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

Part of the Ettore Majorana International Science Series book series (EMISS, volume 53)


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 .


Lorentz Force Coil Head Radial Force Multipole Expansion Straight Part 


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  1. 1.
    C. Daum and D.ter Avest, Three-dimensional computation of the magnetic fields and Lorentz forces of an LHC dipole magnet, NIKHEF-H 89/12 and LHC note No. 94.Google Scholar
  2. 2.
    The large Hadron Collider in the LEP Tunnel, Eds.G.Briànti and K. Hübner, CERN 87–05, 27 May 1987.Google Scholar
  3. 3.
    D. Leroy, R.Perin, G. de Rijk, W. Thomi, Design of a High Field Twin Aperture Superconducting Dipole Model, CERN SPS/87–32 (EMA), LHC note No 62.Google Scholar
  4. 4.
    TOSCA, Vector Fields, Oxford, UK.Google Scholar
  5. 5.
    POISSON, CERN program library, T604.Google Scholar
  6. 6.
    K.H. Mess, P. Schmuser, Superconducting Accelerator Magnets, DESY HERA 89–01, and in the Proceedings of the CERN Accelerator School on Superconducivity in Particle Accelerators, Ed. S. Turner, CERN 89–04, p. 87.Google Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • C. Daum
    • 1
  1. 1.NIKHEF-HAmsterdamNetherlands

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