No abstract

Neutral particles in the plasma edge of fusion devices based on magnetic confinement are described by a transient kinetic equation incorporating ionization, recombination, and charge-exchange collisions. In charge-exchange dominated regimes, the neutral particle velocity distribution approaches the drifting Maxwellian defined by the mean velocity and temperature of the plasma. This enables model order reduction from the kinetic equation to approximate fluid models. We derive transient fluid models consistent with the kinetic equation by exploring a splitting based approach. We split the kinetic equation in sources and sinks on the one hand, and transport combined with charge-exchange on the other hand. Combining transport with charge-exchange collisions allows for deriving Hilbert expansion based fluid models. The retrieved fluid models depend on the assumed importance (scaling) of the different terms in the split equation describing transport and charge-exchange. We explore two scalings: the hydrodynamic scaling and the diffusive scaling. The diffusive scaling fluid model closely resembles phenomenological fluid models for describing neutral particles in the plasma edge that have been derived in the past. Therefore, the Hilbert expansion based fluid models can serve as a theoretical basis for such phenomenological fluid models and elucidate some of their properties. The performance of the fluid models with respect to a discrete velocity model and a Monte Carlo reference solver is assessed in numerical experiments. The code used to perform the numerical experiments is openly available.

One of the key aspects when simulating the plasma edge is the treatment of the neutral particles. Neutral particles can be described by a kinetic equation, which is difficult to solve due to the high dimensionality of the phase space and the high collisionality between the neutral particles and the plasma background, especially in the (partially) detached regimes anticipated for future reactors. We consider a recently proposed hybrid fluid‐kinetic method that is based on a micro–macro decomposition of the kinetic equation and mitigates the problems related to both the high dimensionality and the high collisionality. However, this method is prone to cancellation errors due to the introduction of particles with both positive and negative weights. In each iteration of the method, the particles undergo a weight projection step, which we identify as the main source of cancellation errors. We use techniques from numerical linear algebra for solving ill‐conditioned linear systems to improve the numerical stability of the weight projection step and reduce the cancellation errors. The reduction of cancellation errors allows for further speedup in the hybrid fluid‐kinetic method.

Recently, asymptotic‐preserving Monte Carlo simulation methods have been developed to simulate the Boltzmann‐BGK equation with advective–diffusive limiting behaviour over a broad range of regimes. These simulation methods hybridize a particle tracing Monte Carlo scheme for the kinetic equation and a random walk (RW) Monte Carlo simulation for the advection–diffusion limit, combining the precision of the former with the efficiency of the latter. In the RW part of the simulation, details of the travelled path are absent. This complicates the extraction of integral quantities of interest such as mass, momentum, and energy sources. Here, we present a new estimation strategy that couples the RW parts of the particle trajectories with a deterministic simulation of the corresponding fluid model. The contributions of the RW parts to quantities of interest are then computed from a single time step of this fluid model in a post‐processing step. We illustrate this new estimation strategy for a fusion‐relevant test‐case and focus on the bias and variance present when using this estimator.