The growth of the tearing mode: Boundary and scaling effects

The linear development of the resistive tearing instability in a sheet pinch is investigated numerically. Particular emphasis is placed on effects which differentiate magnetic tearing in astrophysical situations from that in laboratory devices. These include extreme values of the parameters determining the mode growth and a variety of boundary conditions. Eigenfunction profiles for long and short wavelengths are computed and the applicability of the ‘‘constant Ψ’’ approximation is investigated. Nearby conducting walls tend to validate this condition and reduce the growth rate, especially for the long wavelength modes which, otherwise, disturb a larger region of the plasma than do short wavelength modes. Finally, the growth rate p is computed for values of the magnetic Reynolds number S up to 1012 and of the dimensionless wavelength parameter α down to 10−3. The results demonstrate, without approximation, the S2/5 scaling of p at large α (constant Ψ) and the S2/3 scaling at small α (nonconstant-Ψ). The α and S variation of the growth maximum, which would provide the dominant excitation in the absence of nearby boundaries, is specified for both single- and multiple-tearing layers. The growth maximum is shown to occur in a parametric regime where the constant Ψ approximation is not valid.