Abstract
Beginning with the Green function for a rod beam in a round beam pipe we derive the space charge induced average energy change and rms spread for relativistic beams that are slowly converging or diverging in round beam pipes, a result that tends to be much larger than the 1/{gamma}{sup 2} dependence for parallel beams. Our results allow for beams with longitudinal-transverse correlation, and for slow variations in beam pipe radius. We calculate, in addition, the space charge component of energy change and spread in a chicane compressor. This component indicates source regions of coherent synchrotron radiation (CSR) energy change in systems with compression. We find that this component, at the end of example compressors, approximates the total induced voltage obtained by more detailed CSR calculations. Our results depend on beam pipe radius (although only weakly) whereas CSR calculations do not normally include this parameter, suggesting that results of such calculations, for systems with beam pipes, are not complete.
Highlights
The Sub-Picosecond Photon Source (SPPS) is a new modification of the Stanford Linear Accelerator that promises to generate high peak current, femtosecond electron bunches that will pass through an undulator to produce synchrotron light [1]
One component of the longitudinal coherent synchrotron radiation (CSR) force, which we here call the ‘‘space charge fields,’’ generates an energy change in the beam equal to the negative of the potential difference between an initial and a final state of the beam; it is the component termed the ‘‘compression work’’ by Dohlus when applied to compressors [4]. (Note that another part of the fields, called space charge, that depends on 1=2, with the Lorentz energy factor, and that is small for relativistic beams will not be considered here.) In this report we will focus on the space charge component, though, in general, one needs to consider all components to understand the longitudinal fields, for example, in a chicane
Beginning with the Green function for a rod beam oriented parallel to the axis of a round beam pipe we have derived the space charge induced energy shift and spread for relativistic beams that are slowly converging or diverging, a result that tends to be larger than the 1=2 dependence for parallel beams
Summary
The Sub-Picosecond Photon Source (SPPS) is a new modification of the Stanford Linear Accelerator that promises to generate high peak current, femtosecond electron bunches that will pass through an undulator to produce synchrotron light [1]. To achieve the performance goals of the SPPS it is important that coherent synchrotron radiation (CSR) generated in the chicane not increase the beam energy spread and through it the emittance of the beam by a significant amount. Such a problem was studied by Zimmermann and Raubenheimer [5] These authors noticed that in a converging (or diverging) relativistic beam the longitudinal space charge force no longer is proportional to 1=2 , and can be a much larger effect than for the case of a parallel moving beam. In this report we first study the longitudinal space charge effect of converging/diverging relativistic beams in a circular beam pipe and apply the results to the drift region before the last bend in the SPPS chicane. We calculate the space charge part of the induced energy spread over the entire SPPS chicane beam line
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