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PreprintCC BY 4.0arXiv

Beam Transport Through a Quadrupole with Offsets in Both Transverse Planes

  • Sergey Tomin
Open at sourcePDFDOICite

Abstract

In accelerator switchyards with shared magnets, a beam may traverse a quadrupole with offsets in both transverse planes, a configuration that cannot be represented by a single conventional horizontal or vertical combined-function bend. Such an off-axis quadrupole bends the reference trajectory and generates dispersion simultaneously in both planes. We derive a compact analytical 6×6 transfer matrix about the curved reference trajectory. The model is formulated in Bishop coordinates using a weak-curvature approximation that retains the longitudinal variation of both reference-curvature components and the resulting dispersion in both transverse planes. The analytical linear model is compared with a sliced representation based on conventional second-order combined-function bend maps and with direct numerical integration of the Lorentz equations in the ideal Cartesian quadrupole field.

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Cite

BibTeXRIS
BibTeX
@misc{tomin2026beam,
  title = {{Beam Transport Through a Quadrupole with Offsets in Both Transverse Planes}},
  author = {Sergey Tomin},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06730},
  eprint = {2611.06730},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06730},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Beam Transport Through a Quadrupole with Offsets in Both Transverse Planes
AU  - Sergey Tomin
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06730
UR  - https://arxiv.org/abs/2611.06730
AB  - In accelerator switchyards with shared magnets, a beam may traverse a quadrupole with offsets in both transverse planes, a configuration that cannot be represented by a single conventional horizontal or vertical combined-function bend. Such an off-axis quadrupole bends the reference trajectory and generates dispersion simultaneously in both planes. We derive a compact analytical 6×6 transfer matrix about the curved reference trajectory. The model is formulated in Bishop coordinates using a weak-curvature approximation that retains the longitudinal variation of both reference-curvature components and the resulting dispersion in both transverse planes. The analytical linear model is compared with a sliced representation based on conventional second-order combined-function bend maps and with direct numerical integration of the Lorentz equations in the ideal Cartesian quadrupole field.
ER  -