence the formation of the doubly-trapped regions, and therefore have a direct impact in the local electron cooling. As commented before, Kim et al [24,25] also found different polytropic indices when varying the strength and configuration of the magnetic nozzle.…”

“…Little and Choueiri in [23] characterized the axial variation of macroscopic quantities in a RF plasma beam and investigated the electron cooling phenomena, comparing its results with a fluid 1D model that included electron heat conduction and revealing the critical need for improved 1D models to describe the MN expansion. More recently, experimental studies performed by Kim et al in [24,25] showed the coexistence of adiabatic expanding electrons and isothermal confined electrons along the MN of an ECR thruster. In this sense, the requirement for accurate experimental data and validation of advanced theoretical models for MNs is clear.…”

Physics of E × B discharges relevant to plasma propulsion and similar technologies

“…those flowing downstream with the ions) tend to be adiabatic (i.e. γ=5/3 in three dimensions), while confined ones (included double-trapped) are isothermal [401], [402]. Further evidences are needed.…”

“…Many of these measurements to be carried out in the laboratory require high-quality, sophisticated, diagnostics equipment, such as accurate thrust balances, magnetic probes, and non-intrusive and intrusive devices able to characterize the non-Maxwellian VDFs of the ions and (mainly) the electrons. For instance, although there is some experimental evidence of the presence of doubly trapped electrons [401], [402], a good characterization of them under different conditions is primordial due to their probable large influence in the plasma expansion profiles. Also, measuring the beam temperature anisotropy has been proven to be very challenging and seems to require designing specific probes.…”