Traveling convection vortices (TCV) are studied using a theoretical ideal MHD model for the equilibrium and perturbed plasma. In this first approach, we do not consider the viscosity and the flow of the plasma column in the equilibrium. The linearized equations are solved using normal mode analysis. The solutions show an m = 1 kink instability which is in good agreement with the experimental data. It is calculated numerically a growth rate of 28 minutes to be compared with experimental data, indicating a quite good result with our model. Clearly, the results indicate the behaviour of the TCV as a kind of kink instability as supported by the agreement between theoretical and experimental values for the growth rate. Also the filamentation currents calculated through the theoretical model agree quite well with the experimental observations by satellites.
