# Magnetic design of twin aperture cos-theta superconducting dipoles with a semi-analytic approach

## TL;DR

This paper introduces a semi-analytic magnetic design method for twin aperture cos-theta superconducting dipoles, effectively accounting for cross-talk and iron yoke effects, demonstrated on LHC upgrade magnets.

## Contribution

A novel semi-analytic model for twin aperture dipole design that considers cross-talk and iron yoke effects, improving upon purely analytic approaches.

## Key findings

- The model accurately predicts magnetic field harmonics considering cross-talk.
- Iron yoke effects do not alter the optimal configuration significantly.
- Two electromagnetic designs for LHC D2 dipole are presented.

## Abstract

The magnetic design is a basic aspect of the superconducting magnets for particle accelerators. When dealing with single aperture cos-theta type dipoles, at the first order, the design can be performed with an analytic approach based on a sector dipole approximation followed by a numerical optimization. For double aperture dipoles the magnetic cross-talk between apertures makes this approach unfeasible. We have developed a semi-analytic model, which starting from a sector dipole approximation, allows to consider the cross-talk between the two apertures. We also demonstrate that the iron yoke contribution to harmonics, although dominant, does not change the optimal configuration found in its absence. As examples, we show two possible electromagnetic designs for the D2 dipole of the High Luminosity upgrade of LHC. The semi-analytic model can be generalized to a larger class of magnets.