A globally diagonalizable alpha^2-dynamo operator, SUSY QM and the Dirac equation

TL;DR

This paper introduces a new class of semi-analytically solvable alpha^2-dynamo models using global diagonalization, linking them to SUSY quantum mechanics and the Dirac equation to gain spectral insights.

Contribution

It presents a novel approach to solving alpha^2-dynamo operators by global diagonalization, establishing connections to SUSY QM and the Dirac equation for spectral analysis.

Findings

New class of semi-analytically solvable dynamo models

Relation established between dynamo operators and Dirac equation

Analytical insights into the dynamo spectrum

Abstract

A new class of semi-analytically solvable MHD alpha^2-dynamos is found based on a global diagonalization of the matrix part of the dynamo differential operator. Close parallels to SUSY QM are used to relate these models to the Dirac equation and to extract non-numerical information about the dynamo spectrum.