Helmholtz operators on harmonic manifolds

Rainer Schimming; Henrik Schlichtkrull

doi:10.1007/bf02398435

Helmholtz operators on harmonic manifolds

Acta Mathematica ◽

10.1007/bf02398435 ◽

1994 ◽

Vol 173 (2) ◽

pp. 235-258 ◽

Cited By ~ 3

Author(s):

Rainer Schimming ◽

Henrik Schlichtkrull

Keyword(s):

Harmonic Manifolds ◽

Helmholtz Operators

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Almansi Decomposition for Dunkl-Helmholtz Operators

Wavelet Analysis and Applications - Applied and Numerical Harmonic Analysis ◽

10.1007/978-3-7643-7778-6_4 ◽

2007 ◽

pp. 35-42

Author(s):

Guangbin Ren ◽

Helmuth R. Malonek

Keyword(s):

Helmholtz Operators

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Locally excited magnethohydrodynamic waves in a uniform cylindrical plasma waveguide

Journal of Plasma Physics ◽

10.1017/s0022377800020614 ◽

1977 ◽

Vol 17 (2) ◽

pp. 281-300 ◽

Cited By ~ 3

Author(s):

W. N-C. Sy

Keyword(s):

Differential Operators ◽

Current Source ◽

Plasma Waveguide ◽

Mhd Waves ◽

Cylindrical Plasma ◽

Characteristic Roots ◽

Guided Modes ◽

Homogeneous Wave ◽

Helmholtz Operators ◽

Homogeneous Wave Equation

The guided modes of Woods' magnetohydrodynamic waveguide for a uniform, cylindrical plasma are shown to satisfy a homogeneous wave equation whose differential operator is the product of eight Helmholtz operators. The propagation constants of the Helmholtz operators are the characteristic roots of an 8 × 8 matrix which is derived and written down explicitly. This reformulated theory is extended to include localized sources which excite the guided modes. For certain cases, the Green's functions for the differential operators can be represented by Dini expansions in terms of modal eigenfunctions, which manifestly satisfy the boundary conditions. For the case of MHD waves excited by an azimuthally symmetric current source in a resistive, pressureless, inviscid, fully ionized plasma, a detailed solution is obtained which is in good qualitative agreement with experiments.

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