Modeling the fringe field of permanent magnet multipoles using numerical simulations

Area of Science:

• Physics
• Accelerator Science
• Computational Electromagnetics

Background:

• Permanent magnet multipoles (PMMs) are crucial for particle beam focusing and plasma confinement in accelerators.
• Current methods rely on computationally intensive 3D magnetic field maps or simplified "hard-edge" models that neglect fringe fields.

Purpose of the Study:

• To develop an accurate and efficient analytical model for PMM fringe fields.
• To provide an alternative to complex simulations and inaccurate "hard-edge" models for accelerator design and analysis.

Main Methods:

• Developed an analytical model for PMM magnetic fields using Fourier multipole expansion.
• Introduced a general axial potential function dependent on PMM length and a parameter λ.
• Derived a first-order analytical model satisfying Maxwell's equations and assessed higher-order models using χ² estimators.

Main Results:

• The proposed analytical model accurately reproduces PMM magnetic fields, including fringe fields.
• A simple first-order model is derived, suitable for fast analytical calculations.
• The model's quality is validated, and the parameter λ is related to PMM geometry (quadrupole, hexapole, multipole).

Conclusions:

• The developed analytical model offers an advantageous replacement for the "hard-edge" model in applications requiring fast calculations.
• The model's dependence on PMM geometry allows for direct integration into simulation programs.
• This work enhances the capability for precise and efficient magnetic field modeling in accelerator physics.