Strong Relativistic Collisionless Shock

A direct numerical simulation of a strong relativistic collisionless shock propagating into an unmagnetized medium has been performed in two spatial dimensions. It is found that: (i) collisionless shock exists, (ii) particle acceleration is insignificant, (iii) the shock does not generate “quasi-static” magnetic fields, contrary to recent claims by other authors. All our results agree with a simple plasma-physical model of collisionless shocks. On the other hand, astrophysical evidence indicates that shocks do accelerate charged particles, and GRB phenomenology indicates that shocks do generate strong magnetic fields. The conflict between the simplest plasma-physical model and astronomical observations of collisionless shocks is discussed. Subject headings: magnetic fields – shock waves – acceleration of particles 1. Strong relativistic shocks We will discuss strong relativistic shock waves. These shocks should generate magnetic fields and accelerate charged particles in radio supernovas (Chevalier 1982, Fransson & Bjornsson 1998) and gamma-ray bursts (Sari, Piran, Narayan 1997, Gruzinov & Waxman 1998, Gruzinov 2001). The magnetic field of the unshocked plasma is probably insignificant in radio supernovas, and is certainly negligible in GRB afterglows. For GRB afterglows, for example, magnetic energy in the shocked plasma is of order GeV per particle. Magnetic energy must be less than T per particle in the unshocked plasma, where T is the temperature of the unshocked plasma. Therefore simple shock compression of the pre-existing field is irrelevant, the magnetic field should be generated by the shock (see Gruzinov 2001 for a detailed discussion). For all practical purposes, the unshocked plasma is cold and unmagnetized. The shocks are collisionless (Sagdeev 1966 gives a good introduction), meaning that the shock transition is accomplished by electromagnetic fields, rather than particle collisions. These shocks are turbulent, involving fluctuating electromagnetic fields and particle distribution functions. There are only two reliable tools for studying such shocks: numerical simulations and common sense. A direct numerical simulation in two spatial dimensions (Kazimura et al 1998) has apparently demonstrated: “generation of a small-scale quasi-static magnetic field”. And also that “particles