A new type of Alfven vortices which can exist in a plasma of very low pressure beta identical to pi p/B02<me/mi as well as with beta >me/mi is found. The reduced equations of drift-Alfven waves (DAW) are obtained. The vortices being solutions of the DAW equations have the analogous structure in both cases. With the help of the solutions the estimation on the main vortex parameters phi approximately A approximately ur0 is done which gives the values of a characteristic rotational velocity and a perturbation of the magnetic field in the vortex. Energy of the vortex tubes per length unit is calculated and it is shown that in both cases the vortex energy is negative. This means that in dissipative media the vortex energy is growing in absolute value (their size as well as the rotational velocity becomes higher).