Helicity Injection Fluxes of Twist and Writhe

Abstract

We consider helicity flux equations proposed by previous authors and offer interpretations of these helicity injection equations with twist and writhe. At first, comparing Pariat’s helicity flux equation (2005, A&A, 439, 1191) with Longcope’s (2007, ApJ, 668, 571), we find that the Pariat’s helicity injection equation shows helicity evolution of continuous magnetic field lines, which is an extreme case of the Longcope’s multiple flux tube model. Next, we investigated Berger’s helicity flux density (1984, J. Fluid Mech., 147, 133) and Pariat’s on the positive and negative polarities, and confirmed that these equations produce different helicity fluxes on the positive and negative polarities. Under the idea of the multiple flux tube model, we propose two interpretations of helicity injection fluxes of twist and writhe; the single flux tube model and the continuous field line model. Recent results of helicity flux injections need to be reanalyzed.