Abstract
A helical quadrupole focusing channel has continuous field symmetry and a stronger focusing power compared with a conventional FODO focusing channel. The good field symmetry allowed us to construct an explicit transfer matrix under the paraxial approximation. In the present paper, we report the paraxial analysis of the helical quadrupole focusing channel and compare its characteristics with those of a conventional FODO focusing channel.
Highlights
A helical quadrupole focusing channel (HQFC), a variation of a quadrupole focusing channel, consists of a long quadrupole field continuously twisted along the beam axis
In order to examine the valid range of the linear approximation, we obtained the following expansions by Taylor series: 0
The helical quadrupole field satisfying the Maxwell equation is expressed by the following form using a modified Bessel function: r; ; z
Summary
Where k is 2=L and L is the period of the magnetic field (the period of a pole is 2L). For a good linear approximation, the nonlinear terms in the Br , B , and Bz components have to be negligible compared with the pure quadrupole component. 10% deviation is allowed for either the Br or the B component, the maximum r coordinate rbore has to keep the following condition: rbore & 0:12L:
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