A Numerical Instability in an ADI Algorithm for Gyrokinetics

Technical Report · Fri Dec 17 04:00:00 EST 2004

DOI:https://doi.org/10.2172/836494· OSTI ID:836494

Belli, E A ^[1]; Hammett, G W

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1. Princeton Plasma Physics Laboratory

We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving one spatial and two velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams-Bashforth algorithm, where the parallel motion operator v{sub {parallel}} {partial_derivative}/{partial_derivative}z is treated implicitly and the field terms are treated with an Adams-Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms.

• Research Organization: Princeton Plasma Physics Lab., Princeton, NJ (US)
• Sponsoring Organization: USDOE Office of Science (SC) (US)
• DOE Contract Number: AC02-76CH03073
• OSTI ID: 836494
• Report Number(s): PPPL-4034
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ALGORITHMS
COMPUTATIONAL PHYSICS
DIMENSIONS
DISTRIBUTION FUNCTIONS
ELECTRIC FIELDS
GYROKINETIC EQUATIONS
IMPLEMENTATION
INSTABILITY
KINETICS
NUMERICAL METHODS
PLASMA
STABILITY
VELOCITY
WAVELENGTHS