Speaker
Description
We revisit Carlsten’s slice-expansion treatment of emittance compensation for space-charge dominated beams and derive a generalisation that makes the underlying slice conditions explicit. Starting from Carlsten’s self-field expansion, we obtain a sequence of constraints that must be satisfied to make the transverse envelope independent of a slice about a reference slice. Using a simple transport-matrix argument, we show that a single static linear focusing element can at best satisfy the first, linear space-charge term in this sequence and therefore cannot, in general, remove higher-order slice dependence. Motivated by this limitation, we introduce a time-dependent focusing strength written as a series in the slice parameter and derive recursive relations for its coefficients, providing a framework for RF focusing schemes, including harmonic cavities, that could potentially compensate higher-order slice-dependent space-charge effects.
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