Nuclear Science and Engineering / Volume 36 / Number 1 / April 1969 / Pages 97-104
Technical Paper / dx.doi.org/10.13182/NSE69-A18860
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Solutions obtained by expansion in a series of spatial modes and by an iterative method are compared for both space and space-time problems. In the space problem, the modal expansion is used to justify the iterative results. A useful nonlinear transformation is introduced to aid in solving multi-mode approximations. The space-dependent fast adiabatic excursion model, or Fuchs-Nordheim model, is solved by a novel iterative approach. This iterative solution is valid for large disturbances, as well as small, thus improving results obtained by approximate modal expansions. The derivation of the space-independent Fuchs-Nordheim model from the space-dependent equation is shown to follow in a more straightforward manner than derivations based on modal approximations.