Understanding Cx and Cy

[tennant]

Hi,

When I run a beam with CSR I can see orbit excursions (Cx and Cy) through bunch compressors due to particles losing energy in a dispersion region and then betatron oscillating. When I turn the charge to zero (i.e. no CSR), I still see remnant excursions in Cx and Cy. Granted, they are orders of magnitude less, but I'd like to know how to interpret them. It's not clear to me what process could be causing it.

Thanks,
chris

[michael_borland]

Chris,

How large are the values?

Have you tried increasing the N_KICKS parameter?

--Michael

[tennant]

Michael,

The values peak at +/-2e-04 m. I changed all the CSRCSBENDs to SBENDs and the centroid positions do not change.

--chris

[michael_borland]

Chris,

This seems odd. Can you post the files or send them to me via email.

--Michael

[michael_borland]

Chris,

Thanks for sending the lattice file.

This appears to be a result of nonlinearities in the transport. If I take your lattice that uses SBENs, and set default_order=1 in &run_setup, I don't see the variation of Cx or Cy. If I set default_order=2, I see it. I also see considerable growth in the emittances (looking at ecnx and ecny from the sigma output of &run_setup), which also indicates strong nonlinearities.

You can easily see how this might happen. Suppose there is a quad of focal length f in a region where the dispersion is eta. The horizontal coordinates of the particles at the quad entrance are x=delta*eta. The kick to each particle is dx' = -x/f/(1+delta), which to second order is dx' = -(delta*eta/f)*(1-delta). Clearly, <dx'> = <delta^2>*eta/f, resulting in a non-zero centroid kick if the energy spread is non-zero.

--Michael

[tennant]

Michael,

Thanks for the explanation. That makes sense.

--chris