Transfer matrices of superimposed magnets and RF cavity
Superimposed magnets often occur in accelerators, such as in the interaction regions of colliders. This note presents the linear transfer matrices of various superimposed magnets. Since readers of this note are probably well informed, the authors simply list the results without derivation. The method used to calculate the linear transfer matrices is outlined elsewhere. The authors list the Hamiltonian H and the corresponding matrix e{sup :-sH:} for several combinations of common magnets (only sector magnets without fringe field) used in accelerators. Magnetic fields and vector potentials (in Coulomb gauge) are also listed for reference. The usual (x, y, s) coordinate system is used. The transfer matrices are for the commonly used canonical variables (x, P{sub x}, y, P{sub y}, z, {delta}). For those cases when the transfer matrices depend on the gauge selection, the authors also list the matrices for the coordinates and kinetic momenta (x, p{sub x}, y, p{sub y}). The magnetic fields and Hamiltonians are correct only up to the order appropriate for linear optics. In this computer age, complicated analytical results may lose their usefulness and attractiveness in many applications. However, the authors hope their exact analytic results to linear order are still useful for particle dynamics studies in superimposed magnet systems.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 486015
- Report Number(s):
- SLAC/AP--106; ON: DE97006546
- Country of Publication:
- United States
- Language:
- English
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