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Languages : en
Pages : 3
Book Description
Linear Coupling Correction and the Nu(sub X) + Nu(sub Y) Harmonics
Author: Linear Coupling Correction and The???????? +?{sub Y} Harmonics
Author: Linear Coupling Correction and The. Nu. Sub X +. Nu. Sub Y Harmonics
Author: Linear Coupling Correction and the Harmonics
Author: A Simulation Study of Linear Coupling Effects and Their Correction in RHIC.
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Languages : en
Pages : 8
Book Description
This paper describes a possible skew quadrupole correction system for linear coupling for the RHIC92 lattice. A simulation study has been done for the correction system. Results are given for the performance of the correction system, and the required strength of the skew quadruple correctors. An important effect of linear coupling in RHIC is to shift the tune [nu][sub x] [nu][sub y], sometimes called tune splitting. Most of this tune splitting can be corrected with a two family skew quadrupole correction system. For RHIC92, the same 2 family correction system will work for all likely choices of [beta]*. This was not the case for the RHIC91 lattice where different families of correctors were needed for different [beta]*. The tune splitting described above which is corrected with a 2 family correction system is driven primarily by the [nu][sub x] [minus] [nu][sub y] harmonic of the skew quadrupole field given by the field multipole [alpha]l. There are several other effects of linear coupling present which are driven primarily by the [nu][sub x] + [nu][sub y] harmonics of the skew quadrupole field, [alpha]l. These include the following: (1) A higher order residual tune shift that remains after correction with the 2 family correction system. This tune shift is roughly quadratic in [alpha]l; (2) Possible large changes in the beta functions; (3) Possible increase in the beam size at injection due to the beta function distortion and the emittance distortion at injection.
The Residual Tune Splitting in the Presence of Linear Coupling
Author: THE RESIDUAL TUNE SPLITTING IN THE PRESENCE OF LINEAR COUPLING.
Author: G. PARZENEmittance and Beam Size Distortion Due to Linear Coupling
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Languages : en
Pages : 4
Book Description
At injection, the presence of linear coupling may result in an increased beam emittance and in increased beam dimensions. Results for the emittance in the presence of linear coupling will be found. These results for the emittance distortion show that the harmonics of the skew quadrupole field close to [nu][sub x] + [nu][sub y] are the important harmonics. Results will be found for the important driving terms for the emittance distortion. It will be shown that if these driving terms are corrected, then the total emittance is unchanged, [var epsilon][sub x] + [var epsilon][sub y] = [var epsilon][sub 1] + [var epsilon][sub 2]. Also, the increase in the beam dimensions will be limited to a factor which is less than 1.414. If the correction is good enough, see below for details, one can achieve [var epsilon][sub 1] = [var epsilon][sub x], [var epsilon][sub 2] = [var epsilon] where [var epsilon][sub 1], [var epsilon][sub 2] are the emittances in the presence of coupling, and the beam dimensions are unchanged. Global correction of the emittance and beam size distortion appears possible.
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