Longitudinal phase space tracking in dual energy storage ring

[Dhital]

Dear All,

I have a dual energy storage ring, one ring at lower energy and another at higher energy connected by RF. I tried single particle tracking and found that after certain passes, particle gets lost. However, applying "magnify" element after the RF cavity ( to make transverse co-ordinates zero, Michael's suggestion) , it does wok. Going from 55 MeV (Lower ring, fixed energy value) to 500 MeV (Higher ring), and applying "magnify" element after RF cavity to make transverse co-ordinates zero does not work ( 0 particle transmitted after 0 turns). It does work up to higher energy about 455 MeV( High energy ring). What may be the reason behind this problem?

Question 1 : Is this a right way to make transverse co-ordinates (x,x') zero and do tracking? What if I want to create a beam distribution and do tracking for many passes?
I tried this but unable to get the periodic solution.
My ring has Line=(Low energy ring(55 MeV), accelerating RF, Harmonic RF1, High energy ring(455 meV), Bunching RF, Decelerating RF,Harmonic RF2)

Question 2 : During a bunched beam tracking with many particle, First I calculate one loop transfer map through the whole ring and apply the stability condition. This gives me the phase advance and finally the longitudinal twiss parameters which is used to create an initial beam distribution. Is this a right way to create a beam distribution in bunched beam tracking with many particles? I used an assumed value of beam emittance.

Actually there are two possible cases, first tracking with synchrotron radiation off and second with radiation on.
Here, I want to study longitudinal beam dynamics stability in my system with radiation off.
Is there anything wrong with my set up?

Thank you,
Bhawin

[Dhital]

Hi Michael,

Last time you suggested to use "magnify" element to make (x,x')=0 for the longitudinal study. That works. But what if you decided to see the effect of synchrotron radiation?
If (x,x')!=0, then particles get lost after few number of passes in the ring. I have attached lattice file and elegant run file for this problems.

I tried to use the artificial damping element (Sreffect) that requires the transverse co-ordinates.

Actually I need to run the bunch(having many particles) for couple of thousand passes to get the damped emittance value in my dual energy ring. The point to be remember is that one ring is at lower energy (say 55 MeV) and the another ring is at higher energy (say 455 MeV) connected by the RF cavities just to gain and lose the energy based on whether it is accelerating or decelerating passes.

Is there any limitations to elegant to work on this type of problems? We are working with higher RF frequency ~476 MHz.

Please any kind of help would be great.

Sincerely,
Bhawin

[michael_borland]

Bhawin,

Sorry for not being more prompt in my responses. I think this is a real instability that originates in the effect of the large energy changes on the transverse dynamics. Although px and py are conserved in a cavity, the downstream propagation of the particles depends on the slopes (px/pz and py/pz), which will change when pz changes. Any small x' or y' at the entrance to the decelerating cavity gets turned into a much larger x' or y' at the exit. This is only partially canceled when the beam is re-accelerated, because the phase advance between the cavities in not n*2*Pi.

I observed that things blow up in the horizontal plane very rapidly, with the vertical plane being more controlled. I suspect this a result of residual dispersion coupled with small synchrotron oscillations. This provides small x and x' errors that get magnified by the above-described instability.

You might try modifying the lattice so that the phase advance from the de-accelerating cavity to the accelerating cavity is n*2*pi, while avoiding total tunes close to integer or half-integer values. If that reduces the problem, it supports my explanation.

--Michael