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Title:
Statistically averaged rate equations for intense non-neutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations
Authors:
Davidson, Ronald C.; Lee, W. Wei-Li; Stoltz, Peter
Affiliation:
Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543
Publication:
Physics of Plasmas, Volume 5, Issue 1, pp. 279-291 (1998). (PhPl Homepage)
Publication Date:
01/1998
Origin:
AIP
Keywords:
P700350BEAM-PLASMA SYSTEMS, CHARGED-PARTICLE TRANSPORT, BOLTZMANN-VLASOV EQUATION, FOCUSING, NEUTRAL BEAM SOURCES, ANGULAR MOMENTUM, plasma-beam interactions, particle beam focusing
Abstract Copyright:
(c) 1998: American Institute of Physics.
DOI:
10.1063/1.872708
Bibliographic Code:
1998PhPl....5..279D

Abstract

In this paper we present a detailed formulation and analysis of the rate equations for statistically averaged quantities for an intense non-neutral beam propagating through a periodic solenoidal focusing field Bsol(x) with axial periodicity length S=const. The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius rb<<S, and small transverse momentum and axial momentum spread in comparison with the directed axial momentum pz=γbmβbc. The global rate equation is derived for the self-consistent nonlinear evolution of the statistical average <χ>=Nb-1∫dXdYdX'dY'χFb, where χ(X,Y,X',Y',s) is a general phase function, and Fb(X,Y,X',Y',s) is the distribution function of the beam particles in the transverse phase space (X,Y,X',Y') appropriate to the Larmor frame. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum <Pθ>, center-of-mass motion for <X> and <Y>, mean kinetic energy (1/2)<X'2+Y'2>, mean-square beam radius <X2+Y2>, and coupled rate equations for the unnormalized transverse emittance ɛ(s) and root-mean-square beam radius Rb(s)=<X2+Y2>1/2. Most importantly, the present derivation of nonlinear rate equations for various statistical averages <χ> allows for general azimuthal variation (∂/∂θ≠0) of the distribution function and self-field potential, and therefore represents a major generalization of earlier calculations carried out for the case of axisymmetric beam propagation.
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