Hello Mohammad, thank you for your answer. Unfortunately, this is a transfer line, not a ring structure so it's a single turn system and by BPM I meant beam position monitors, sorry, I should be careful with acronyms.

The problem is that you can measure the beam position and angle before the turnaround loop, but synchrotron radiation will introduce some uncorrelated jitter when the bunches get to the kickers, which reduces the performance of the feed forward system. This is a low emittance machine and the feed forward system is needed to maintain low emittance through the downstream collimators. The synchrotron radiation in the turnaround loop seems to be the limiting factor according to my simulations, but I currently don't know how to simulate the sychrotron radiation quantitatively.

Thank you very much for your help.

Hello Mohammad, I have attached a quick schematic diagram to explain the situation. Hopefully this makes sense to you.

We do have developed a very compact device to measure the ion beam profile, beam distribution and emmitance.

http://accelconf.web.cern.ch/AccelConf/IPAC2013/papers

Thank you Shixiang, however, this is more of a theoretical problem at the moment as I am currently designing the optics, rather than an experimental problem requiring beam instrument.

This is just an ignorant guess, but I expect you'd want to take the d^2N/dEd\Omega distribution for synchrotron radiation at each position and take into account the quantization of the individual photons, giving their momenta, which are then subtracted abruptly from that of the emitting electron to produce "jitter". It would be an "interesting" stochastic calculation, if I have understood correctly. Of course, if you make a FEL, there is coherence involved, which obviates the above stochastic description. I feel certain that someone has already tackled this, but I've been wrong before. :-)

You may find the answer in a recent paper out of Cornell. Please see the preprint at the following url: http://www.lns.cornell.edu/~dlr/papers/1-s2.0-S0168900212014441-main.pdf

Thank you Jess and Lorraine. Jess, I think you pretty much understand exactly what I am trying to do, though your choice of the word "interesting" pretty much sums it up. It is relatively straight forward to calculate the synchrotron radiation power loss and spectrum at a given point, so you can find the expectation value of the instantaneous change in momentum of the bunch, but integrating this over the entire arc is not as easy. The beam optics will be changing and I need to keep it as general as possible.

Lorraine, thank you for the link, I read through it and unfortunately it describes a beam size monitor using visible synchrotron radiation. I think it's a paper related to Mohammad's link. Though I thoroughly appreciate the help.

So far, I have managed to find a few documents describing emittance growth due to coherent and incoherent synchrotron radiation (though incoherent seems to be the dominant effect) such as the following lecture notes:

http://www.lns.cornell.edu/~ib38/uspas08/lec1.pdf

From the emittance growth, I am assuming that the jitter will scale with the square root of the emittance, which is normally true, but I'm not sure if this applies for synchrotron radiation because the emitted photons kick the beam, which is a different process not normal jitter.

Calculate the number of photons you expect to be emitted by synchrotron radiation, take the square root and dive by the number and you have the variation in the energy lost by the bunch.

You may be more interested in emittance change in which case you can look at each electron individually .

Thanks Amos, I think that sounds like a good suggestion, then from the RMS energy loss I can determine the RMS position jitter at the end of the arc. This sounds like the most promising idea.

I had been looking at the emittance growth and then using this to estimate the jitter since the two are related when the emittance growth is due to wakefields; but I don't think the same relationship holds for synchrotron radiation, so it was an educated guess at best...

Thanks a lot, this should make my simulations more reliable.