  In this paper we study the scaling relations for the triggering of the fast,
or "ideal", tearing instability starting from equilibrium configurations
relevant to astrophysical as well as laboratory plasmas that differ from the
simple Harris current sheet configuration. We present the linear tearing
instability analysis for equilibrium magnetic fields which a) go to zero at the
boundary of the domain and b) contain a double current sheet system (the latter
previously studied as a cartesian proxy for the m=1 kink mode in cylindrical
plasmas). More generally, we discuss the critical aspect ratio scalings at
which the growth rates become independent of the Lundquist number $S$, in terms
of the dependence of the $\Delta'$ parameter on the wavenumber $k$ of unstable
modes. The scaling $\Delta'(k)$ with $k$ at small $k$ is found to categorize
different equilibria broadly: the critical aspect ratios may be even smaller
than $L/a \sim S^{\alpha}$ with $\alpha=1/3$ originally found for the Harris
current sheet, but there exists a general lower bound $\alpha\ge1/4$.
