Physics of relativistic collisionless shocks: The scattering center frame. (arXiv:1907.07750v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Pelletier_G/0/1/0/all/0/1">G. Pelletier</a> (IPAG), <a href="http://arxiv.org/find/astro-ph/1/au:+Gremillet_L/0/1/0/all/0/1">L. Gremillet</a> (CEA), <a href="http://arxiv.org/find/astro-ph/1/au:+Vanthieghem_A/0/1/0/all/0/1">A. Vanthieghem</a> (IAP), <a href="http://arxiv.org/find/astro-ph/1/au:+Lemoine_M/0/1/0/all/0/1">M. Lemoine</a> (IAP)
In this first paper of a series dedicated to the microphysics of
unmagnetized, relativistic collisionless pair shocks, we discuss the physics of
the Weibel-type transverse current filamentation instability (CFI) that
develops in the shock precursor, through the interaction of an
ultrarelativistic suprathermal particle beam with the background plasma. We
introduce in particular the notion of “Weibel frame”, or scattering center
frame, in which the microturbulence is of mostly magnetic nature. We calculate
the properties of this frame, using first a kinetic formulation of the linear
phase of the instability, relying on Maxwell-J”uttner distribution functions,
then using a quasistatic model of the nonlinear stage of the instability. Both
methods show that: (i) the Weibel frame moves at subrelativistic velocities
relative to the background plasma, therefore at relativistic velocities
relative to the shock front; (ii) the velocity of the Weibel frame relative to
the background plasma scales with $xi_{rm b}$, i.e., the pressure of the
suprathermal particle beam in units of the momentum flux density incoming into
the shock; and (iii), the Weibel frame moves slightly less fast than the
background plasma relative to the shock front. Our theoretical results are
found to be in satisfactory agreement with the measurements carried out in
dedicated large-scale 2D3V PIC simulations.
In this first paper of a series dedicated to the microphysics of
unmagnetized, relativistic collisionless pair shocks, we discuss the physics of
the Weibel-type transverse current filamentation instability (CFI) that
develops in the shock precursor, through the interaction of an
ultrarelativistic suprathermal particle beam with the background plasma. We
introduce in particular the notion of “Weibel frame”, or scattering center
frame, in which the microturbulence is of mostly magnetic nature. We calculate
the properties of this frame, using first a kinetic formulation of the linear
phase of the instability, relying on Maxwell-J”uttner distribution functions,
then using a quasistatic model of the nonlinear stage of the instability. Both
methods show that: (i) the Weibel frame moves at subrelativistic velocities
relative to the background plasma, therefore at relativistic velocities
relative to the shock front; (ii) the velocity of the Weibel frame relative to
the background plasma scales with $xi_{rm b}$, i.e., the pressure of the
suprathermal particle beam in units of the momentum flux density incoming into
the shock; and (iii), the Weibel frame moves slightly less fast than the
background plasma relative to the shock front. Our theoretical results are
found to be in satisfactory agreement with the measurements carried out in
dedicated large-scale 2D3V PIC simulations.
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