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Effect of Pressure Anisotropy on the m = 1 Small Wavelength Modes in Z-Pinches

A generalization of Freidberg's perpendicular MHD model is used to investigate the effect of pressure anisotropy on the small wavelength internal kink (m = 1) mode instability in a Z-Pinch. A normal mode analysis of perturbed motion of an incompressible, collisionless and cylindrical plasma is performed. The stability criterion is (rΣB2)' ≤ 0, where Σ = 1 - (P|| - P⊥)/B2. It cannot be fulfilled without violation of the fire hose stability condition Σ ≥ 0.