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.
Highlights
The problem of calculating wakefields in a waveguide loaded with dielectric layers has been solved for the case of an infinitely long waveguide and the possibility to apply it for a high gradient accelerator was discussed by several authors [1,2,3,4,5]
Consider a cylindrical cavity bounded by conducting planes at z 1⁄4 0 and z 1⁄4 d, and assume that the cavity is filled with a dielectric
The cavity wakefield can be obtained by properly mirror reflecting the superimposed wakefield from the original beam created at the entrance time and the antibeam created at the exit time
Summary
The problem of calculating wakefields in a waveguide loaded with dielectric layers has been solved for the case of an infinitely long waveguide and the possibility to apply it for a high gradient accelerator was discussed by several authors [1,2,3,4,5]. In order to solve this cavity wakefield problem, one must consider properly the exit boundary conditions in addition to the entrance boundary conditions We accomplished this task by generalizing the image charge method. One succeeded in obtaining nontrivial wakefield solutions that satisfy all the boundary conditions with no source associated inside the cavity If this left propagating wakefield reaches the entrance boundary, one can obtain the reflected wakefield just by performing a simple mirror reflection by the conducting entrance boundary, since no charge is associated with this field. The cavity wakefield can be obtained by properly mirror reflecting the superimposed wakefield from the original beam created at the entrance time and the antibeam created at the exit time. The cavity problem is solved by applying the output boundary condition to the field solution of a semi-infinite waveguide.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
