Modal analysis of the energy loss for an accelerated electron beam passing through a laser-driven RF gun

The energy loss for an accelerated electron beam passing through a laser-driven RF gun has been studied. An analytical formula of the energy loss has been obtained using the time-dependent resonant modes of a cylindrical pill-box cavity. As an approximation, this formalism assumes a rigid beam pulse so the change of pulse shape dealing with space-charge force and wake field force is ignored.