Abstract
Analytical solutions are derived for both transient and steady state gradient distributions in the traveling wave (TW) accelerating structures with arbitrary variation of parameters over the structure length. The results of the unloaded and beam loaded cases are presented. Finally, the exact analytical shape of the rf pulse waveform was found in order to apply the transient beam loading compensation scheme during the structure filling time. The obtained theoretical formulas were cross-checked by direct numerical simulations on the CLIC main linac accelerating structure and demonstrated a good agreement. The proposed methods provide a fast and reliable tool for the initial stage of the TW structure analysis.
Highlights
The steady state theory of beam loading in electron linear accelerators was developed in the 1950s by a number of authors both for constant impedance [1,2,3] and constant gradient [4] accelerating structures
They considered the equation for energy conservation in a volume between any two cross sections; the power gained by the beam or lost in the walls due to the Joule effect results in a reduction of the power flow
In this paper, generalized analytical solutions of the gradient distribution in the traveling wave (TW) accelerating structure with an arbitrary variation of parameters over the structure length are presented for both steady state and transient regimes
Summary
The steady state theory of beam loading in electron linear accelerators was developed in the 1950s by a number of authors both for constant impedance [1,2,3] and constant gradient [4] accelerating structures They considered the equation for energy conservation in a volume between any two cross sections; the power gained by the beam or lost in the walls due to the Joule effect results in a reduction of the power flow. In this paper, generalized analytical solutions of the gradient distribution in the TW accelerating structure with an arbitrary variation of parameters over the structure length are presented for both steady state and transient regimes It is based on the method suggested earlier by one of the coauthors [14] and is similar to the classical approach [1,2,3,4,5,6,7,8,9]. 230 mm 0.5 ns 3:7 Â 109 312 22 ns 67 ns 61.3 MW time of flight of the beam through the structure are much less than the filling time of the structure
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