Abstract
A formal eigenmode method to solve for electromagnetic fields in a longitudinally translationally invariant multizone dielectric-lined waveguide is presented. The method is specialized to the development of wakefield theory for rectangular dielectric-lined structures which have an arbitrary number of dielectric layers. It is shown that the fields excited by a drive particle moving through the vacuum beam channel in such a structure can simultaneously include both propagating and decaying modes. The decaying modes characterize the short-range self-fields that move together with the particle, while the propagating modes characterize the long-range radiation fields or wakefields that carry energy away from the particle. It is also shown that the formal solution obtained in rectangular structures is applicable to all translationally invariant dielectric-lined waveguides, for example, cylindrical structures. Two important identities which the method relies upon are computationally confirmed for rectangular two-zone dielectric-lined structures. This theory may be employed for calculations of space charge effects, particularly for low or moderate-energy beams where self-field effects cannot be neglected.
Highlights
Recent interest has been directed towards wakefield accelerators [1,2,3,4,5,6,7,8,9,10,11], in which an electron bunch generates Cerenkov radiation in a dielectric-loaded waveguide (DLW)[12] and leaves the radiation behind the bunch, forming wakefields that can accelerate a closely following bunch
Acceleration structure has been proposed [10], where the arrangement of dielectric slabs is not symmetric. This necessitates development of wakefield theory for general rectangular DLW structures which have any number of dielectric layers
A formal eigenmode method in general translationally invariant DLW structures has been presented. This method has been employed to solve for fields excited by a moving charged particle in a rectangular DLW
Summary
Recent interest has been directed towards wakefield accelerators [1,2,3,4,5,6,7,8,9,10,11], in which an electron (drive) bunch generates Cerenkov radiation in a dielectric-loaded waveguide (DLW)[12] and leaves the radiation behind the bunch, forming wakefields that can accelerate a closely following (test) bunch. A rectangular two-beam DLW acceleration structure has been proposed [10], where the arrangement of dielectric slabs is not symmetric. This necessitates development of wakefield theory for general rectangular DLW structures which have any number of dielectric layers. The present work can be considered to be an extension of previous work [2,6] to include decaying modes, and to generalize to a translationally invariant waveguide having an arbitrary number of dielectric-lined layers—so long as eigenmodes of the waveguide structures are known. Ing space charge effects, for low or moderateenergy beams where self-field effects are not negligible
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