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 4050% 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 23 times the expected damping time using Pelegant (23e4 turns)
 plot Sdelta as a function of Pass (or Pass times revolution time, here 548e9 s)
 fit f(x)=a*exp(x/tau)+offset via a,tau and offset
> tau is only 5060% 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?
Thanks in advance!
Jan
radiation damping from tracking
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 Joined: 19 May 2008, 09:33
 Location: Argonne National Laboratory
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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
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
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)
By the way, USE_RAD_DIST=1 is rarely needed. It just makes it slower.
Michael
 Attachments

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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
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

 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 SLACReport 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
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
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 SLACReport 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,
Michael