Fully kinetic model of plasma expansion in a magnetic nozzle

Abstract

A self-consistent model is presented for performing steady-state fully kinetic Particle-in-Cell simulations of magnetised plasma plumes. An energy-based electron reflection prevents the numerical pump instability associated with a typical open-outflow boundary, and is shown to be sufficiently general that both the plume kinetics and plasma potential demonstrate domain independence (within 4\%). This is upheld by non-stationary Robin-type boundary conditions on the Poisson's equation, coupled to a capacitive circuit that allows physical evolution of the downstream potential drop in the transient. The method has been validated against experiments, providing results that fall within the uncertainty of measurements. Simulations are then carried out to study collisional xenon discharges into axisymmetric diverging magnetic nozzles. Particular discussion is given to the identification of a collision-enhanced potential well arising from charge separation at the plume periphery, the role of ion-neutral charge exchange, and a three-region piecewise polytropic cooling regime for electrons. The polytropic index is shown to depend on the degree of magnetisation. Specifically, in the region near the thruster outlet, the plume is weakly-magnetised due to the cross-field diffusion of electron-heavy particle collisions. Downstream, a strongly-magnetised region of near-isothermal expansion occurs. Finally, in the detached region, the polytropic index tends to that of a more adiabatic unmagnetised case. With an increasing magnetic nozzle field strength, an inferior limit is found to the average polytropic index of γe ∼ 1.16.

The fully-kinetic investigations on the ion acceleration mechanisms in an electron-driven magnetic nozzle

“…Rather, they both decrease until the edge of MN, and rise again to form a outside the plume edge. Note that this is not a artificial but a one also observed in experiments [31,33] and other numerical simulations [34,35]. According to our previous research [16] the study of Singh et [32], the ions are accelerated by the electric field generated near the of the MN, and overshoot the The electrons are restrained within the MDML, resulting in a accumulation of positive charges outside the edge of the nozzle, which leads to a high region, i.e.…”

“…This mechanism is called recombination detachment. However, in our simulation and many other full-PIC simulations of magnetic nozzles [15,32,35], the recombination collision is not considered. This may overestimate the deceleration effects of P mag,E×B .…”

Different fluid strategies for the simulation of a Helicon Plasma Thruster

“…Moreover, the implementation of the energy equations for the heavy species will be considered to accurately predict the neutral temperature and heat fluxes. Finally, a comparison against the results obtained with a PIC-MCC [10,11] model will be performed as means of verification of the codes implementation, and a comparison of the models will be made with respect to experimental data taken from literature for validation purposes.…”

“…Many numerical methods have been used in literature for modelling plasma production and acceleration. The most important approaches are fluid, [5,7] kinetic, [7] Particle-In-Cell with Monte-Carlo Collisions (PIC-MCC), [8][9][10][11] and hybrid. [9,12] In the fluid approach, the particle distribution function is assumed (usually Maxwellian) and the plasma is described in terms of continuity, momentum, and energy equations.…”

Magnetic Nozzle and RPA Simulations vs. Experiments for a Helicon Plasma Thruster Plume

“…Numerical models for the magnetized plasma plume expansion through a magnetic nozzle are of different types. A first approach is that of the kinetic approaches, which can be split into methods solving a simplified Boltzmann's equation for the ion and electron distribution functions in a low dimensional space (typically 1D, [18]), and full particle-incell (PIC) models [19,20], featuring particle ions/electrons, collisions through Montecarlo approaches [21], and generally limited to 2D to reduce the computational cost. An alternative approach, which is computationally cheaper, is that of hybrid codes, in which electrons are modeled as a fluid, while neutrals and ions are followed as macro-particles of a PIC sub-model featuring Montecarlo collisions.…”