# Statistically-averaged rate equations for intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations [electronic resource].

- Published:
- Washington, D.C. : United States. Dept. of Energy. Office of Energy Research, 1997.

Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy. - Physical Description:
- 40 pages : digital, PDF file
- Additional Creators:
- Princeton University, United States. Department of Energy. Office of Energy Research, and United States. Department of Energy. Office of Scientific and Technical Information

##### Access Online

- Restrictions on Access:
- Free-to-read Unrestricted online access
- Summary:
- 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} ≪ S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub θ}{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 ′2} + Y{sup ′2}{r_angle}, mean-square beam radius {l_angle}X² + Y²{r_angle}, and coupled rate equations for the unnormalized transverse emittance ε(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X² + Y²{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for ε(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.
- Report Numbers:
- E 1.99:pppl--3258

pppl--3258 - Subject(s):
- Other Subject(s):
- Note:
- Published through SciTech Connect.

08/01/1997.

"pppl--3258"

"DE98050122"

Lee, W.W.; Davidson, R.C.; Stoltz, P. - Funding Information:
- AC02-76CH03073

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