Title: Estimate of Joule Heating in a Flat Dechirper,
Abstract: We have performed Joule power loss calculations for a flat dechirper. We have
considered the configurations of the beam on-axis between the two plates---for
chirp control---and for the beam especially close to one plate---for use as a
fast kicker. Our calculations use a surface impedance approach, one that is
valid when corrugation parameters are small compared to aperture (the
perturbative parameter regime). In our model we ignore effects of field
reflections at the sides of the dechirper plates, and thus expect the results
to underestimate the Joule losses. The analytical results were also tested by
numerical, time-domain simulations. We find that most of the wake power lost by
the beam is radiated out to the sides of the plates. For the case of the beam
passing by a single plate, we derive an analytical expression for the
broad-band impedance, and---in Appendix B---numerically confirm recently
developed, analytical formulas for the short-range wakes. While our theory can
be applied to the LCLS-II dechirper with large gaps, for the nominal apertures
we are not in the perturbative regime and the reflection contribution to Joule
losses is not negligible. With input from computer simulations, we estimate the
Joule power loss (assuming bunch charge of 300 pC, repetition rate of 100 kHz)
is 21~W/m for the case of two plates, and 24 W/m for the case of a single
plate.