## 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:

MIT-PSFC

77 Mass Ave.

Cambridge, MA 02139

USA

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.,

http://www.lodestar.com/LRCreports/kwavelets.pdf

(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.

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