Is Momentum Aperture really deterministic?

[GPenn]

Hi,

This may seem like a philosophical question but I am having some substantive issues with calculating the MA for the ALS-U storage ring. This is a very nonlinear lattice with strong bends and sextupoles, not to mention that the fractional horizontal and vertical tunes are almost identical. I set the parameters, including correcting the tunes, before doing the momentum aperture calculation, sometimes using elegant and sometimes using Pelegant. As a result the last significant digit in the quads used for tuning can be different. I was shocked to find that only switching between these two sets of parameter files can give significant differences (as big as 10%) in the momentum aperture in certain locations. There don't seem to be any random number inputs, so I suppose this is just a consequence of tracking chaotic orbits.

I have been trying to make the calculations go quickly, so in momentum_aperture I usually use step_back=1 and splits=1. Is there a more reliable way you would recommend? Maybe exploring the boundary with at least a few extra passes would help make the result less jittery? It might help to allow for a more probabilistic definition of the boundary, although that would be a more expensive calculation. I am concerned about the size of the variation because I am using the MA as an input for calculating losses with touschek_scatter, and it makes the default value of 0.85 for Momentum_Aperture_scale seem risky.

I am attaching some files and results using the SPEAR lattice, it's not as dramatic as the ALS-U runs but I think it makes the point about how small changes can impact the momentum aperture. I added tiny (about 10^-9 T in one case, 10^-12 T in the last case) quadrupole errors and still see some impact on the MA. I did have to set a very large physical aperture to get that kind of impact.

Thank you,
Gregg

[michael_borland]

Gregg,

I'm looking at your files now, but one quick observation is that running without synchrotron radiation effects (as you are) can give odd results. The reason is that radiation damping plus rf has the effect of varying the momentum offset over a range of values, giving the beam the chance to hit a resonance. Without this, the resonance can be missed, particularly if the step size is large (as it is in your case).

E.g., imagine that the beam crosses the integer resonance for delta=0.0201 and again for delta=0.0600 that you have a step size of 0.01. You will miss the first crossing and (ideally) find the second. Changing the quadrupoles slightly might result in not seeing the delta=0.0600 crossing either, or you might find that delta=0.0201 suddenly appears. However, if you have radiation damping and rf, the value of delta varies and you are much less likely to miss the first resonance.

My suggestion is never to run LMA for a ring without rf and synchrotron radiation. I use much smaller step sizes, typically 2e-4, then turn off back-stepping and splitting. I also set delta_negative_start and delta_positive_start so that I don't waste time on particles I'm pretty sure are stable. Setting soft_failure=1 means elegant won't exit if it fails to find a stable particle, but will report a zero momentum aperture for the location in question.

--Michael

[GPenn]

Thank you for the information, Mike. I will try your way of scanning momentum offests. I was all set to go the opposite route and try going backwards lots of steps.

For my ALS-U runs, I do use the RF acceleration and SYNCH_RAD=1. I had it in my head it would be simpler to give an example using SPEAR, but I will try to simplify what I have for the ALS-U and upload an example for that. It could be specific to that kind of lattice.

Cheers,
Gregg