  A first-principles method to calculate the critical temperature gradient for
the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is
presented. We find that conventional notions of the connection length
previously invoked in tokamak research should be revised and replaced by a
generalized correlation length to explain this onset in stellarators. Simple
numerical experiments and gyrokinetic theory show that localized "spikes" in
shear, a hallmark of stellarator geometry, are generally insufficient to
constrain the parallel correlation length of the mode. ITG modes that localize
within bad drift curvature wells that have a critical gradient set by peak
drift curvature are also observed. A case study of nearly helical stellarators
of increasing field period demonstrates that the critical gradient can indeed
be controlled by manipulating magnetic geometry, but underscores the need for a
general framework to evaluate the critical gradient. We conclude that average
curvature and global shear set the correlation length of resonant ITG modes
near the absolute critical gradient, the physics of which is included through
direct solution of the gyrokinetic equation. Our method, which handles general
geometry and is more efficient than conventional gyrokinetic solvers, could be
applied to future studies of stellarator ITG turbulence optimization.
