Theory of wakefields in a dielectric-filled cavity

Abstract

An analytical solution of a wakefield from a charge moving on the axis of a dielectric-filled cylindrical cavity is derived. A solution to the wakefield in a waveguide with only a boundary at the cavity entrance is already known. To take into account a boundary at the cavity exit, we introduce an imaginary antibeam, with opposite charge, which is created at the same time when the beam passes the exit boundary and continues to move along with the original beam at the same velocity. Although the beam has been annihilated in the net effect, the original beam and the antibeam produce their own wakefields, respectively, because they were created at different times. These superimposed fields are then mirror reflected as usual by the conducting exit boundary and the wakefield can be obtained by properly mirror reflecting them whenever it reaches a boundary. We find a resonance condition to enhance wakefields with multiple bunches of charges, and show that the acceleration gradient increases under that condition.