ON THE STABILITY OF A RIGIDLY ROTATING LIQUID COLUMN WITH AXIAL MAGNETIC FIELD

Abstract

We have discussed the stability of a rigidly rotating infinite liquid column ofinfinite conductivity in the presence of a uniform axial magnetic field. We have derived the dispersion: relation in the general case taking the cylinder to be self-gravitating and accounting for the surface tension forces on the free surface of the liquid. We have shown that previous results obtained by Rayleigh Hocking and Simon are particular cases of the present dispersion relation. We have discussed the present disperion relation for large wave-length disturbances neglecting surface tension forces in the cases of (i) non-gravitating cylinder with the velocity of rotation small on the surface compared with the Alfven wave velocity (ii) nongravitating cylinder with velocity of rotation large on the surface compared with the Alfven wave velocity and (iii) gravitating cylinder. We find that in case (i) there is stability but in the other two cases disturbances are unstable.