Magnetic mirrors / Fermi acceleration

(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).

A cosmic ray proton is trapped between two moving magnetic mirrors with mirror ratio \(R_m=5\). Initially its energy is $W=1$ keV and $v_\perp = v_\parallel$ at the midplane. Each mirror moves toward the midplane with a velocity $v_m=10$ km/s and the initial distance between the mirrors is $L=10^{10}$ km.