# 17th Advanced Accelerator Concepts Workshop

31 July 2016 to 5 August 2016
Gaylord Hotel and Conference Center
US/Eastern timezone

## Controlling the Numerical Cerenkov Instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

1 Aug 2016, 15:50
20m
Chesapeake L (Gaylord Conference Center)

### Chesapeake L

#### Gaylord Conference Center

Oral Working Group 2

### Speaker

Mr. Fei Li (Tsinghua University)

### Abstract

We present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma relativistically drifts on the simulation grid. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along the plasma drifting direction using a local FFT based current correction scheme.

### Summary

We control the EM dispersion curve in the direction of the plasma drift ($\hat{1}$-direction) of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along $\hat{1}$-direction. We show that this eliminates the main NCI modes with moderate |k|, while keeps additional main NCI modes well outside the range of physical interest with higher |k|. It is found that a high-order FDTD solver has similar NCI properties to that of a fully spectral solver or a hybrid Yee-FFT solver. By reducing the time step, the fastest growing $(\mu,\nu_1)=(0,\pm1)$ NCI modes and $(\mu,\nu_1)=(0,0)$ NCI modes can reside very close to the edge of the fundamental Brillouin zone. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone.

The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along $\hat{1}$-direction which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss' Law is satisfied.

We have shown how the customized solver, together with its NCI elimination scheme, can systematically eliminate the NCI in a single drifting plasma. We have also shown how this scheme can be applied to relativistic shock simulation, with excellent NCI elimination achieved without sacrificing the parallel scalability of an FDTD EM-PIC code for problems with disproportionate number of cells in one direction. We have also shown the usefulness of the proposed high-order solver combined with local FFTs by conducting full 3D LWFA simulations in a Lorentz boosted frame.

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### Primary author

Mr. Fei Li (Tsinghua University)

### Co-authors

Adam Tableman (University of California, Los Angeles) Dr. Asher Davidson (UCLA) Dr. Fiuza Frederico (SLAC National Accelerator Laboratory) Dr. Frank Tsung (University of California, Los Angeles) Dr. Peicheng Yu (University of California, Los Angeles) Prof. Ricardo Fonseca (ISCTE - Instituto Universitário de Lisboa) Thamine Dalichaouch (UCLA Physics) Dr. Viktor Decyk (University of California, Los Angeles) Prof. Warren Mori (University of California, Los Angeles) Prof. Wei Lu (Tsinghua) Dr. Weiming An (University of California Los Angeles) Dr. Xinlu Xu (University of California, Los Angeles)

### Presentation Materials

 Slides
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