Abstract
Approximate periodically focused solutions to the nonlinear Vlasov-Maxwell equations for intense beam propagation through an alternating-gradient field configuration
Highlights
Periodic focusing accelerators and transport systems [1,2,3,4,5] have a wide range of applications ranging from basic scientific research to applications such as heavy ion fusion, tritium production, spallation neutron sources, and nuclear waste treatment, to mention a few examples [6,7,8,9]
At the high beam currents and charge densities of practical interest, are the combined effects of the applied focusing field and the intense selffields produced by the beam space charge and current on determining detailed equilibrium, stability, and transport properties [1]
Despite the extensive literature on intense beam equilibrium and stability properties, until the present paper, the Kapchinskij-Vladimirskij (KV) beam equilibrium [10,11], including its recent generalization to a rotating beam in a periodic-focusing solenoidal field [21,22,23], has been the only known periodically focused equilibrium solution to the nonlinear Vlasov-Maxwell equations for an intense beam propagating through an alternating-gradient quadrupole or solenoidal field configuration
Summary
Periodic focusing accelerators and transport systems [1,2,3,4,5] have a wide range of applications ranging from basic scientific research to applications such as heavy ion fusion, tritium production, spallation neutron sources, and nuclear waste treatment, to mention a few examples [6,7,8,9]. To assure transverse confinement of the beam particles, the space-charge potential cx, y, sin Eq (6) is, smaller than or comparable in size to the applied focusing potential, ͑1͞2͒ ͓kxsx kysy2͔, and the kinetic energy contribution, ͑1͞2͒ ͑x02 1 y02͒, is allowed to be comparable in size to the applied focusing potential in the sense of a maximal ordering analysis In this regard, treating the single-particle Hamiltonian to be of order e ø 1, where e is proportional to the focusing-field strength, is similar to the assumption made in standard analyses of the particle dynamics in intense charged particle beams at moderate values of phase advance [1,2,3,4,5].
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