Implementation of the Quiet Implicit PIC (QIP) moment equations in toroidal geometry

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:489382

Nystrom, W D; Barnes, D C; Nebel, R A ^[1]

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1. Los Alamos National Lab., NM (United States)

The Quiet Implicit PIC (QIP) method separates the distribution function into a bulk distribution f{sub 0}, describing the fluid-like behavior, and a remaining part {delta}f, describing the intrinsically kinetic behavior. For fusion plasmas, f{sub 0} is chosen as a local Maxwellian distribution. The evolution of f{sub 0} is governed by Maxwell`s equations and a set of moment equations which include closure terms depending on {delta}f. The evolution of {delta}f is represented by marker particles which follow the characteristics of the kinetic equation in the PIC (Particle In Cell) technique. The attractiveness of the QIP equations is the potential to efficiently and accurately model the fluid-like behavior of low-collisionality plasmas while retaining kinetic effects through {delta}f. Shot noise is sufficiently low that physically important fluctuations are resolved. The numerical closure of the moment equations provided by QIP also provides more insight into analytical closure schemes. The implementation of QIP divides into two parts. First, the moment equations coupled to Maxwell`s equations are solved on a computational grid. Second, particle equations of motion determine {delta}f which is then used to close the moment equations. Disparate time scales of the plasma require implicit time differencing for the moment equation solution. This leads to a large, stiff linear system, whose solution presents the major numerical challenge. Implementation of the first part of the QIP algorithm has recently been completed in the TPCN code by the addition of the pressure evolution equation. Additionally, TPCN now solves the implicitly time-differenced moment-Maxwell equations in a numerically generated orthogonal equilibrium flux coordinate system using the orthogonal trajectory method. This greatly facilitates separating the disparate scales associated with modes parallel and perpendicular to the equilibrium magnetic field.

• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 489382
• Report Number(s): CONF-960354--
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ALGORITHMS
DISTRIBUTION FUNCTIONS
GEOMETRY
MAXWELL EQUATIONS
PLASMA SIMULATION
TOROIDAL CONFIGURATION