Dispersion optimization with an offset beam

[Jafarinia]

Hi Michael,

If I inject a beam with an offset into a quadrupole, the quadrupole would act like a dipole and so it gives dispersion to the beam (beam with energy spread). But there is no dispersion in .twi file. How can I get this dispersion? One way is to compute S16/S6*S6 in .sig file but I was wondering if there is another way to compute the dispersion due to the offset. (since I want to continue the beam line with more elements and optimize it for required dispersion at the end)

Thanks,
Farzad

[Jafarinia]

Also I realized that Ss (bunch length) would not be affected by this offset. In a dipole the bunch length would be increased proportional to deflection angle and since the quadrupole with an offset acts like a dipole with a deflection angle (k*x*L) it must increases the bunch length. I checked the result with ASTRA and there is an increase about a factor of 7 in ASTRA simulation while ELEGANT doesn't show any increase in bunch length.!!!!

Farzad

[michael_borland]

Farzad,

I'm not sure how you got these results, but they don't agree with my simulations.

I used the following lattice

Code: Select all

Q1: quad,l=1,k1=5,dx=0.01
D1: drift,l=1
bl: line=(Q1,10*D1)

Using twiss_output, I get the following dispersion:

I also tracked a bunch with initial zero bunch length and 0.01% rms energy spread. The change in bunch duration is small but clear.

See attached files.

--Michael

[Jafarinia]

Hi Michael,

I have attached my lattice. I don't see any increase in bunch length in my simulation.

Regards,

Farzad

Track.ele

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S5.lte

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[michael_borland]

Farzad,

You are using MALIGN elements instead of the DX and DY parameters on the QUAD elements. Using these combined with CENTER elements is not the correct way to misalign elements. You won't get the right transport matrix, since the CENTER element always suppresses the centroid from upstream, regardless of its source.

Also, if you are looking a very small changes in path length and time of flight, it is best to use the KQUAD and EDRIFT elements. Otherwise, you are getting only the terms up to second order (there are also fourth and higher order terms that will be missed).

When I make these changes, I see a pretty clear change in bunch duration.

--Michael

[Jafarinia]

Hi Michael,

Thank you for your reply. But I want to bring the beam back to the center after quad 2 and 3 (like a dipole). How can I do that while getting right transport matrix?

Farzad

[michael_borland]

Farzad,

The issue is that a quadrupole doesn't change the reference trajectory the way a dipole does, so the trajectory is real and usually should not be suppressed. For example, the trajectory from the first misaligned quadrupole will affect how much offset the beam has in the downstream quadrupoles. This significantly changes the results.

If you insist (e.g., if your quadrupoles are really repositioned to follow the beam), using CENTER is ok for tracking, but don't expect agreement between matrix and twiss parameter calculations and tracking, since these do not include the effect of the CENTER element. You can get around this by using MALIGN elements instead of CENTER, since those actually have a matrix, but you'll have to figure out the DX and DXP values by hand using tracking. (CENTER elements don't have one because it would have to depend on the upstream matrix, which gets complicated.)

--Michael

[Jafarinia]

Michael,

I just realized that using center element not right after the misaligned quad but after the drift and before the next misaligned quad would give the correct result.!!!!!

Farzad

[michael_borland]

Farzad,

I'm not sure I understand that. Can you upload the modified lattice?

Thanks--Michael

[Jafarinia]

Michael,

I have attached the modified lattice. There is still difference between etax and s16/s66*s66 but I think that is due to nonlinearity in the beam line. But the bunch length is correct.

Farzad

S5_M.lte

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