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SHARP: A Spatially Higher-order, Relativistic Particle-in-cell Code

Shalaby, Mohamad and Broderick, Avery E. and Chang, Philip and Pfrommer, Christoph and Lamberts, Astrid and Puchwein, Ewald (2017) SHARP: A Spatially Higher-order, Relativistic Particle-in-cell Code. Astrophysical Journal, 841 (1). Art. No. 52. ISSN 1538-4357.

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Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher-order accurate relativistic PIC algorithm in one spatial dimension, which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher-order interpolation functions to achieve a spatially higher-order accurate algorithm (up to the fifth order). We validate our algorithm against several test problems—thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutions of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second-order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., those that lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables us to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Shalaby, Mohamad0000-0001-9625-5929
Broderick, Avery E.0000-0002-3351-760X
Chang, Philip0000-0002-2137-2837
Pfrommer, Christoph0000-0002-7275-3998
Lamberts, Astrid0000-0001-8740-0127
Additional Information:© 2017 The American Astronomical Society. Received 2017 February 15; revised 2017 April 5; accepted 2017 April 10; published 2017 May 23. We would like to thank Anatoly Spitkovsky for providing access to TRISTAN-MP, substantial guidance in its use, and a number of constructive comments on the manuscript. M.S. and A.E.B. receive financial support from the Perimeter Institute for Theoretical Physics and the Natural Sciences and Engineering Research Council of Canada through a Discovery Grant. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. P.C. gratefully acknowledges support from the NASA ATP program through NASA grant NNX13AH43G, and the NSF through grant AST-1255469. C.P. gratefully acknowledges support by the European Research Council through ERC-CoG grant CRAGSMAN-646955 and by the Klaus Tschira Foundation. E.P. gratefully acknowledges support by the Kavli Foundation. Support for A.L. was provided by an Alfred P. Sloan Research Fellowship, NASA ATP Grant NNX14AH35G, and NSF Collaborative Research Grant #1411920 and CAREER grant #1455342.
Funding AgencyGrant Number
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
European Research Council (ERC)CRAGSMAN-646955
Klaus Tschira FoundationUNSPECIFIED
Kavli FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:instabilities; methods: numerical; plasmas; relativistic processes
Issue or Number:1
Record Number:CaltechAUTHORS:20170523-094819529
Persistent URL:
Official Citation:Mohamad Shalaby et al 2017 ApJ 841 52
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77652
Deposited By: Tony Diaz
Deposited On:23 May 2017 18:18
Last Modified:03 Oct 2019 18:00

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