Tune versus delta

[A.V.Bogomyagkov]

Hello,

I calculated nu versus delta by tracking and using sddsnaff, and tune_footprint.
The results are different as could be seen in the attached pictures.
Could you explain the difference?

Using the tune_footprint is straightforward and the code is in tunefootprint.zip

Tracking requires postprocessing and gives the same nu vs delta dependance as in MAD-X PTC.
Results of the tracking I postprocess as following (track-centroid.zip)

Code: Select all

sddscollapse results/ct_ring.fin results/ct_ring.finc

sddsnaff results/ct_ring.w1 -pipe=out -column=Pass,Cx,Cy -terminate=frequencies=1 \
 | sddscombine -merge -pipe \
 | sddsxref -pipe results/ct_ring.finc -take=MAL.DP -rename=column,MAL.DP=delta \
 | sddsmpfit -pipe  -indep=delta -depen=CxFrequency,CyFrequency -terms=7 \
 | sddsxref -pipe results/ct_ring.twi -leave=* -transfer=param,nu?,dnu?/dp \
 | sddsprocess -pipe=in results/ct_ring.fit

and draw delta,CxFrequency,CyFrequency.

Respectfully,
Anton

[A.V.Bogomyagkov]

I guess the difference is that tracking is done with dx=1e-6 with respect to closed orbit for given delta.

The tune_footprint does not center on the closed orbit, it is always centered on the on-momentum reference orbit; therefore, dx=1e-6 is added (or subtracted) to additional coordinate shift from dispersion times delta. Thus, tune_footprint does not give nu with respect to delta but nu with respect to delta plus nu with respect to x.

Anton

[michael_borland]

Anton,

Thanks, that's a very interesting observation. Probably I never noticed it because the lattices I work with tend to have zero dispersion at the start.

I'll see what I can do to improve this.

--Michael

[A.V.Bogomyagkov]

Michael,

The linear dispersion is zero, but nonlinear is not.

I am a newbie with elegant and trying to understand. And I was wondering if my conclusion is valid. The coordinate shift from tracking corresponds to x=d1*delta^2.

Can you advise on how to optimize 5d or 6d DA? Optimization of tunes variation with respect to coordinates or momentum deviation is not direct, while optimization of DA square is straight forward.
The "find_aperture" only finds DA for on momentum particle. Can I use MALIGN element to set dp and find DA? But how do I use DaArea variable at different dp?

The other way is to find the aperture in x and delta with given initial Y, and optimize the square. Is there an option to find_aperture but in x delta plane?

Anton

[michael_borland]

Anton,

I'll check out your finding in the next few days (I hope) and let you know what I find. I think it is correct that the tune footprint should use tracking centered on the off-momentum closed orbit.

For optimization, by far the best approach is to use an external optimizer (such as our mogaRing optimizer) to run elegant. That allows you to, for example, ring DA several times at various momentum offsets and then optimize a penalty function based on those results. My colleague Yipeng Sun did something very similar to what you are describing. See his IPAC18 paper TUPMF013, page 1276. You can contact him at the email address in the paper for assistance.

-Michael

[A.V.Bogomyagkov]

Thank you Michael.

Anton