Kinetic simulations of collision-less plasmas in open magnetic geometries ^*

Abstract

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (1) Scrape-Of-Layer (SOL) and divertor regions in toroidal confinement fusion devices , (2) linear divertor simulators, (3) plasma-based thrusters and (4) magnetic mirrors. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic Particle-In-Cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (1) the effect of non-uniform magnetic fields, (2) finite fully-absorbing boundaries for the particles and (3) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. Results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, inclusion of a Monte-Carlo based Fokker-Planck collision operator is discussed in the context of future work.

Parallel transport modeling of linear divertor simulators with fundamental ion cyclotron heating *

“…The term 'hybrid' in this paper refers to the process of describing ions kinetically while electrons as a fluid. More details of the hybrid approach can be found in [21,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”

“…These rules are chosen to simulate a variety of boundary conditions and volumetric particle sources. This is described in more detail in [21].…”

“…The two red lines at x = −2 m and at x = 8 m are the representative of the left and right boundaries respectively. Particles leaving these two boundaries are reinjected back to the source location centered around x = 0 m with a completely new identity via a set of rules as described in [21]. These reinjected particles are used as the fueling source with new computational weight and with a gaussian spread of 0.3 m in physical space (see the thick dashed curve at x = 0 in figure 6) and with random pitch angle in velocity space.…”

“…However, in the ICH region the distribution function is significantly anisotropic. The steady-state momentum transport equation along the magnetic flux [21] is given in equation (37). This expression includes the effect of magnetic compression arising due to a non-uniform magnetic field.…”

“…More specifically, we aim to explore the effect of RF heating on the shape of the ion distribution function at the target, kinetic effects on parallel transport and modification of the background helicon plasma. The transport problem is addressed by solving the Vlasov equation coupled to electromagnetic fields [6] using the so-called 'hybrid' particlein-cell (PIC) approach [20,21] and adapted to the present scenario (volumetric particle sources, non-uniform magnetic field, open magnetic field lines, RF heating, Coulomb collisions). The term 'hybrid', in this context, refers to the process of describing ions kinetically and electrons as a fluid.…”