Inhomogeneous plasma filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves; in our case the Frenet frame changes in time and also depends upon the other coordinates taking into account the inhomogeneity of the plasma. The exponential perturbation method so commonly used to describe cosmological perturbations is applied to magneto hydrodynamic (MHD) plasma equations to find longitudinal modes describing Alfven wave's propagation modes describing plasma waves in the medium. Stability is investigated in the imaginary axis of the spectra of complex frequencies ω or Im(ω) ≠ 0.
Plasma MHD instability, Frenet frame, Alfven waves, planar filaments
