Intense electron beams which are partially current neutralized can be unstable to transverse modes which form small pinch structures. Beams guided by strong $B_z$ fields experience a circular particle drift at frequency $\frac{{{\omega }_{\beta }}^2}{{\omega }_c}$, which proves highly destabilizing for filamentary modes. Growth rates considerably exceed the resistive diffusion rates normal for a resistive instability. The mode may be difficult to distinguish experimentally from interchange, but our computed growth rates are in qualitative agreement with present experiments.

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