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A finite element wave packet approach to solving the plasma wave equations

US-Japan Workshop
Author: John C. Wright
Requested Type: Oral Presentation
Submitted: 2007-07-06 19:26:26

Co-authors: H. Kohno, P. T. Bonoli, J. P. Freidberg

Contact Info:
77 Mass Ave.
Cambridge, MA   02139

Abstract Text:
The use of the Fourier basis to evaluate the plasma
dielectric response and solve the Maxwell-Vlasov plasma wave
equations has a long history in the plasma community. This
is in part due to its success and appropriateness but also
in part to legacy. Wave techniques have continually built
upon the initial homogenous work. Dispersion relations and
plasma dielectrics were all derived in infinitely homogenous
media. They continued to be used in full wave and ray
tracing codes with inhomogenous media because in the former
case, it was still a good approximation that the
wave-particle interaction was local, and in the later case
through the use of the WKB approximation. In addition,
using Fourier basis, either in Cartesian space, or in
poloidal and toroidal periodic dimensions permitted an easy
identification of the parallel wavenumber and a connection
back the large body of homogeneous theory. These techniques
have worked well and enjoyed great success, especially
recently with the advent of wide access to massively
parallel computers (1). An unfortunate consequence to using
a global basis such as Fourier, is the large dense numerical
systems that result, and their poor scaling in terms of
physics/FLOP. That is, because the matrices are fully dense
or composed of dense blocks, doubling the resolution
requires eight times more cpu-hours. Building on previous
efforts using Morlet wavelets (2) and Gabor transforms
(3,4), we are motivated to explore the use of discrete
finite time transforms as a finite elements basis.
Specifically, we use a quadratic envelope windowed Fourier
transform. This avoids the periodicity needed by Morlet
wavelets and the infinite support of the Gabor transform.
We demonstrate the techniques performance on the model
problems of the Airy and Wasov equations, and show how the
plasma dielectric may be formulated in this basis.

(1) J. C. Wright et al., Nucl. Fusion, 2005, 45, 1411-1418

(2) D. A. D'Ippolito, J.R. Myra et al.,

(3) A. Pletzer, C. K. Phillips, D. N. Smithe, "Gabor
Wave Packet Method to Solve Plasma Wave Equations", 15th
Topical Conference on Radio Frequency Power in Plasmas. AIP
Conference Proceedings, Volume 694, pp. 503-506 (2003)]

(4) S. Smith, C. Phillips, E. Valeo, "The Wavelet Approach
to Solving the Mode Conversion Wave Equation", 2006 48th
Annual Meeting of the Division of Plasma Physics

*This work was supported by the CSWIM Fusion Simulation Project. CSWIM is jointly funded by the Office of Fusion Energy Sciences (FES) and the Office of Mathematical, Information, and Computational Science (MICS) of the U. S. Dept. of Energy Office of Science.