Analytical expression of a finite, long, conical canted-cosine-theta coil for particle collider interaction regions

Journal Article · Mon Oct 27 00:00:00 EDT 2025 · Physical Review Accelerators and Beams

DOI:https://doi.org/10.1103/n8tc-1334· OSTI ID:3004779

Yang, Ye ^[1]; Caspi, Shlomo ^[1]; Brouwer, Lucas ^[1]

---

1. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Magnets in the accelerator interaction region (IR) present significant challenges because of high field requirements and limited available space. Conical-shaped magnets offer advantages in these environments by allowing closer placement to the interaction point while maintaining clearance from synchrotron radiation. Interestingly, numerical studies have shown that conical canted-cosine-theta (CCT) designs produce a constant field distribution along the axial direction in the IR quadrupoles for the Electron-Ion Collider (EIC) at Brookhaven National Laboratory. However, the field harmonics generated by conical CCT windings are not yet fully understood. This paper presents an analytical approach to describe the magnetic field produced by a conical surface current and proposes a method for designing conical CCT magnets for accelerator applications. First, we begin with a surface current sheet having a general cosine-theta distribution in spherical coordinates and solve the vector potential using the Green’s function. The magnetic fields generated by the conical current sheet are expressed using associated Legendre polynomials. These results are then related to circular field harmonics and integral field harmonics for designing a coil that produces a pure multipole field. Next, a single layer of the conical CCT winding path is produced based on the cosine-theta current distribution. Finally, the magnetic field quality of dipole and quadrupole conical CCT coils with multiple layers is verified using the Biot-Savart law.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 3004779
• Journal Information: Physical Review Accelerators and Beams, Journal Name: Physical Review Accelerators and Beams Journal Issue: 10 Vol. 28; ISSN 2469-9888
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English