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Register a new userAnalytical Formulas for Short Bunch Wakes in a Flat Dechirper
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We develop analytical models of the longitudinal and transverse wakes, on and off axis for realistic structures, and then compare them with numerical calculations, and generally find good agreement. These analytical first order formulas approximate the droop at the origin of the longitudinal wake and of the slope of the transverse wakes; they represent an improvement in accuracy over earlier, zeroth order formulas. In example calculations for the RadiaBeam/LCLS dechirper using typical parameters, we find a 16% droop in the energy chirp at the bunch tail compared to simpler calculations. With the beam moved to 200~$mu$m from one jaw in one dechiper section, one can achieve a 3~MV transverse kick differential over a 30~$mu$m length.
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In previous work [1] general expressions, valid for arbitrary bunch lengths, were derived for the wakefields of corrugated structures with flat geometry, such as is used in the RadiaBeam/LCLS dechirper. However, the bunch at the end of linac-based X-ray FELs--like the LCLS--is extremely short, and for short bunches the wakes can be considerably simplified. In this work, we first derive analytical approximations to the short-range wakes. These are generalized wakes, in the sense that their validity is not limited to a small neighborhood of the symmetry axis, but rather extends to arbitrary transverse offsets of driving and test particles. The validity of these short-bunch wakes holds not only for the corrugated structure, but rather for any flat structure whose beam-cavity interaction can be described by a surface impedance. We use these wakes to obtain, for a short bunch passing through a dechirper: estimates of the energy loss as function of gap, the transverse kick as function of beam offset, the slice energy spread increase, and the emittance growth. In the Appendix, a more accurate derivation--than is found in [1]--of the arbitrary bunch length wakes is performed; we find full agreement with the earlier results, provided the bunches are short compared to the dechirper gap, which is normally the regime of interest. [1] K. Bane and G. Stupakov, Phys. Rev. ST Accel. Beams 18, 034401(2015).
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.
We give formulas for the longitudinal, transverse, and quad point charge wakes for a short bunch of electrons passing by one plate of a flat dechirper.
We briefly compare in numerical simulations the relativistic ionization front and electron bunch seeding of the self-modulation of a relativistic proton bunch in plasma. When parameters are such that initial wakefields are equal with the two seeding methods, the evolution of the maximum longitudinal wakefields along the plasma are similar. We also propose a possible seeding/injection scheme using a single plasma that we will study in upcoming simulations works.
We discuss several analytical models for impedances of very short bunches. The approximate analytical models are compared with direct solution of Maxwells equations.
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