Intense nonneutral beam propagation in a periodic solenoidal field using a macroscopic fluid model with zero thermal emittance Page: 4 of 26
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I. INTRODUCTION
Periodic focusing accelerators"4 have a wide range of applications varying from basic
scientific research to industrial applications. There is growing interest in developing an
improved theoretical understanding of the nonlinear dynamics, and stability and transport
properties of nonneutral charged particle beams in advanced high-current accelerators57
for applications such as heavy ion fusion, tritium production, and nuclear waste treatment.
Indeed, in many regimes of practical interest, the beam intensity (as measured by the charge
density and current density) is sufficiently high that self-field effects dominate the thermal
effects associated with the spread in momentum of the beam particles. A kinetic treatment of
beam propagation based on the nonlinear Vlasov-Maxwell equations, 1,8-14 although provid-
ing a complete description of collective processes, is often difficult to implement analytically.
It is the purpose of this paper to develop a macroscopic cold-fluid model15 that provides an
adequate treatment of intense beam propagation through a periodic focusing solenoidal field
in circumstances where space-charge effects dominate the effects of thermal beam emittance.
By way of background, kinetic models of intense beam propagation based on the Vlasov-
Maxwell equations describe the nonlinear evolution of the distribution function fb(x, p, t) in
the phase space (x, p) and the interaction of the beam particles with the average electric and
magnetic fields, E(x, t) and B(x, t). On the other hand, a macroscopic fluid model of intense
beam propagation describes the nonlinear evolution of bulk beam properties such as the
beam density nb(x, t) = f dapfb and average flow velocity Vb(x, t) = n-1 f d3pvfb, and also
requires ancillary assumptions (such as negligibly small thermal emittance, or an assumed
equation of state for the pressure tensor) in order to truncate the macroscopic moment
equations. While not containing the detailed information on the distribution of particles in
momentum space, a macroscopic fluid model does describe the evolution in configuration
space of macroscopic quantities such as nb(x, t) and Vb(x, t). Such a macroscopic description
is intrinsically simpler theoretically than a kinetic model which describes the evolution of
the distribution function in the phase space (x, p).2
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Davidson, R. C.; Stoltz, P. & Chen, C. Intense nonneutral beam propagation in a periodic solenoidal field using a macroscopic fluid model with zero thermal emittance, report, August 1, 1997; Princeton, New Jersey. (https://digital.library.unt.edu/ark:/67531/metadc684231/m1/4/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.