Solenoidal Optics

Preliminary studies on neutrino factories se solenoids at di .erent stages. Often quoted is the adiabatic device,a long solenoid with a slowly decreas- ing .eld sed to capture pions behind the target.In cooling sections as well, design reports show lattices using solenoids with alternating .eld to contain the beam.This note describes the transverse behaviour of charged parti- cles in a solenoidal .eld.First,a general description of the magnetic .eld is reviewed with emphasis on particular features,s ch as the canonical momen- tum formalism.Then,a complete study of the adiabatic device is presented, along with tracking simulations based on hamiltonian mechanics.Eventu- ally,the case of solenoidal focusing within the short lens approximation is discussed following either the paraxial ray equation approach or the matrix formalism.