Synchrotron motion in a damping ring

[hezhao]

Dear all,

I have a damping ring with a series of wigglers (cwiggler) in the lattice. I was trying to simulate the synchrotron motion, but I found the result seems not correct. As shown below, the dp/p reachs to 0.15, which is huge. In the tracking, the particle (only one) was on-mementum and I used rf_setup for RF. The synchrotron radiation was turned on in the cwiggler element. With this rf setting and the radiation damping, I think the synchrotron motion shouldn’t be so strange.

I have also tried replacing the cwiggler elements by CSBEND (of course I did some matching work), and it gives a reasonable result. Could this issue be caused by the cwiggler elements? Or is there anything I did wrong in the tracking?

Thanks,
He

[michael_borland]

He,

The problem is that elegant uses some approximate formulae to compute the radiation integrals for CWIGGLER elements. It seems that the estimated actual energy loss in going through the CWIGGLER is different from what's estimated by about 20%, which means that rf_setup doesn't give the right rf parameters.

In light of this, I suggest you don't trust the radiation properties computed by twiss_output, nor should you use rf_setup for this problem. Instead, track a single particle through the beamline to get the energy loss per turn (look at the centroid output file, for example), then set up the rf cavities "by hand." Then, you can use the moments_output command to compute the equilibrium beam properties.

--Michael

[hezhao]

Hi Michael,

Thanks for your explanation. But the value of energy loss seems not the answer.

Actually, I’ve tried to turn-off the radiation damping in the lattice and I confirmed that the momentum value keeps a constant during tracking (without RF). But when I added the RFCA element (phase=180) with no radiation damping, the synchrotron motion was also strange, as shown below. As the momentum spread increasing, the particle will loss because of the tune shift in horizontal. I still don’t know what’s going on?

Do you have some suggestions?

Thank you very much,
He

[hezhao]

Hi Michael,

I found that during tracking:
1. Without RF and turn off the radiation damping, I get this (see picture)
2. without RF, turn on the radiation damping, I get this (see picture)
Both results give a deltaT shift in longitudinal phase space. I thought this deltaT shift is unreasonable because the shift should be zero when dp/p=0, and negative when dp/p<0. This deltaT shift would cause a mismatch in synchrotron motion when applying a RF.

He

[michael_borland]

He,

Sorry it has taken so long to get back to you. This was a challenging problem. I think the basic issue is that the path length of the reference particle is rather different from the nominal path length, presumably because of the large losses due to synchrotron radiation.

I made a number of changes to your files, as described in the Notebook file in the attachment.

• Use symplectic elements (CSBEND, KQUAD, KSEXT), so I can include SR in all elements
• Redefine CWIGGLER as a single element.
• Adjusted length of DCOOL to close the ring.
• Set chromaticity to zero.
• Set rf frequency based on single-turn tracking.
• Set reference frequency for the WATCH elements to match the revolution frequency from tracking.

With these changes, the phase space motion looks normal:

--Michael

[hezhao]

Michael,

Thank you so much. I'm very grateful.

Thanks for you help on my work.
He