The problem of self-consistent particle phase space distributions for periodic focusing channels
arXiv (Cornell University)(2023)
摘要
Charged particle beams that remain stationary while passing through a
transport channel are represented by “self-consistent” phase space
distributions. As the starting point, we assume the external focusing forces to
act continuously on the beam. If Liouville's theorem applies, an infinite
variety of self-consistent particle phase space distributions exists then. The
method is reviewed how to determine the Hamiltonian of the focusing system for
a given phase space density function. Subsequently, this Hamiltonian is
transformed canonically to yield the appropriate Hamiltonian that pertains to a
beam passing through a non-continuous transport system. It is shown that the
total transverse beam energy is a conserved quantity, if the beam stays
rotationally symmetric along the channel. It can be concluded that charged
particle beams can be transmitted through periodic solenoid channels without
loss of quality. Our computer simulations, presented in the second part of the
paper, confirm this result. In contrast, the simulation for a periodic
quadrupole channel yields a small but constant growth rate of the
rms-emittance.
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关键词
particle,phase,channels,focusing,self-consistent
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