Use of triplet quadrupole magnets for symmetric focusing of the electron beam

Dear FLUKA users and experts!!!

I am trying to focus 22 MeV electron beam for different RMS sizes using a triplet quadrupole magnets.

In the attachment you can find the simulation input files (focus_beam.flair (57.1 KB)
focus_beam.inp (22.1 KB)) and the custom routin magnets field (Q1Q3magfld.f (3.5 KB)) that I use in my simulation.

Figure shows (see below) the distribution of the electron beam in the XZ and YZ planes along the direction of the beam for various RMS sizes and resalution (results obtain from USRBIN(BEAMPART)).

The title of each picture is written RMS and the resolution that corresponds to the result.
As you can see, when RMS is 1 mm, 2 mm or less, the beam focusing is fine, but as the RMS beam is 5 mm, 10 mm or more, the focusing area becomes worse (as far as I know, the beam focusing of the electron beam is independent of beam RMS value when neglecting space charge effect (is it right?)).

I would like to obtain a symmetrical focusing electron beam for different RMS beam sizes.

Could you please help me figure this out and tell me what is missing in my simulation and how can I get a symmetric focusing electron beam for different RMS beam sizes?

1_RMS-1mm_BEAM_W0_X
1_RMS-1mm_BEAM_W0_X
1_RMS-1mm_BEAM_W0_Y01_1mm
1_RMS-1mm_BEAM_W0_X02_1mm
1_RMS-2mm_BEAM_W0_Y
1_RMS-2mm_BEAM_W0_X
1_RMS-2mm_BEAM_W0_Y01_1mm
1_RMS-2mm_BEAM_W0_X02_1mm
1_RMS-5mm_BEAM_W0_Y
1_RMS-5mm_BEAM_W0_X
1_RMS-5mm_BEAM_W0_Y01_1mm
1_RMS-5mm_BEAM_W0_X02_1mm
1_RMS-10mm_BEAM_W0_Y
1_RMS-10mm_BEAM_W0_X
1_RMS-10mm_BEAM_W0_Y01_1mm
1_RMS-10mm_BEAM_W0_X02_1mm

Thanks in advance for any help
Best regards
Zohrab Amirkhanyan

Dear @zamirkhanyan ,

Thank you for your question,
I’m trying to address the problem.

Could you just tell me why you are using these particular characteristics for your magnets (length, field strength, etc?

What you said is correct:
“the beam focusing of the electron beam is independent of beam RMS value when neglecting space charge effect”

BUT, just in thin lenses. In Thick lenses (like in this case) you have to be careful with some effect related to the transport of the particles through the magnet. You can see in the next plot that you are ‘losing’ or deviating particles which are far from the center:

Let me know and we keep discussing,
Cheers,

André

Dear André

Thank you very much for your response. First of all, could you please explain to me how can I make the picture you attached?

Now I try to focus the beam with thin lenses (increasing the field strength), but still keep the asymmetry of the beam at the focal point position.

Also, I could not understand the following results that I got in the case of a single lens with a 1 cm thickness and beam rms is 30 mm (attached plot). We can see that the asymmetry of the beam is still maintained at the focus point position, although I expected the beam to focus in one plane and defocus in another plane.
1_RMS-10mm_BeamTEST_2D_Y01_01mm

Please, could you take a look at your instinct and help me figure this out?

focus_Q5.flair (17.7 KB)
focus_Q5.inp (20.9 KB)
Q1Q3magfld.f (3.8 KB)

Best regards
Zohrab

Dear @zamirkhanyan,

“First of all, could you please explain to me how can I make the picture you attached?”

Sure, you need to use this card:
Screenshot from 2021-08-25 10-58-19

This will dump a file that you can use to plot in the Geometry the track of your particles.
Follow the steps in the 5th post of this Thread:

“Now I try to focus the beam with thin lenses (increasing the field strength), but still keep the asymmetry of the beam at the focal point position.”

After discussing with some experts, it seems that the problem is due to the fact that when you are using large beam size, some of those particles are in regions of very high field. Those are the particles that are deviated, as we observed in the plot I attached in my previous post, which are deviated through a dipolar field component. That seems to be the reason why some of the particles are focused on a different focal point.

So, it seems that the the RMS limit depends on the beam energy and the field intensity. I could not obtain a way to quantify this limits for the moment. But I let you know If I find it.

As a final comment, I wanted to add that this problem is actually
related to beam optics, and FLUKA is not really intended for this.

Having said this, you understand that this topic is out of scope for this forum
and we recommend you to use a beam optics tool.

Best,
André

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