Benjamin Sturdevant

Low frequency fully kinetic simulation of the toroidal ion temperature gradient instability

A fully kinetic ion model is useful for the verification of gyrokinetic turbulence simulations in certain regimes, where the gyrokinetic model may break down due to the lack of small ordering parameters. However, for a fully kinetic model to be of value, it must first be able to accurately simulate low frequency drift-type instabilities typically well within the domain of gyrokinetics. Here, a fully kinetic ion model is formulated with weak gradient drive terms and applied to the toroidal ion-temperature-gradient (ITG) instability for the first time. Implementation in toroidal geometry is discussed, where orthogonal coordinates are used for particle dynamics, but field-line-following coordinates are used for the field equation allowing for high resolution of the field-aligned mode structure. Variational methods are formulated for integrating the equation of motion allowing for accuracy at a modest time-step size. Linear results are reported for both the slab and toroidal ITG instabilities. Good agreement ...

An implicit δf particle-in-cell method with sub-cycling and orbit averaging for Lorentz ions

A second order implicit ?f Lorentz ion hybrid model with sub-cycling and orbit averaging has been developed to study low-frequency, quasi-neutral plasmas. Models using the full Lorentz force equations of motion for ions may be useful for verifying gyrokinetic ion simulation models in applications where higher order terms may be important. In the presence of a strong external magnetic field, previous Lorentz ion models are limited to simulating very short time scales due to the small time step required for resolving the ion gyromotion. Here, we use a simplified model for ion Landau damped ion acoustic waves in a uniform magnetic field as a test bed for developing efficient time stepping methods to be used with the Lorentz ion hybrid model. A detailed linear analysis of the model is derived to validate simulations and to examine the significance of ion Bernstein waves in the Lorentz ion model. Linear analysis of a gyrokinetic ion model is also performed, and excellent agreement with the dispersion results from the Lorentz ion model is demonstrated for the ion acoustic wave. The sub-cycling/orbit averaging algorithm is shown to produce accurate finite-Larmor-radius effects using large macro-time steps sizes, and numerical damping of high frequency fluctuations can be achieved by formulating the field model in terms of the perturbed flux density. Furthermore, a CPU-GPU implementation of the sub-cycling/orbit averaging is presented and is shown to achieve a significant speedup over an equivalent serial code.

Finite time step and spatial grid effects in δf simulation of warm plasmas

This paper introduces a technique for analyzing time integration methods used with the particle weight equations in ?f method particle-in-cell (PIC) schemes. The analysis applies to the simulation of warm, uniform, periodic or infinite plasmas in the linear regime and considers the collective behavior similar to the analysis performed by Langdon for full-f PIC schemes 1,2. We perform both a time integration analysis and spatial grid analysis for a kinetic ion, adiabatic electron model of ion acoustic waves. An implicit time integration scheme is studied in detail for ?f simulations using our weight equation analysis and for full-f simulations using the method of Langdon. It is found that the ?f method exhibits a CFL-like stability condition for low temperature ions, which is independent of the parameter characterizing the implicitness of the scheme. The accuracy of the real frequency and damping rate due to the discrete time and spatial schemes is also derived using a perturbative method. The theoretical analysis of numerical error presented here may be useful for the verification of simulations and for providing intuition for the design of new implicit time integration schemes for the ?f method, as well as understanding differences between ?f and full-f approaches to plasma simulation.

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.