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The linear perturbation equation of the tearing instability derived in LSCtheory (Loureiro, Schekochihin, and Cowley, PoP2007) is numerically examined asan initial value problem, where the inner and outer regions are seamlesslysolved under uniform resistivity. Hence, all regions are solved as theresistive MHD (magnetohydrodynamics). To comprehensively study physicallyacceptable perturbation solutions, the behaviors of the local maximum pointsrequired for physically acceptable solutions and zero-crossing points, at which\phi=0 and \psi=0, are examined. Eventually, the uniform resistivity assumed inthe outer region is shown to play an important role in improving someconclusions derived from the theory. In conclusion, the upper limit\lambda_{up} of the growth rate obtained in the improved (modified) LSC theoryis shown to be regulated by the Alfven speed measured in the outer region. Itis also shown to be partially consistent with the growth rate in the lineardeveloping stage of the impulsive tearing instability observed in thecompressible MHD simulation of the plasmoid instability (PI) based on uniformresistivity.

A New Approach of Linear Theory of Tearing Instability in Uniform Resistivity