Space-charge effects in warm ion sheet beams in the Vlasov--Maxwell approximation

Journal Article · Sat Sep 01 04:00:00 EDT 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859403· OSTI ID:6361407

Abraham-Shrauner, B ^[1]; Anderson, O A ^[2]

---

1. Department of Electrical Engineering, Washington University, St. Louis, MO (USA)
2. Lawrence Berkeley Laboratory, University of California, Berkeley, CA (USA)

A warm, intense, externally focused ion sheet beam is analyzed: a bounded one-component plasma that not only has practical interest but is well-suited for illustrating the use of some powerful new tools based on the use of Liouville invariants and Lie point group symmetries. The two-dimensional, time-independent Vlasov--Maxwell equations are shown to reduce to a set of one-dimensional, time-dependent, nonlinear Vlasov--Maxwell equations. Special examples of analytic solutions are given for two cases: (1) a uniform, but axially varying, warm ion beam and (2) a nonuniform, axially stationary, warm ion beam.With the spatial dependence of the ion beam density chosen, analytic expressions for the ion distribution function, electric fields, transverse bulk flow velocity, rms beam size, and rms emittance are derived. Some of these results corroborate previous work while others are new. In this derivation the usual Vlasov--Poisson equations for the ion beam are replaced by the self-consistent Vlasov--Maxwell equations; this generalization will be important for extensions of this treatment to asymmetric problems. A careful discussion of boundary conditions and of the simplifications used in the derivation is included.

• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6361407
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 2:9; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200 -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
BEAM EMITTANCE
BEAM NEUTRALIZATION
BEAMS
BOLTZMANN-VLASOV EQUATION
BOUNDARY CONDITIONS
COLLISIONLESS PLASMA
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EARTH ATMOSPHERE
EARTH MAGNETOSPHERE
ELECTRIC FIELDS
EQUATIONS
FOCUSING
FUNCTIONS
INVARIANCE PRINCIPLES
ION BEAMS
LIE GROUPS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
PLASMA SHEET
SPACE CHARGE
SPACE DEPENDENCE
STEADY-STATE CONDITIONS
SYMMETRY GROUPS
TIME DEPENDENCE
TWO-DIMENSIONAL CALCULATIONS