Undulator dipoles

[simoneliuzzo]

I try to add a method to create an undulator made of dipoles.

an example demo is provided in the pyat/examples/undulators

How to merge such list of elements (that gives the correct emittance and energy loss) with an IdTablePass element?

[oscarxblanco]

Good question @simoneliuzzo ,

I was thinking to use a wiggler element, and did try to use pyat to calculate the radiation integrals with no sucess.
I'll have a look on your example asap.

o

[simoneliuzzo]

Thank you @oscarxblanco
there is no urgency, as you see I do not even pass the tests yet!

[simoneliuzzo]

@lcarver and @swhite2401 suggested to give the possibility to define an undulator that has both the radiation effects and the kick map effects. However both elements are thick. How to put them together? @oscarxblanco and @lfarv may be have some ideas?

[swhite2401]

Hello @simoneliuzzo do you want me to review this PR?

[simoneliuzzo]

Dear @swhite2401,
If you want, but it is still a draft.
Basically I uploaded here the functions I prepared for the study of wiggler impact on the EBS.
I look for a way to implement simultaneously the dipole model (giving correct energy loss and emittances) and the kick map.
Both are thick elements, so it is unclear to me how to use them together.
Once we sort this out, I will add the InsertionDeviceKickMap elements to the undulator model, add unit tests, and ask for review.

[simoneliuzzo]

Dear @oscarxblanco ,

do you know if we can put 0 length in InsertionDeviceKickMap element?
that may be an easy solution to make the two work together.

thank you
best regards

[oscarxblanco]

@simoneliuzzo It is not possible because Length is divided by 2Nslice in IdTablePass.c (line 56).

I would suggest to create a new element with Length and IntegratedLength.
Length coud be varied as needed for plots, slices and so on.
IntegratedLength is always kept unchanged and passed to the InsertionDeviceKickMap.

That new element should inherit (all or most) properties from InsertionDeviceKickMap.

Best regards,
o

[lfarv]

Hi all, sorry to come late in the discussion, but I have strong concerns about what you can get out of this model…

The field model that you build with this method is a succession of hard-edge dipoles. This is unrealistic, the field cannot jump from positive to negative so what you simulate has nothing to do with a real undulator field. For standard dipoles, you know that taking into account the fringe field is tricky and uses empirical approximations: see the different methods presently implemented. Usually the fringe field effect is neglected (which is probably sometimes wrong). But an insertion device in only fringe fields, nowhere you'll get a flat top ! The simplest field model for insertion devices is Halbach's field expansion which is used if WiggLinearPass.

With k_x² + k_x² = k². As you can see, it's rather different from a succession of dipoles. For instance, B_y(s) is a cosine wave. For a realistic field, you need to combine several harmonics in k.

So now, what you can get from this "dipole" model:

• contribution to the emittance: it's the only way, as up to now no other method is available. You'll get a largely over-estimated radiated power because of the difference between the square field variation with z, as simulated by dipoles, and the sine wave-like real field, but at least you get something. Do you have a comparison with analytical values for the radiated power?
• tune shifts should be approximately correct, but again for this you can compare with the analytical value,
• but NEVER USE THIS MODEL FOR TRACKING, except for very long period devices (few pole wigglers). Your model is 1-dimensional: B_x=0, B_y=B(z), B_z=0 while the real field is 3-D. The B_y field is constant along z, while its variation may be responsible for aperture limitations (plus the contributions of B_x and B_z fields). And don't even think of adding multipoles: multiple expansion is valid only for infinitely long magnets…

As a 1st check: could you make a comparison with WiggLinearPass for the same (strong) device ? With a single field harmonic.

The problem with WiggLinearPass is that it is based on a theoretical field model, and real undulator field can be quite different from that. But at least the model satisfies Maxwell's equations, which is not the case of your "dipole" model.

The only correct passmethod for insertion device is "IDTablePass": it's the only way to define a realistic field, in particular the decay of the B_y field along x, critical for the horizontal aperture. I don't see how you could "combine" dipoles and ID tables: you must forget the dipoles in tracking

I am not an expert in insertion devices, most of what I know comes from discussions with P. Elleaume, who was very suspicious about models based on Halbach's field expansion. You have at ESRF experts in IDs, a discussion of ID field modelling would be very useful to clarify all this!

