Scattering in a magnetic field

A scheme of ionization cooling proposed at Fermilab involves energy loss by passing a muon beam through liquid hydrogen. Focussing is done by solenoids. A particle travelling in a straight line, will, after being scattered, follow a helical trajectory. After a full circle is made, the trajectory will be downstream at a point where some of the previously unscattered particles will now scatter. The portions of phase space occupied in the two scatterings now overlap and will occupy less space than if there were no overlap. Results of detailed calculations and approximations made will be discussed.