Abstract
We present a theoretical formulation for calculating the electromagnetic space-charge fields within a simplified electron source geometry using time-dependent Green's function methods. The source geometry is assumed to be comprised of a flat cathode along with a pipe of arbitrary but uniform cross section. Under the assumption that the beam currents are parallel to the pipe axis, we derive exact solutions for the electromagnetic potentials in the Lorentz gauge. In addition, for the special case of a pipe with rectangular cross section, we present the exact solutions of the electromagnetic potentials for arbitrary beam currents. Finally, we show the results of an analytical benchmark study in which the electromagnetic fields that are solved using the Green's function method are in excellent agreement ($<1%$ error) with the benchmark fields.
Highlights
Modern high-energy electron accelerators require electron sources, such as photocathode sources, that produce high-brightness, space-charge dominated beams [1]
Laboratory 2.856 GHz rf photocathode source [2], the beam which is generated by a laser pulse is initially bunched with a bunch length that is small compared to the wavelength of the rf electric field
The bunch is rapidly accelerated from nonrelativistic energies near the cathode, to relativistic speeds of order 0:8c–0:9c within a quarter wavelength of the rf field. Both of these properties imply that the space-charge fields within an rf photocathode source will be highly time dependent, and the effects of causality can be extremely important
Summary
Modern high-energy electron accelerators require electron sources, such as photocathode sources, that produce high-brightness, space-charge dominated beams [1]. The bunch is rapidly accelerated from nonrelativistic energies near the cathode, to relativistic speeds of order 0:8c–0:9c within a quarter wavelength of the rf field Both of these properties imply that the space-charge fields within an rf photocathode source will be highly time dependent, and the effects of causality can be extremely important. Electromagnetic particle-in-cell (PIC) codes, such as MAFIA [5], can calculate space-charge fields in the presence of arbitrary conducting boundary conditions by using grid based field solving methods, such as Yee’s algorithm [6]. There have been analytical methods developed for calculating the space-charge fields in a photocathode source in the presence of a conducting cathode and circular pipe [8,9] These methods expand the potentials using a Fourier transform for the longitudinal direction and a Bessel function expansion in the transverse direction.
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