A new variational formulation of kinetic plasma theory and the application of moving finite elements
Conference
·
OSTI ID:5499989
A new variational formulation has been developed for the system of equations governing kinetic plasmas and electromagnetic fields. It is used to apply the method of Moving Finite Elements to the electromagnetic fields. The fields are expanded in a basis of linear finite elements on a movable, unstructured grid of triangles in 2D or tetrahedra in 3D, while the plasma distribution function is expanded in a basis of super particles. Minimization of the variational with respect to the time derivatives of the field quantities yields a coupled system of equations for simultaneously advancing the amplitudes and node positions, resulting in adaptive grid motion. The adaptivity of the grid may save a large factor in the size of the grid and the number of particles required in many problems. Minimization of the variational with respect to the time derivatives of the particle positions and velocities gives the equations of motion, providing consistent prescriptions for assigning particles to the grid and fields to the particles. Orthogonality conditions on the particles are derived as conditions for keeping their equations of motion independent. Collisions can be included in a natural way. The relationship between PIC methods and alternative methods of discretizing phase space is clarified.
- Research Organization:
- Los Alamos National Lab., NM (United States)
- Sponsoring Organization:
- DOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 5499989
- Report Number(s):
- LA-UR-91-2242; CONF-9109108--6; ON: DE91016072
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700103* -- Fusion Energy-- Plasma Research-- Kinetics
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
BOLTZMANN-VLASOV EQUATION
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
EQUATIONS OF MOTION
FINITE ELEMENT METHOD
FUNCTIONS
MATHEMATICAL SPACE
MAXWELL EQUATIONS
MOVING-BOUNDARY CONDITIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
PLASMA
PLASMA SIMULATION
SIMULATION
SPACE
VARIATIONAL METHODS
700103* -- Fusion Energy-- Plasma Research-- Kinetics
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
BOLTZMANN-VLASOV EQUATION
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
EQUATIONS OF MOTION
FINITE ELEMENT METHOD
FUNCTIONS
MATHEMATICAL SPACE
MAXWELL EQUATIONS
MOVING-BOUNDARY CONDITIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
PLASMA
PLASMA SIMULATION
SIMULATION
SPACE
VARIATIONAL METHODS