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Register a new userImplementation of higher-order velocity mapping between marker particles and grid in the particle-in-cell code XGC
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The global total-$f$ gyrokinetic particle-in-cell code XGC, used to study transport in magnetic fusion plasmas, implements a continuum grid to perform the dissipative operations, such as plasma collisions. To transfer the distribution function between marker particles and a rectangular velocity-space grid, XGC employs a bilinear mapping. The conservation of particle density and momentum is accurate enough in this bilinear operation, but the error in the particle energy conservation can become undesirably large in special conditions. In the present work we update XGC to use a novel mapping technique, based on the calculation of a pseudo-inverse, to exactly preserve moments up to the order of the discretization space. We describe the details of the implementation and we demonstrate the reduced interpolation error for a neoclassical tokamak test case by using $1^{mathrm{st}}$- and $2^{mathrm{nd}}$-order elements with the pseudo-inverse method and comparing to the bilinear mapping.
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A fully implicit particle-in-cell method for handling the $v_parallel$-formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the $v_parallel$-formalism, we avoid introducing the non-physical skin terms in Amp`{e}res law, which are responsible for the well-known ``cancellation problem in the $p_parallel$-formalism. The $v_parallel$-formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional $delta f$ scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfv{e}n wave propagation in addition to a case demonstrating the ITG-KBM transition. The ITG-KBM transition case is compared to results obtained from other $delta f$ gyrokinetic codes/schemes, whose verification has already been archived in the literature.
We construct a particle integrator for nonrelativistic particles by means of the splitting method based on the exact flow of the equation of motion of particles in the presence of constant electric and magnetic field. This integrator is volume-preserving similar to the standard Boris integrator and is suitable for long-term integrations in particle-in-cell simulations. Numerical tests reveal that it is significantly more accurate than previous volume-preserving integrators with second-order accuracy. For example, in the $E times B$ drift test, this integrator is more accurate than the Boris integrator and the integrator based on the exact solution of gyro motion by three and two orders of magnitude, respectively. In addition, we derive approximate integrators that incur low computational cost and high-precision integrators displaying fourth- to tenth-order accuracy with the aid of the composition method. These integrators are also volume-preserving. It is also demonstrated that the Boris integrator is equivalent to the simplest case of the approximate integrators derived in this study.
We present the Photon-Plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation scheme for particle-to-cell interpolation and charge deposition. It includes powerful diagnostics tools with on-the-fly particle tracking, synthetic spectra integration, 2D volume slicing, and a new method to correctly account for radiative cooling in the simulations. A robust technique for imposing (time-dependent) particle and field fluxes on the boundaries is also presented. Using a hybrid OpenMP and MPI approach the code scales efficiently from 8 to more than 250.000 cores with almost linear weak scaling on a range of architectures. The code is tested with the classical benchmarks particle heating, cold beam instability, and two-stream instability. We also present particle-in-cell simulations of the Kelvin-Helmholtz instability, and new results on radiative collisionless shocks.
As an alternative option to kinetic electrons, the gyrokinetic total-f particle-in-cell (PIC) code XGC1 has been extended to the MHD/fluid type electromagnetic regime by combining gyrokinetic PIC ions with massless drift-fluid electrons analogous to Chen and Parker, Physics of Plasmas 8, 441 (2001). Two representative long wavelength modes, shear Alfven waves and resistive tearing modes, are verified in cylindrical and toroidal magnetic field geometries.
We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we calculate kinetic entropy in two forms -- the ``combinatorial form related to the logarithm of the number of microstates per macrostate and the ``continuous form related to $f ln f$, where $f$ is the particle distribution function. We discuss the advantages and disadvantages of each and discuss subtleties about implementing them in PIC codes. Using collisionless PIC simulations that are two-dimensional in position space and three-dimensional in velocity space, we verify the implementation of the kinetic entropy diagnostics and discuss how to optimize numerical parameters to ensure accurate results. We show the total kinetic entropy is conserved to three percent in an optimized simulation of anti-parallel magnetic reconnection. Kinetic entropy can be decomposed into a sum of a position space entropy and a velocity space entropy, and we use this to investigate the nature of kinetic entropy transport during collisionless reconnection. We find the velocity space entropy of both electrons and ions increases in time due to plasma heating during magnetic reconnection, while the position space entropy decreases due to plasma compression. This project uses collisionless simulations, so it cannot address physical dissipation mechanisms; nonetheless, the infrastructure developed here should be useful for studies of collisional or weakly collisional heliospheric, planetary, and astrophysical systems. Beyond reconnection, the diagnostic is expected to be applicable to plasma turbulence and collisionless shocks.
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