Constraining the Magnetic Field in Gamma Ray Burst Blast Waves
  We point out that the already existing literature on relativistic collisionless MHD shocks show that the parameter sigma= upstream proper magnetic energy density/upstream rest mass energy density, plays an important role in determining the structure and accelerating properties of such shocks. By adopting a value of sigma= 0.002 which corresponds to the relativistic shock associated with the Crab nebula, and by using appropriate relativistic shock jump conditions, we obtain here a generous upper-limit on the value of (proper) the magnetic field, B ~ 1.5 10^{-3} eta n^{1/2} G, for gamma ray burst (GRB) blast wave. Here, eta= E/Mc^2, where E is the energy and M is the mass of the baryons entrained in the original fireball (FB), and n is the proper number density of the ambient medium. Further, we point out that, in realistic cases, the actual value B could be as low as 5 10^{-6} eta n^{1/2} G. for realistic cases. 
Abhas Mitra