CSR induced energy spread

[Seong-Yeol Kim]

Dear all,

Hello, I am currently studying the CSR induced energy spread and the emittance growth.
Following the references (PRST-AB 4, 070701, PRST-AB 17, 060701, etc ...), rms energy spread induced by CSR can be calculated
by the equation (related to the beam charge, dipole length and bending radius, energy, and bunch length).

Using the equation, when the beam charge is 100 pC, bunch length of 60 um, energy of 165 MeV, arclength of 0.1 m, and bending angle of 10 deg,
the rms energy spread induced by the CSR is about 8.2135E-5.

However, when I ran the simulation using real beam distribution, and using the ideal beam generated from ELEGANT,
the CSR induced energy spread is totally different. In this case I obtained this energy spread from 'Sdelta_B1 - Sdelta_i'
where Sdelta_B1 is the energy spread after passing through the dipole magnet, and Sdelta_i is the initial energy spread.

- Concerning this issue, I have some questions.
1. I was wondering if the energy spread induced only by CSR can be estimated by above approach (Sdelta_B1 - Sdelta_i).
If it is not, how can I estimate only the CSR induced energy spread from the ELEGANT results?

2. In the case of ideal beam (also longitudinal Gaussian distribution), energy spread after dipole magnet is extremely small.
I would like to know why the energy spread is really small, and to know how to estimate this small value (if there is some analytic formula?)

3. On the other hand, real beam case I can see some increases of the energy spread, but it is still smaller than the value from equation.
I also check the longitudinal histogram, but it is somewhat similar to the Gaussian distribution.
Does this longitudinal distribution (phase space) play a role of the CSR induced energy spread?

Please find attached files for the .ele and .lte file for the details.
Thank you for your help in advance...!

[michael_borland]

Seong-Yeol,

You shouldn't expect that CSR will simply increase the rms energy spread according to the simple equation, for several reasons:

1. The default CSR algorithm in elegant includes the build-up transient, whereas the equation assumes steady state CSR. You can force elegant to do steady-state CSR using STEADY_STATE=1.
2. The elegant simulation includes the variation of the bunch duration through the dipole, which changes the CSR effect, particularly if there is large energy spread at the entrance to the dipole
3. CSR modulates the energy profile of the bunch vs time. You can't just add the rms energy spread from this modulation to an existing incoherent energy spread.
4. You have ISR=1, which includes another contribution to the energy spread that isn't in the CSR equation.
5. You have SG_HALFWIDTH=6, which is probably too much smoothing.

A clean comparison can be obtained by setting STEADY_STATE=1, ISR=0, SG_HALFWIDTH=1, initial energy spread to zero, initial emittance to zero. In that case, elegant gives an energy spread of 8.22x10^-5, in good agreement with expectations.

--Michael

[Seong-Yeol Kim]

Dear Michael,

Thank you for your detailed explanation.
As a matter of fact, I played with this by changing SG_halfwidth, number of kicks and bins, ISR, but basically the amount of energy spread by CSR was still small. However, I understood that the reason why there is a difference is due to the algorithm (build-up transient // steady-state).

Following your explanation, I have another questions.

1. When I set the SG_halfwidth=1, noise of the DeltaGamma in .WKE file is significant, so that I just changed to 6.
Actually I have noticed from the manual that it is encouraged to set the SG_halfwidth=1, but I was wondering why the smoothing parameter should not be too large.

2. Following your suggestion, I also check that the equation is valid when there is no initial energy spread and initial emittance.
However, when I used non-zero initial energy spread and emittance, I got different energy spread (3.5E-6). Why is there a difference and why do we need to force the initial energy spread and emittance to be zero?

3. Then I was wondering if the (very) small increases of the energy spread is still valid result, with the setup of 'steady-state = 0'.
Because initially obtained increases of the energy spread was in the order of 1E-7, which is indeed very small in the ideal Gaussian distribution.

- I wonder why there is difference between the result obtained by the build-up transient algorithm and by steady-state.
Is this due to the difference in the calculation algorithms? To my knowledge, the steady-state is 'the assumption' in the CSR calculation.
Then, can this steady-state assumption be correct or not depending on the phase space distribution, or something another factor?

Thank you!
Seong-Yeol