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A New Normal Form for Multidimensional Mode Conversion.
- Source :
-
AIP Conference Proceedings . 9/15/2007, Vol. 933 Issue 1, p463-466. 4p. - Publication Year :
- 2007
-
Abstract
- 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 N×N-system of wave equations to a 2×2 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 2×2 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 2×2 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 933
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 26887839
- Full Text :
- https://doi.org/10.1063/1.2800532