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Dear Michael,

I used frequency map analysis to calculate the tunes and diffusion. But I noticed the tunes from fma are different from those from twiss parameter, even if I looked into the particle near zero offset. (Also I noticed the algorithm seems not to calculate the tunes at the origin.) Do you know the reason? I am attaching my files. nux from fma is about 0.84. but nux from twiss is .42.
Thanks,
Zhenghao Gu

Zhenghao,

The problem is the definition of the KQUAD elements, which does not specify the N_KICKS parameter. The default value (4) is insufficient for accurate tracking results in rings. Meanwhile, twiss_output uses the thick-element matrix, which is unaffected by N_KICKS.

If you use, for example N_KICKS=24, you'll get very good agreement. This value should be varied until the agreement is acceptable.

--Michael

Thank you so much. This answers the puzzle that I had since long time ago. Another question that I came up with is that in frequency map analysis, the particles near x=0 or y=0 usually behave strangely. Here are two graphs. In the graph of diffusion, the diffusion of the particle near the origin is obviously larger than its neighbors. In the second graph, the particles along the axis x=0 all have very different nux. So is this physical nature or because of the algorithm of frequency map analysis? Or again i made a mistake in the setting code? Thank you.

This happens because of cross-plane coupling. If, for example, x is near zero, large motion in y that gets coupled into the x plane will cause horizontal motion that is not a simple oscillation at the horizontal tune. This causes the FMA routine to get unpredictable values for the tunes and thus diffusion. To avoid this, I try to choose the parameters such that x=0 and y=0 are not included. However, this doesn't guarantee that you won't see the problem for sufficiently small x or y.

--Michael