Transverse oscillation of particles in the vicinity of resonances for a cyclotron
Transverse oscillation is an important issue in beam dynamics of cyclotrons and can be described by the Mathieu equation. We review the standard form of the Mathieu equation, d^{2}u/dθ^{2}+(δ+ϵ·cos2θ)u=0, and propose a modification of the method of multiple scales (i.e., a perturbation method) so th...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2019-10-01
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| Series: | Physical Review Accelerators and Beams |
| Online Access: | http://doi.org/10.1103/PhysRevAccelBeams.22.104001 |