New Techniques for Future Accelerators III pp 107-114 | Cite as

# Three-Dimensional Computation of Magnetic Fields and Lorentz Forces of an LHC Dipole Magnet

## Abstract

For the design of magnets, a detailed knowledge of fields and forces is needed as well in the straight sections of the coil as in the coil heads. The method of computation presented here is designed for structures with shell coils around a cylindrical aperture surrounded by a cylindrical iron yoke. The effect of the iron is taken into account using the method of image currents for a fixed value of the permeability, and, hence, the variation of the permeability in the iron is not taken into account. The fields and forces are calculated as the sum of the fields and forces of the strands out of which the conductors are composed. The strands are “ideal” strands, i.e. they are parallel to the axis of the conductor and thus do not follow the actual layout of the strands in a Rutherford cable. The current is concentrated in the centre of the strands. The magnetic field due to a single strand is calculated with the Biot-Savart law using delta functions for the radial and angular current distributions. The integrals in the Biot-Savart law can now be evaluated. Fields are always calculated as the sum of the contributions of the individual strands. A detailed description is used for constant perimeter coil heads. Lorentz forces are calculated at the centre of either the strands, or the conductors, or the blocks with the current concentrated at the centre. Results on magnetic fields and field integrals, a multipole expansion of the field integrals, and the magnetic length are presented. An extensive account of the method is given in Ref . 3 .

## Keywords

Lorentz Force Coil Head Radial Force Multipole Expansion Straight Part## Preview

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## References

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