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IBS Calculation Using BETACOOL
He Zhang2/26/2013 Jlab MEIC R&D Group Meeting
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He Zhang ---2---
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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He Zhang ---4---
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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He Zhang ---6---
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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He Zhang ---11---
IBS rise time calculation using BETACOOL
Calculate the growth rate
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Discussion about couplingLijun’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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He Zhang ---16---
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.