[simoneliuzzo]

Dear @lfarv

I understand and completely agree with your description.

The problem for me is that there is no wiggler or undulator method doing really all that we would like to see from an ID or wiggler pass. IdTablePass and WigglerLinearPass do not give the correct emittance and energy loss. Dipoles model do not give the correct tracking.

This pull request is open simply to point out this rather important missing feature for a code that is used mostly by synchrotron light sources.

I did not intend to merge the methods I have submitted, but only to trigger this discussion (and share the files) to think about what should be done in order to have what we we really need: a method to add to an AT lattice an ID that gives the correct tracking and global parameters.

Concerning the dipole model we recently compared the radiated power computed by the dipole model and the values obtained from formulas and from the control system:

93KeV from the dipoles model, 100KeV from the cavities.

[simoneliuzzo]

I am preparing the test with wiggler pass and will share the result as soon as they are ready

[simoneliuzzo]

Here a first figure: beta-beating and dispersion deviation with kickmpas (IdTablePass), dipoles, WigglerLinearPass

WigglerLinearPass gives result rather different from IdTablePass and dipole model.
In particular there is no dispersion modulation (invisible inside the element) nor horizontal beta-beating.

Thanks to this figure, I am an even more "confused" user.

[simoneliuzzo]

I am unable to continue the tests with Wiggler element.

Even if the optics are visible with plot_beta(), at.envelope_parameters gives an error: Unstable Ring.

and the lattice file if you want to try your self.
ring_w150_wiggler_25mm.mat.zip

I now realize that the Wiggler Element does not use WigglerLinearPass but GWigSymplecticPass!
So I have to repeat everything. I try changing the default pass method for a Wiggler element. If it does not work I will give up.

[simoneliuzzo]

I switched pass Method for the wiggler element to WiggLinearPass.

now the optics return nan
and the tracking fails with error 'Wiggler' object has no attribute 'InvRho'

So I think that the either the Wiggler element has some problem or I am not using the correct element. Likely the second.
Please advise.

[simoneliuzzo]

Lattice with WiggLinearPass element:
ring_WiggLinearPass.mat.zip

[lfarv]

@simoneliuzzo: I'm sorry, I made a confusion for passmethods: the right one should be GWigSymplecticPass, so your first series of tests was correct, forget WiggLinearPass.

You are talking of a W150 ID. With this long period of 150 mm, you are in a favorable situation for the dipole model ! On the other hand, GWiggSymplectic pass in penalised, because one would need additional 3rd, 5th and more harmonics to describe really the field shape. Then I have a few questions on you results:

1. Energy loss: both Matlab and python version compute the ID energy loss. With the "integral" method, this uses the analytical formula. What does this give, compared to the 100 keV (cavities), and the 93 keV (dipole model) ? For the dipole model, did you take the peak field to determine the slice bending angle, or a kind of effective field ? I expected a difference opposite to what you get (over-estimation of the dipole model). That's already a 1st surprise.

2. Beta beating. I'm a bit confused by the number of curves: I'm looking for "dipole model", labeled "dipoles" I guess, "WiggLinearPass", (should be GWiggSymplecticPass) labeled "wiggler" probably, and kick maps: where is it among the other curves ? And what are the disturbing other curves ?
   Do we expect any dispersion modulation from a perfect wiggler ? Normally not. Did you put half slices at the extremities of your dipole sequence ? You should check that when inputing zeros(6) at the input, you get zeros(6) at output. Take care in particular to a possible position offset.

I have other questions, so I'll continue later

[simoneliuzzo]

Dear @lfarv, @oscarxblanco, @swhite2401 and @lcarver,

@lcarver noticed that the new passmethod #632 could solve the problem we are discussing here. By adding to the undulator pass also the energy loss field, we may have an undulator model for AT that reproduces both the kickmaps effects and the energy loss per turn.
The energy loss would need to be computed before hand with this solution.

regards
simone