Linear Coupling for B-Factory Tilted Solenoid
In this thesis they have presented the transfer matrix for B Factory tilted solenoid with the expansion of magnetic field up to the fifth order. Starting with the general theory of linear coupling, we got the Hamiltonian for solenoid with the bending magnet and quadrupole inside. The solenoid axis is tilted by 20 mrad horizontally w.r.t. the collision axis and at the entrance and the exit of the solenoid the beam will sense transverse and longitudinal non-linear fields. To account both this effects the expansion of the magnetic field was done. The code of coordinate transformation, which relates the frame of the reference orbit to the frame of the collision axis and to the solenoid frame, has been introduced. They tried to show that not symplectic fourth-order Runge Kutta integration method, which had been used for integration of the Hamiltonian equations, might be used as a model for ''not tracking'' problems. The deviation from a symplectic transfer matrix is smaller than 10{sup -5}. Using the transfer matrix, the change in beam shape and blow up of emittance, due to the solenoid coupling, was discussed. In order to compensate this effect they used 4 tilted quadrupoles on each side of the IP. The method based on the Hamiltonian in Eq.19 integrates along a reference orbit which is defined only by the horizontal and vertical bending fields and not by the tilted solenoid. In order to get the Hamiltonian, which is associated with a non-planar curvature of the reference orbit, it is necessary to account the effect of torsion. In that case the transformation between the three different coordinate systems will become more complicated.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 839748
- Report Number(s):
- SLAC-R-742; TRN: US0503305
- Country of Publication:
- United States
- Language:
- English
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