PREPRINT

# Plasma planar filament instability and Alfven waves

Inhomogeneous plasmas 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 perturbatons is applied to magnetohydrodynamic (MHD) plasma equations to find longitudinal modes describing Alfven waves propagation modes describing plasma waves in the medium. Stability is investigated in the imaginary axis of the spectra of complex frequencies $\omega$ or $Im\left(\omega \right)\ne 0$.