Adequacy of Mathematical Models
in Dense Relativistic Electron Beam Optics

V. A. Syrovoi

Received May 23, 2002

Abstract—The problem of intrinsic adequacy of approximate and numerical approaches is investigated. Unlike
the problem of extrinsic adequacy (agreement of the hydrodynamic description with the experiment), the above
problem must be solved within the framework of a mathematical model itself. Extraordinary results obtained
using the trajectory analysis and traditional paraxial theory algorithms are illustrated by several examples which
indicate that the regions where these most widespread approaches can be applied have not been determined so
far. The principles of constructing numerical models in the vicinity of the cathode and symmetry axis, which
are specific regions, are formulated. Algorithms are developed for calculating the characteristics of systems
with substantially different scales. The set of reference exact solutions providing tests of approximate and
numerical models is studied. Calculation results obtained using the trajectory analysis algorithms for essentially
three-dimensional (3D) configurations (multibeam systems) and highly compressed flows are estimated. Appli-
cation of the paraxial theory to solving problems of beam propagation in the presence of specified external
fields, which are traditionally treated using the trajectory analysis, is discussed. Requirements of approximate
and numerical models are formulated which ensure investigations of the physical nature of a phenomenon
rather than the intrinsic properties of a model.

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