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Nash, B.

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TUZAAB01 Equilibrium Beam Distribution in Electron Storage Rings near Synchrobetatron Coupling Resonances 789
  • B. Nash
    BNL, Upton, Long Island, New York
  Linear dynamics in a storage ring can be described by the one-turn map matrix. In the case of a resonance where two of the eigenvalues of this matrix are degenerate, a coupling perturbation causes a mixing of the uncoupled eigenvectors. A perturbation formalism is developed to find eigenvalues and eigenvectors of the one-turn map near such a linear resonance. Damping and diffusion due to synchrotron radiation can be obtained by integrating their effects over one turn, and the coupled eigenvectors can be used to find the coupled damping and diffusion coefficients. Expressions for the coupled equilibrium emittances and beam distribution moments are then derived. In addition to the conventional instabilities at the sum, integer, and half-integer resonances, it is found that the coupling can cause an instability through antidamping near a sum resonance even when the symplectic dynamics are stable. E. G., the case of linear synchrobetatron coupling is analyzed where the coupling is caused by dispersion in the rf cavity, or by a crab cavity. Explicit closed-form expressions for the sum/difference resonances are given along with the integer/half-integer resonances.  
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FRPMS113 Touschek Lifetime Calculations and Simulations for NSLS-II 4375
  • C. Montag, J. Bengtsson, B. Nash
    BNL, Upton, Long Island, New York
  Funding: Work performed under the auspices of the US Department of Energy.

The beam lifetime in most medium-energy synchrotron radiation sources is limited by the Touschek effect, which describes the momentum transfer from the transverse into the longitudinal direction due to binary collisions between electrons. While an analytical formula exists to calculate the resulting lifetime, the actual momentum acceptance necessary to perform this calculation can only be determined by tracking. This is especially the case in the presence of small vertical apertures at insertion devices. In this case, nonlinear betatron coupling leads to beam losses at these vertical aperture restrictions. In addition, a realistic model of the storage ring is necessary for calculation of the equilibrium beam sizes (particularly in the vertical direction) which are important for a self-consistent lifetime calculation.