Cosmic rays accelerated by a shock form a streaming distribution of outgoing particles in the foreshock region .
If the ambient fields are negligible compared to the shock and cosmic ray energetics , a stronger magnetic field can be generated in the shock upstream via the streaming ( Weibel-type ) instability .
Here we develop a self-similar model of the foreshock region and calculate its structure , e.g. , the magnetic field strength , its coherence scale , etc. , as a function of the distance from the shock .
Our model indicates that the entire foreshock region of thickness \sim R / ( 2 \Gamma _ { sh } ^ { 2 } ) , being comparable to the shock radius in the late afterglow phase when \Gamma _ { sh } \sim 1 , can be populated with large-scale and rather strong magnetic fields ( of sub-gauss strengths with the coherence length of order 10 ^ { 17 } { cm } ) compared to the typical interstellar medium magnetic fields .
The presence of such fields in the foreshock region is important for high efficiency of Fermi acceleration at the shock .
Radiation from accelerated electrons in the foreshock fields can constitute a separate emission region radiating in the UV/optical through radio band , depending on time and shock parameters .
We also speculate that these fields being eventually transported into the shock downstream can greatly increase radiative efficiency of a gamma-ray burst afterglow shock .