BPM noise error simulation

[Alea88]

Dear elegant community of users and collaborators,

I want to set up a simulation with non-zero BPM noise level, but not necessarily &correct on . Is there a way embedded in elegant to retrieve the values of the centroid of the beam read by the BPMs with noise on in such a case? Or this is possible only when trajectory/orbit correction &correct module is on?

Thanks for your suggestions,
best regards.
Giovanna

[michael_borland]

Giovanna,

The only way to see the effect of BPM noise is through the &correct command. Otherwise, all output from elegant shows the actual beam positions or particle coordinates, rather than what is measured by the BPMs. You can always add readout noise after the fact using, e.g., sddsprocess. If you say a little bit more about what you are trying to achieve, I might be able to make a more concrete suggestion.

--Michael

[Alea88]

Dear Micheal,
thanks for the clarification. I am simulating beam based alignement (DFS) of a LINAC and I would like to see the performance with BPM noise on, I am having a bit of difficulties in figuring out how to extract the information relative to this ...
I use &correct command to extract the response matrix and then multiply it and the dispersion matrix for the correctors and retrieving the information about correctors from the system SVD. I read here in the forum that neither the response matrix takes into account the bpm noise presence thought...

I'd be very glad to receive your input on this,
thanks in advance.
Giovanna

[michael_borland]

Giovanna,

You are correct that the response matrix doesn't include the effect of BPM noise. It's a a computation of the exact response matrix for the lattice (possibly with optical errors).

You can estimate the error in the response matrix elements using error standard error propagation techniques. Assume that the response for each corrector is measured using N excitation values, theta[1], ..., theta[N] and that the BPMs have rms readout noise of sigma_x. In that case, the variance for the response is N*(sigma_x)^2/Delta, where Delta=N*Sum{i=1, N} theta^2 - (Sum{i=1,N} theta)^2.

This is covered, for example, in Bevington's book on data reduction, but I think most textbooks on the subject should cover it.

--Michael

[Alea88]

Dear Michael,
thanks for your detailed answer and suggestions!
Regards,
Giovanna