Torsional Alfven waves in small scale current threads of the solar corona

Context. The magnetic field structuring in the solar corona occurs on large scales (loops and funnels), but also on small scales. For instance, coronal loops are made up of thin strands with different densities and magnetic fields across the loop. Aims. We consider a thin current thread and model it as a magnetic flux tube with twisted magnetic field inside the tube and straight field outside. We prove the existence of trapped Alfven modes in twisted magnetic flux tubes (current threads) and we calculate the wave profile in the radial direction for two different magnetic twist models. Methods. We used the Hall MHD equations that we linearized in order to derive and solve the eigenmode equation for the torsional Alfven waves. Results. We show that the trapped Alfven eigenmodes do exist and are localized in thin current threads where the magnetic field is twisted. The wave spectrum is discrete in phase velocity, and the number of modes is finite and depends on the amount of the magnetic field twist. The phase speeds of the modes are between the minimum of the Alfven speed in the interior and the exterior Alfen speed. Conclusions. Torsional Alfven waves can be guided by thin twisted magnetic flux-tubes (current threads) in the solar corona. We suggest that the current threads guiding torsional Alfven waves, are subject to enhanced plasma heating due to wave dissipation.