A New Normal Form for Multidimensional Mode Conversion

Journal Article · Fri Sep 28 00:00:00 EDT 2007 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2800532· OSTI ID:21035907

Tracy, E R; Richardson, A S ^[1]; Kaufman, A N ^[2]; Zobin, N ^[3]

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1. Physics Department, William and Mary, Williamsburg, VA 23187-8795 (United States)
2. Lawrence Berkeley National Laboratory and Physics Department, UC Berkeley, Berkeley, CA 94720 (United States)
3. Mathematics Department, William and Mary, Williamsburg, VA 23187-8795 (United States)

Linear conversion occurs when two wave types, with distinct polarization and dispersion characteristics, are locally resonant in a nonuniform plasma [1]. In recent work, we have shown how to incorporate a ray-based (WKB) approach to mode conversion in numerical algorithms [2,3]. The method uses the ray geometry in the conversion region to guide the reduction of the full NxN-system of wave equations to a 2x2 coupled pair which can be solved and matched to the incoming and outgoing WKB solutions. The algorithm in [2] assumes the ray geometry is hyperbolic and that, in ray phase space, there is an 'avoided crossing', which is the most common type of conversion. Here, we present a new formulation that can deal with more general types of conversion [4]. This formalism is based upon the fact (first proved in [5]) that it is always possible to put the 2x2 wave equation into a 'normal' form, such that the diagonal elements of the dispersion matrix Poisson-commute with the off-diagonals (at leading order). Therefore, if we use the diagonals (rather than the eigenvalues or the determinant) of the dispersion matrix as ray Hamiltonians, the off-diagonals will be conserved quantities. When cast into normal form, the 2x2 dispersion matrix has a very natural physical interpretation: the diagonals are the uncoupled ray hamiltonians and the off-diagonals are the coupling. We discuss how to incorporate the normal form into ray tracing algorithms.

• OSTI ID: 21035907
• Journal Information: AIP Conference Proceedings, Vol. 933, Issue 1; Conference: 17. topical conference on radio frequency power in plasmas, Clearwater, FL (United States), 7-9 May 2007; Other Information: DOI: 10.1063/1.2800532; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ALGORITHMS
CONVERSION
COUPLING
EIGENVALUES
GEOMETRY
HAMILTONIANS
MATHEMATICAL SOLUTIONS
MATRICES
MODE CONVERSION
PHASE SPACE
PLASMA
PLASMA INSTABILITY
PLASMA WAVES
POLARIZATION
RF SYSTEMS
WAVE EQUATIONS