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|Title:||Numerical instability due to relativistic plasma drift in EM-PIC simulations|
Martins, S. F.
Tsung, F. S.
Decyk, V. K.
Fonseca, R. A.
Silva, L. O.
Mori, W. B.
|Keywords:||Particle in cell|
Relativistic plasma drift
Numerical dispersion relation
Numerical Cherenkov radiation
|Abstract:||The numerical instability observed in electromagnetic particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity, and find an instability attributed to the intersection between beam resonances and the electromagnetic modes in the drifting plasma. The intersection can occur in the fundamental Brillouin zones when EM waves with phase velocities less than the speed of light exist, and from aliasing beam resonances and aliasing EM modes. The unstable modes are neither purely transverse nor longitudinal. The characteristic patterns of the instability in Fourier space for various simulation setups and Maxwell equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns, we derive an asymptotic expression for the instability growth rate. The asymptotic expression greatly speeds up the calculation of the instability growth rate and makes the parameter scans for minimal growth rate feasible even for full three dimensions. The results are compared against simulation results, and good agreements are found. These results can be used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a low pass filter with a cutoff value of vertical bar(k) over right arrow vertical bar essentially eliminates the instability while not modifying modes of physical interest. The use of a spectral solver also provides minimal errors to electromagnetic modes in the lowest Brillouin zones.|
|Description:||WOS:000324664100017 (Nº de Acesso Web of Science)|
|Publisher version:||The definitive version is available at: http://dx.doi.org/10.1016/j.cpc.2013.07.003|
|Appears in Collections:||CTI-RI - Artigos em revistas científicas internacionais com arbitragem científica|
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|publisher_version_Computer Physics Communications 2013 Xu.pdf||1.9 MB||Adobe PDF||View/Open Request a copy|
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