Wake and Impedance

A systematic exposition of the basic concepts of wakes and impedances is given for relativistic beams in accelerators.Comment: Lecture presented at JAS'2000 Accelerator School On Frontiers Of Accelerator Technology: High Quality Beams, St. Petersburg - Moscow, Russia, 1-7 July 200

Wake excited in plasma by an ultrarelativistic pointlike bunch

We study propagation of a relativistic electron bunch through a cold plasma assuming that the transverse and longitudinal dimensions of the bunch are much smaller than the plasma collisionless skin depth. Treating the bunch as a point charge and assuming that its charge is small, we derive a simplified system of equations for the plasma electrons and show that, through a simple rescaling of variables, the bunch charge can be eliminated from the equations. The equations demonstrate an ion cavity formed behind the driver. They are solved numerically and the scaling of the cavity parameters with the driver charge is obtained. A numerical solution for the case of a positively charged driver is also found.Department of Energy DE-AC03-76SF00515U.S. Department of Energy DEFG02-04ER54742 DE-SC0007889 DE-SC0010622Air Force Office of Scientific Research (AFOSR) FA9550-14-1-0045Physic

Shielding and synchrotron radiation in toroidal waveguide

We develop a new approach to the calculation of the synchrotron radiation in a toroidal vacuum chamber. Using a small parameter ɛ = √ a/R, wherea is the characteristic size of the cross section of the toroid and R is the bending radius, we simplify Maxwell’s equations assuming that the characteristic frequency of the modes ω ∼ c/aɛ, and neglecte terms of higher order in ɛ. For a rectangular cross section of the waveguide, we find an analytical solution of the equations and analyze their asymptotics at very high frequency. We then obtain an equation which gives radiation into each synchronous mode. We demonstrate the flexibility of the new method by calculating the frequencies and the loss factors for the lowest modes in a square and round waveguides. For short bunches of high-energy electrons or positrons, typical for modern accelerators and photon sources, one of the important elements of the beam dynamics is the effect of coherent synchrotron radiation (CSR) of the beam [1]. In vacuum, if the reduced wavelength of the radiation exceeds the bunch length, the beam radiates coherently, and the power of the radiation increases many orders of magnitude relative to the incoherent radiation at the sam