Implications of the Electrostatic Approximation in the Beam Frame on the Nonlinear Vlasov-Maxwell Equations for Intense Beam Propagation
Abstract
This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.
- Authors:
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (US)
- OSTI Identifier:
- 792583
- Report Number(s):
- PPPL-3625
TRN: US0200782
- DOE Contract Number:
- AC02-76CH03073
- Resource Type:
- Technical Report
- Resource Relation:
- Other Information: PBD: 8 Nov 2001
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOLTZMANN-VLASOV EQUATION; ELECTROSTATICS; FOCUSING; POLARIZATION; SPACE CHARGE; CHARGED PARTICLES; PARTICLE BEAMS; BEAM BUNCHING
Citation Formats
Davidson, Ronald C, Lee, W Wei-li, Qin, Hong, and Startsev, Edward. Implications of the Electrostatic Approximation in the Beam Frame on the Nonlinear Vlasov-Maxwell Equations for Intense Beam Propagation. United States: N. p., 2001.
Web. doi:10.2172/792583.
Davidson, Ronald C, Lee, W Wei-li, Qin, Hong, & Startsev, Edward. Implications of the Electrostatic Approximation in the Beam Frame on the Nonlinear Vlasov-Maxwell Equations for Intense Beam Propagation. United States. https://doi.org/10.2172/792583
Davidson, Ronald C, Lee, W Wei-li, Qin, Hong, and Startsev, Edward. 2001.
"Implications of the Electrostatic Approximation in the Beam Frame on the Nonlinear Vlasov-Maxwell Equations for Intense Beam Propagation". United States. https://doi.org/10.2172/792583. https://www.osti.gov/servlets/purl/792583.
@article{osti_792583,
title = {Implications of the Electrostatic Approximation in the Beam Frame on the Nonlinear Vlasov-Maxwell Equations for Intense Beam Propagation},
author = {Davidson, Ronald C and Lee, W Wei-li and Qin, Hong and Startsev, Edward},
abstractNote = {This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.},
doi = {10.2172/792583},
url = {https://www.osti.gov/biblio/792583},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Nov 08 00:00:00 EST 2001},
month = {Thu Nov 08 00:00:00 EST 2001}
}