RF Cavities Loaded with Dielectric for Muon Facilities

This report discusses RF cavities loaded with dielectric that could be used in various ways for muon facilities. The examples given are for 400 and 800 MHz cavities. Our initial motivation was to use dielectric to reduce the radial size of gas-filled cavities in helical cooling channels, but dielectric might also be useful in vacuum cavities for suppression of dark current emission. We also studied cavities that can be used for the phase rotation channel in the front end of a muon collider or neutrino factory. INTRODUCTION For construction of compact and hence efficient helical cooling channels (HCC), the space available for RF cavities is limited. Based on his simulations, Balbekov [1] has suggested a relationship between the radial size of the coils in a HCC and the maximum RF frequency that can be used to contain the beam longitudinally. For a channel that uses 400MHz, the largest gas-filled cavity that will fit inside a coil has a radius of 16 cm, and the beam radius is 6 cm [2]. The required electric gradient is 16 MV/m. The channel would benefit from near-continuous acceleration. The conventional way of making the cavity radius smaller is to make the cavity re-entrant, but in that case there is a large drift space without accelerating field, reducing the average accelerating gradient. Here we take a different approach. The standard formula for the resonant frequency of a pill box cavity filled with dielectric of relative permittivity er and relative permeability μr is given by r r R c μ e ω 405 . 2 = This suggests that the cavity radius can be made smaller for a given resonant frequency if part of the cavity volume is filled with dielectric or magnetic material. For the HCC, magnetic material is not an option: the strong magnetic fields will be distorted, and most of the magnetic material would be brought into saturation and lose its desired magnetic property. Also, magnetic materials are lossy at RF frequencies. So the only viable option is dielectric material. Once the cavity is loaded with dielectric, the quality factor Q and RF power loss in the cavity will be changed. The Q for a cavity loaded with dielectric is given by diel wall Q Q Q 1 1 1 + = , where δ e e tan 1 = ′ ′ ′ = diel Q These relations are derived below: The quality factor Q is defined as the energy stored W divided by the power loss per cycle Ploss /ω