An Algorithm for Toroidal Field Harmonics Computation in Arbitrary Magnetic Configurations

Abstract

Toroidal magnetic configurations are widely exploited in industry and scientific research, involving a vast spectrum of applications, such as thermonuclear fusion, particle detectors, SMES systems and medical devices. To properly design and analyse these systems, it is crucial to determine the magnetic field generated by different configurations. The multipole expansion theory can be applied to the analysis of toroidal configurations, by solving the Laplace equation for the magnetic scalar potential in toroidal coordinates. Contrarily to the case of accelerator magnets with straight axis, in this case the correlation between the current distribution and the field harmonics cannot easily be identified. This paper proposes a methodology for the computation of field harmonics in toroidal coordinates, which is validated by comparison with the results obtained through the Biot-Savart law. This work was carried out in the frame of the GaToroid project ongoing at CERN.

Particle tracking and beam optics analysis on a toroidal gantry for proton therapy

“…Somewhat related to beam optics and tracking is the expansion in series of the toroidal field. Harmonics expansion of toroidal magnetic field are described by van Milligen and Lopez Fraguas (1994), and numerically developed in Brouwer et al (2013), Gambini et al (2020). However, to our knowledge, there is no theory that can support the analysis of the beam optics features of a toroidal gantry for hadron therapy.…”