Analysis of the Force Exerted on an Accelerated Beam of Electrons by Its Own Wakefield in the Laser-Driven Rf-gun

Analytical expressions for the wakefield force acting on an electrons beam, in the RF-photoinjector, during the beam extraction from the cathode, are derived. These expressions are obtained by taking space charge effects and beam motion into account. The former is described in terms of the field's components due to Lienard-Wiechert potential and the method of images, close to the cathode surface. The beam motion is emphasized circumstantiating the fast transition, owing to quick acceleration by the high gradient RF-accelerating field, from thermal velocity, near the immediate vicinity of the cathode, to a non-relativistic velocity at the end of the photoemission. Numerical investigation of the beam wakefield force elicited two significant effects on the beam: the first one, attributable to the longitudinal component of the force, influences the trailing electrons in the beam and changes the energy of the individual electrons, depending on their position. The second one, attributable to the transverse component of the force, deflects the beam trajectory. After all, the electrons within the beam feel, over the beam length, an average deflecting force that is proportional to the radial displacement.