Adiabatic expansion of electron beam

The temperature of electron beam is an important parameter in electron cool ing device. Transverse temperature will be reduced when an electron beam pa sses through a negative gradient magnetic field. Same theoretical approache s on adiabatic expansion are presented here. Adiabatic expansion of the ele ctron beam moving in different magnetic fields with different energy and cu rrent was investigated by computer simulation. The results show that the tr ansverse temperature of the electron beam is reduced by a factor equal to t he ratio between the initial and final magnetic field strengths,provided th at the field change is adiabatic with respect to the cyclotron motion of th e electrons.