Time-Step Considerations in Particle Simulation Algorithms for Coulomb Collisions in Plasmas

Abstract

Abstract-The accuracy of first-order Euler and higher-order time-integration algorithms for grid-based Langevin equations collision models in a specific relaxation test problem is assessed. We show that statistical noise errors can overshadow time-step errors and argue that statistical noise errors can be conflated with time-step effects. Using a higher-order integration scheme may not achieve any benefit in accuracy for examples of practical interest. We also investigate the collisional relaxation of an initial electron-ion relative drift and the collisional relaxation to a resistive steady-state in which a quasi-steady current is driven by a constant applied electric field, as functions of the time step used to resolve the collision processes using binary and grid-based, testparticle Langevin equations models. We compare results from two grid-based Langevin equations collision algorithms to results from a binary collision algorithm for modeling electron-ion collisions. Some guidance is provided on how large a time step can be used compared to the inverse of the characteristic collision frequency for specific relaxation processes.

On the Variation of Solar Flare Coronal X-Ray Source Sizes With Energy

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A grid-based binary model for coulomb collisions in plasmas

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“…When this clamp is not present, occasionally unphysically large jumps in the energy moments of the particle distribution occur. Both TA and Lemons algorithms were implemented in a particle code [11,21] where special relativity was included in the kinematics. In consequence, the procedure for imposing ad hoc energy-momentum conservation uses Eq.…”