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Variable related to phaseamplitude variables 4 3
BEAM OPTICS AND FOCUSING SYSTEMS
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aberration accelerators amplitude analysed angle angular applied approximation arising axial symmetry axis azimuthal behaviour betatron betatron oscillations Brillouin flow bunch calculate cathode charge co-ordinates complicated component configurations considered constant corresponding coupling current density curve cyclotrons cylindrical damping defined denotes described discussed dispersion relation distribution effect electric field ellipse emittance energy equilibrium orbit example expressed finite focusing force frame frequency function given group velocity instability integral ions laminar Landau damping Larmor lens lenses limit linear Liouville's theorem longitudinal longitudinal waves machine magnetic field matrix momentum motion moving negative neutralized non-linear non-relativistic parameters paraxial approximation paraxial equation particle perveance phase space phase velocity physical plane plasma Poisson's equation potential problem properties quadrupole radial radius references relativistic represents scattering self-fields situation solution space-charge spherical aberration stationary storage rings studied synchrotron tion trajectory transverse transverse waves uniform variables wall waves zero