Elegant users forum

Hello Michael,

How does CHANGE_P0 in RFCA affect the quadrupole strengths?
I have an accelerating structure with interleaving quadrupoles.
Twiss output of CHANGE_P0=0 is different from that of CHANGE_P0=1.

Since K1 is a geometric strength, and it is independent of the momentum, what caused the difference?

Thanks.

This isn't related only to the quadrupoles, but also to the RFCAs. The issue is that the computation of the matrix for an RFCA element depends on the defined input and resulting output momenta. With CHANGE_P0=1, the matrix for each RFCA changes along the beamline to reflect the fact that the fractional momentum change decreases with each element. With CHANGE_P0=0, the matrix also changes, but now we count in part on an approximate treatment (including the second order matrix) to account for the eventually large momentum deviation from P0. That has limitations.

You can get better comparison by tracking particles with CHANGE_P0=0 and 1, then comparing emittances, beam sizes, etc. from the sigma output file. You'll see that they agree quite well when the quadrupoles are turned off.

When you turn the quadrupoles on, you don't expect to see agreement. With CHANGE_P0=0, the K1 values are defined for the initial momentum, which is the reference momentum along the beamline; essentially, the quadrupoles have fixed gradients. With CHANGE_P0=1, the K1 values are defined for the changing central momentum due to acceleration; here, the quadrupoles have gradients that increase in proportion to the momentum.

--Michael

Hello Michael,

Thank you for the explanation.