The pseudoHermiticity of MHD dynamo operators
The pseudoHermiticity of MHD dynamo operators
Günther, U.
The presentation provides a short introduction to MHD dynamos and to the pseudoHermiticity properties of the matrix differential operator of the spherically symmetric α^{2}dynamo.
In the first part of the lecture, the underlying physics is described starting from a discussion of the homopolar disk dynamo, of field reversals of the Earth's magnetic field and of the dynamo experiments in Riga and Karlsruhe. Furthermore, a sketchy outline of the helicity based meanfield technique for the MHD induction equation is presented and the closing of the dynamo cycle is discussed.
In the second part, attention is paid to the derivation of the matrix differential operator for the spherically symmetric α^{2}dynamo and its associated quadratic operator pencil. Boundary conditions, pseudoHermiticity and Kreinspace features are used to heuristically explain the levelcrossing properties of the spectrum. Along the lines of [1], the derivation of a constructive nogo theorem for isospectral dynamo configurations is described and interesting open problems are listed.
[1] Günther U. and Stefani F., Isospectrality of spherical MHD dynamo operators: pseudoHermiticity and a nogo theorem,
J. Math. Phys. 44, 2003, 3097, mathph/0208012.

Invited lecture (Conferences)
seminar of the Doppler Institute for mathematical physics at the Czech Technical University, Prague, October 07, 2003.
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