 Diffusive shock acceleration

ID: diffusive-shock-acceleration

Diffusive shock acceleration repeatedly returns particles to a shock wave by scattering them in the upstream and downstream plasma. For fluid speeds

u_{1} > u_{2}

, particle speed

v ≫ u_{1}

r = u_{1} / u_{2}

, the cycle gain is

⟨ Δ p ⟩ / p = 4 (u_{1} - u_{2}) / (3 v)

and the cycle escape probability is

4 u_{2} / v

. Their ratio gives

f (p) \propto p^{- 3 r / (r - 1)}

r = 4

this is

p^{- 4}

, corresponding to

d N / d E \propto E^{- 2}

in the ultrarelativistic regime.

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