Influência do campo magnético sobre uma partícula carregada no bilhar clássico

Abstract

The classic billiard consists of a particle confined in a region by fixed boundary( f(r,θ)= f0) in which the particle moves in a straight line at constant sp eed and collides elastically with the boundary. We will use this mo del to study the effects of a charged particle under the influence of a magnetic field in the billiard. This typ e of study is useful in plasma physics, whichit heavily studiesthe movement ofa particle underthe influence of magnetic fields. Whena particle entersin a region with a constant magnetic field, it starts to describ e orbiting movement, defined as Larmor orbit. Asso ciated with the charged particle orbits we havea magnetic dipole moment that comes to opp osite to the changes in the magnetic fieldflux in the orbits of the particle. We will show that the magnetic dip ole moment is anadiabatic invariantof the system and see how it behaves in a region with nonuniform magnetic field. Following the line of DynamicSystems, wewill study the phase space generated by the billiard and see how it behaves under changes of the magnetic field.