Abstract
The two-fluid resistive tearing mode instability in a periodic plasma cylinder of finite aspect ratio is investigated numerically for parameters such that the cylindrical aspect ratio and two-fluid effects are of order unity, hence the real and imaginary parts of the mode eigenfunctions and growth rate are comparable. Considering a force-free equilibrium, numerical solutions of the complete eigenmode equations for general aspect ratios and ion skin depths are compared and found to be in very good agreement with the corresponding analytic solutions derived by means of the boundary layer theory [A. Ito and J. J. Ramos, Phys. Plasmas 24, 072102 (2017)]. Scaling laws for the growth rate and the real frequency of the mode are derived from the analytic dispersion relation by using Taylor expansions and Padé approximations. The cylindrical finite aspect ratio effect is inferred from the scaling law for the real frequency of the mode.
Highlights
Our previous work [1] studied the linear stability of force-free equilibria in cylindrical geometry against two-fluid resistive tearing modes, extending the corresponding slab geometry theory for general ion skin depths [2] and carrying out a detailed benchmark between a fully numerical solution and an analytic dispersion relation derived by means of the boundary layer theory
We carry out a numerical solution of the eigenmode equations and examine the behavior of the analytic dispersion relation for a choice of parameters that yield a value of cylindrical effect parameter ρ of order unity
In order to further clarify the structure of the two-fluid tearing eigenfunctions and their parametric dependences on the ion skin depth, as well as the parametric dependence of the growth rate eigenvalue, we calculate the eigenfunctions ξand Qthat determine the analytic dispersion relation (26)
Summary
Our previous work [1] studied the linear stability of force-free equilibria in cylindrical geometry against two-fluid resistive tearing modes, extending the corresponding slab geometry theory for general ion skin depths [2] and carrying out a detailed benchmark between a fully numerical solution and an analytic dispersion relation derived by means of the boundary layer theory. We carry out a numerical solution of the eigenmode equations and examine the behavior of the analytic dispersion relation for a choice of parameters that yield a value of cylindrical effect parameter ρ of order unity.
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