Moderators: cyao, michael_borland

jan
Posts: 13
Joined: 02 Oct 2013, 07:20
Location: ELSA, Bonn, Germany

Hi everybody,

for demonstration of synchrotron radiation effects I tracked a bunch of electrons with large initial energy spread and observed the longitudinal radiation damping. Then I determined the damping time from an exponential fit, but the value is 40-50% smaller than expected.

Here is what I did:
- use CSBEND dipoles with use_rad_dist=1
- define a bunched_beam: gaussian with 50 particles, sigma_dp larger than equilibrium
- define a watch element in parameter mode to get energy spread Sdelta
- track 2-3 times the expected damping time using Pelegant (2-3e4 turns)
- plot Sdelta as a function of Pass (or Pass times revolution time, here 548e-9 s)
- fit f(x)=a*exp(-x/tau)+offset via a,tau and offset
-> tau is only 50-60% of the expected value (taudelta from .twi output)
Find the files attached.

It seems not to be a problem of statistics or the fit. I tried with more particles and different seeds. The fit errors are about 1%. Any ideas?

Jan
Attachments
damp.lte
damp.ele

michael_borland
Posts: 1795
Joined: 19 May 2008, 09:33
Location: Argonne National Laboratory
Contact:

### Re: radiation damping from tracking

Jan,

The problem is that the energy spread and bunch length don't decay exponentially. Rather, the square of these quantities decays exponentially. The expression is

Code: Select all

``````(Sdelta)^2 = (SdeltaEq)^2 + (SdeltaIni^2 - SdeltaEq^2)*exp(-2*t/tau)
``````
See the attachment for an corrected comparison. The agreement is very good.

By the way, USE_RAD_DIST=1 is rarely needed. It just makes it slower.

--Michael
Attachments
2017-04-03.zip

jan
Posts: 13
Joined: 02 Oct 2013, 07:20
Location: ELSA, Bonn, Germany

### Re: radiation damping from tracking

Michael,

thank you very much for your reply. I do not understand why exponential decay of the trajectories leads to your expression. Can you give me a reference for the expression?

Thanks a lot!
Jan

michael_borland
Posts: 1795
Joined: 19 May 2008, 09:33
Location: Argonne National Laboratory
Contact:

### Re: radiation damping from tracking

Jan,

I don't know of a reference that has this result in this form, but a good starting point is Matthew Sand's old storage ring paper SLAC-Report 121. In this paper, he gives expressions for the quantum excitation and damping terms. The QE term adds a fixed change in Sdelta^2 each turn, while the damping term fights this. So the differential equation is something like

Code: Select all

``````dZ/dt = QE - 2/tau*Z,
``````
where Z = Sdelta^2. At equilibrium, dZ/dt=0 and Z = SdeltaEq^2, which allows us to conclude that QE=2*SdeltaEq^2/tau. With that, we can perform the integration and get the equation I gave.

--Michael