Astrophysical Jets from accreting Black Holes

II.2 Diffusive shock acceleration
● it follows with
and hence with
● if a “softer” power law is incoming, a power law with slope a will
come out
r = U 1
U 2
r −1p ∂ f 2
∂p =3r f 1− f 2
a= 3r
r −1
f 2 =ap −a
p
∫ p '
0
a−1 f 1p ' dp'