IBS Calculation Using BETACOOL

IBS Calculation Using BETACOOL

He Zhang

2/26/2013 Jlab MEIC R&D Group Meeting

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Outline

• Formulas for IBS rise time

• IBS rise time calculation using BETACOOL

• IBS calculation for MEIC&LEIC

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Formulas for IBS rise time calculation

How to derive the formulas?

• IBS is due to the collisions inside the ion bunch

• Steps to derive the formulas1. In beam frame, two body collision, the change of momentum2. In lab frame, the change of emittance3. Average over all scattering angles4. Average over all particles

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Formulas for IBS rise time calculation

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IBS rise time calculation using BETACOOL

• Set the lattice of the ring• Set ring parameters• Set beam paramters• Choose IBS model• Calculate the growth rate

How to use BETACOOL:

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IBS rise time calculation using BETACOOL

Set the lattice of the ring

Pay attention:

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IBS rise time calculation using BETACOOL

Set ring parameters

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IBS rise time calculation using BETACOOL

Set beam paramters

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IBS rise time calculation using BETACOOL

Choose IBS model

BETACOOL manual suggests:• Use Martini model with

numerical integral over z first. For accuracy<1%, mu, nu, and z need to be a few hundred

• Then choose “Coulomb logarithm”. Compare the result to find a proper value for Lc.

Pay attention: the window value of “Coulomb logarithm” is actually two times “Coulomb logarithm” (2Lc), ~40.

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IBS rise time calculation using BETACOOL

Calculate the growth rate

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IBS rise time calculation using BETACOOL

Calculate the growth rate

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Discussion about coupling

Lijun’s result for MEIC IBS calculation

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Discussion about coupling

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Discussion about coupling

From the physical manual of BETACOOL:

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Discussion about coupling

From the physical manual of BETACOOL:

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IBS calculation for MEIC&LEIC

Future work

• Cooling simualtion• Compare different models and formulas• Get familiar with other functions of BETACOOL

Thanks for your time !

This presentation uses the results from the following persons’ work: A. Piwinski, J. Bjorken, S. Mtingwa, M. Monte, M. Martini, A. Sorensen, F. Zimmermann, J. Wei, G. Parzen, etc.