skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Statistically-averaged rate equations for intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations

Abstract

This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.

Authors:
; ;
Publication Date:
Research Org.:
Princeton Univ., Princeton Plasma Physics Lab., NJ (United States)
Sponsoring Org.:
USDOE Office of Energy Research, Washington, DC (United States); Office of Naval Research, Washington, DC (United States)
OSTI Identifier:
304184
Report Number(s):
PPPL-3258
ON: DE98050122; TRN: 99:003158
DOE Contract Number:  
AC02-76CH03073
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: Aug 1997
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; BEAM DYNAMICS; BEAM TRANSPORT; MAGNETIC FIELDS; NONLINEAR PROBLEMS; BOLTZMANN-VLASOV EQUATION; BEAM EMITTANCE; BEAM FOCUSING MAGNETS; MATHEMATICAL MODELS; CHARGED PARTICLES

Citation Formats

Davidson, R C, Lee, W W, and Stoltz, P. Statistically-averaged rate equations for intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations. United States: N. p., 1997. Web. doi:10.2172/304184.
Davidson, R C, Lee, W W, & Stoltz, P. Statistically-averaged rate equations for intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations. United States. doi:10.2172/304184.
Davidson, R C, Lee, W W, and Stoltz, P. Fri . "Statistically-averaged rate equations for intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations". United States. doi:10.2172/304184. https://www.osti.gov/servlets/purl/304184.
@article{osti_304184,
title = {Statistically-averaged rate equations for intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations},
author = {Davidson, R C and Lee, W W and Stoltz, P},
abstractNote = {This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.},
doi = {10.2172/304184},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1997},
month = {8}
}