The magnetic field produced by a protons beam with the three-axial Gauss distribution

  • Stanisław Bednarek Chair of Informatics, University of Łódź
  • Julian Płoszajski Chair of Informatics, University of Łódź
Keywords: magnetic field, electric field, space distribution, Lorentz transformation, protons bunch, accelerator


This paper contains a description of an original calculations method of electric field intensity and magnetic field induction which were produced by bunches assembling relativistic proton beams. The spatial distribution of electric charge density inside the bunch is described by the three-axial Gauss distribution. The method consists of component calculations of the electric field intensity at the frame of reference moving with the bunch and further, on the application of the Lorentz transformation to electromagnetic fields. As a result, we obtained values of components of electric field intensity and magnetic field induction at the rest frame of reference where could be located examined samples. Formula worked out with the method were discussed and gathered at the tables. Formula were applied to calculations of proton bunches accelerated in the LHC. The collected results were presented in the form of charts and discussed. Useful values of magnetic field induction and electric field intensity were very close to already published at the paper in which one-axial Gauss distribution was applied. The results contained in this paper confirmed possibility of using such particle bunches as sources of strong magnetic field pulses, useful among the others, in solid state physics, condensed phase physics and electronics as well.


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