Variational principles with Padé approximants for tearing mode analysis

Tearing modes occur in several distinct physical regimes, and it is often important to compute the inner layer response for these modes with various effects. There is a need for an approximate and efficient method of solving the inner layer equations in all these regimes. In this paper, we introduce a method of solving the inner layer equations based on using a variational principle with Padé approximants. For all the regimes considered, the main layer equations to be solved are inhomogeneous, and Padé approximants give a convenient and efficient method of satisfying the correct asymptotic behavior at the edge of the layer. Results using this variational principle—Padé approximant method in three of these regimes is presented. These regimes are the constant-ψ resistive-inertial (RI) regime, the constant-ψ viscoresistive regime, and the non-constant-ψ inviscid tearing regime. The last regime includes the constant-ψ RI regime and the inertial regime. The results show that reasonable accuracy can be obtained very efficiently with Padé approximants having a small number of parameters.