Artificial neural networks for the representation of axisymmetric magnetic fields in TWT collectors

The focusing magnetic field in TWT collectors is usually generated by means of permanent magnets suitably positioned along the symmetry axis. In numerical simulations, 3D representations of this axis-symmetric magnetic field are generally built from the knowledge of experimentally measured 1D symmetry-axis values, by using a model based on equivalent ideal loop sources (Vaughan, 1972 and 1974; Stankiewicz, 1979; Jackson, 1999; Coco et al, 2001; Coco and Laudani, 2002). From these sources, off-axis fields are computed (radial and axial components), either by means of exact analytic expressions in terms of elliptic integrals or by means of approximated partial series expansions or Legendre polynomials. The ideal loop model is considered to work satisfactorily if it is able to reproduce correctly the input experimental on-axis values. In this paper a new efficient procedure to calculate the parameters of the equivalent ideal loop representation by using a neural approach is presented. The neural approach allows us to obtain a very accurate representation of complicated shape fields by using only few coils, in such a way as to reduce computational effort.