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Theory of the formation of a collisionless Weibel shock: pair vs. electron/proton plasmas

Published online by Cambridge University Press:  25 April 2016

A. Bret ,
A. Stockem Novo ,
R. Narayan ,
C. Ruyer ,
M. E. Dieckmann  and
L. O. Silva
A. Bret*
Affiliation:
ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071 Ciudad Real, Spain
A. Stockem Novo
Affiliation:
Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- and Astrophysik, Ruhr-Universität, 44801 Bochum, Germany
R. Narayan
Affiliation:
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS-51 Cambridge, MA 02138, USA
C. Ruyer
Affiliation:
High Energy Density Science Division, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
M. E. Dieckmann
Affiliation:
Department of Science and Technology, Linköping University, SE-60174 Norrköping, Sweden
L. O. Silva
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear – Laboratório Associado, Instituto Superior Técnico, Lisboa, Portugal
*
Address correspondence and reprint requests to: A. Bret, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain. E-mail: antoineclaude.bret@uclm.es
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Abstract

Collisionless shocks are shocks in which the mean-free path is much larger than the shock front. They are ubiquitous in astrophysics and the object of much current attention as they are known to be excellent particle accelerators that could be the key to the cosmic rays enigma. While the scenario leading to the formation of a fluid shock is well known, less is known about the formation of a collisionless shock. We present theoretical and numerical results on the formation of such shocks when two relativistic and symmetric plasma shells (pair or electron/proton) collide. As the two shells start to interpenetrate, the overlapping region turns Weibel unstable. A key concept is the one of trapping time τp, which is the time when the turbulence in the central region has grown enough to trap the incoming flow. For the pair case, this time is simply the saturation time of the Weibel instability. For the electron/proton case, the filaments resulting from the growth of the electronic and protonic Weibel instabilities, need to grow further for the trapping time to be reached. In either case, the shock formation time is 2τp in two-dimensional (2D), and 3τp in 3D. Our results are successfully checked by particle-in-cell simulations and may help designing experiments aiming at producing such shocks in the laboratory.

Keywords

Collisionless shocksWeibel instability
Type
Research Article
Information
Laser and Particle Beams , Volume 34 , Issue 2 , June 2016 , pp. 362 - 367
Copyright
Copyright © Cambridge University Press 2016 

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