Hoffmann Chart [SOLVED]

[sarvesh]

I request you explanation of this Hoffmann Chart of the RFQ model. Can we say also that it is plot of σT/σ0T versus σz/σT? Can you please corelate the X and Y axis in this way. What is conclusion of yellow dots which is data from multiparticle simulations. I enabled all 4,3,2 order while plotting this Hoffmann chart. What should be relevant range on X axis?

[npichoff]

Dear Sarvesh,

Can we say also that it is plot of σT/σ0T versus σz/σT?
You are right : w is for x or y, then w=T=transverse (generaly, in linac, the focusing is the same in both transverse directions).

Can you please correlate the X and Y axis in this way.
This is a specific development. Nevertheless, you can plot them by yourself from plots of sigmaX0, sigmaX, sigmaY0, sigmaY for each period.

What is conclusion of yellow dots which is data from multiparticle simulations.
Each dot corresponds to one lattice of your linac.

I enabled all 4,3,2 order while plotting this Hoffmann chart. What should be relevant range on X axis?
Very often, resonances cannot be avoided during your acceleration. In this case, the best is not to stay a long time at this resonance (emittance transfer takes some time). The multiparticle simulations will inform you if there is emittance transfer between plan.

Regards.

Nicolas.

[sarvesh]

I forget to mention that it is plot for RFQ only. Thanks to pointed reply, Can we also say that there is fast crossing of four lattice periods with tune depression more than 0.7 and therefore no significant effect on beam dynamics. I am counting yellow dots for Kz/Kxy = 1. What is the reason for it? Also what is the significance of dotted line?

[npichoff]

For a better understanding of Hoffman chart, may I suggest that you read Ingo's (Hoffmann) paper ?

I forget to mention that it is plot for RFQ only.
OK. this explain the reason why you have a lot of dots with kz<<kw (during the bunching process).

Can we also say that there is fast crossing of four lattice periods with tune depression more than 0.7 and therefore no significant effect on beam dynamics. I am counting yellow dots for Kz/Kxy = 1. What is the reason for it?
I don't really understand your question, can you please rephrase it ?

Also what is the significance of dotted line?
If you are talking about the vertical one, I assume that is corresponds to kz = kw.

[jonathan dumas]

For Ref:
https://cds.cern.ch/record/140869/files/p145.pdf
https://journals.aps.org/pre/pdf/10.110 ... vE.57.4713
https://journals.aps.org/prab/pdf/10.11 ... B.6.024202