Finite-width currents, magnetic shear, and the current-driven ion-cyclotron instability

Earlier results showing that nonlocal effects due to even a small magnetic shear produce a significant reduction of the growth rate of the ion-cyclotron instability driven by a uniform current are now generalized to finite-width currents. Externally prescribed as well as self-consistent shears are considered. If the current width Lc exceeds the shear length Ls, the previous results are recovered. Shear becomes less effective with reduction of Lc, and for typical parameters, the growth rate attains its (shearless) local value for Lc/ Ls ≲10−2. Nonlocal effects of the finite current width itself come into play if Lc is further reduced to a few ion Larmor radii and can quench the instability.