Variational principles and canonical theory for many-component plasmas with self-consistent field

Journal Article · Thu May 01 00:00:00 EDT 1980 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.863099· OSTI ID:5453250

Wilhelm, H E

The Lagrangian L=..integral integral integral..L(q/sub s/,partialq/sub s//partialt,delxq/sub s/)d/sup 3/r and Hamiltonian H=..integral integral integral..H(p/sub s/,q/sub s/,delxq/sub s/)d/sup 3/r for many-component plasmas with self-consistent field interactions are derived. The canonical fields p/sub s/(r,t) and q/sub s/(r,t) are defined by p/sub s/=m/sub s/v/sub s/ and partialq/sub s//partialt=n/sub s/v/sub s/, respectively, where n/sub s/(r,t) is the density and v/sub s/(r,t) is the velocity of the component s, s=1,2,...,N. Based on the action principle, the Lagrange and Hamilton equations of motion for the components (s) are presented as functional derivatives of L and H with respect to the canonical momenta p/sub s/ and q/sub s/. It is shown that the new formulations of many-component plasma dynamics have mathematical advantages compared with the conventional variational principles and hydrodynamic equations.

• Research Organization: Department of Engineering Sciences, University of Florida, Gainesville, Florida 32611
• OSTI ID: 5453250
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 23:5; ISSN PFLDA
• Country of Publication: United States
• Language: English

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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOLTZMANN-VLASOV EQUATION
DIFFERENTIAL EQUATIONS
ELECTROHYDRODYNAMICS
EQUATIONS
EQUATIONS OF MOTION
FLUID MECHANICS
FUNCTIONS
HAMILTONIAN FUNCTION
HYDRODYNAMICS
LAGRANGIAN FUNCTION
MECHANICS
PLASMA
SELF-CONSISTENT FIELD
VARIATIONAL METHODS