Single particle motion
A general three dimensional description of single particle motion is given. The 6×6 transfer matrix describing motion close to a reference particle is explicitly diagonalized to find the three eigentunes and eigenplanes. Within each of these eigenplanes a generalised Twiss parameter description is given. After specialising from six to four dimensional phase space, these formulas can describe coupled transverse motion or synchrobetatron motion. Within eigenplanes the pseudoharmonic description is just like the well-known description of uncoupled motion in a single transverse plane.
Lattice defects and their correction are discussed. A universal detection-adjustment formalism is introduced and applied to the examples of tune adjustment, orbit flattening and decoupling.
Various examples of “map dynamics” are discussed, the most important being the betatron response to external excitation. Also coupled motion is analysed; in one important case the motion in one plane can be regarded as being driven by the motion in the other plane.
KeywordsTransfer Matrix Closed Orbit Phase Advance Open Sector Central Orbit
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