Non-linear visco-resistive MHD modelling of reversed field-pinch fusion plasmas: viscosity coefficient studies

Numerical simulations of non-linear visco-resistive magneto-hydrodynamics (MHD) represent a fundamental tool in modelling magnetically confined fusion plasmas. In the case of the reversed-field pinch (RFP) configuration, SpeCyl [1] simulations have successfully predicted the rise of quasi-periodical oscillating helical self-organized states jointly exploiting two features [2]: the visco-resistive dissipation, represented by the dimensionless Hartmann number [3], and the non-ideal magnetic field helical boundary conditions [4, 5]. This work is focused on the viscosity, which represents the momentum transport coefficient of the model. So far, no unique consensus on the plasma viscosity evaluation in RFP plasmas has been developed [6]: the experimental estimates carried on according to classical [7] or turbulent transport theory [8-10] display orders of magnitude differences. As consequence of it, only a uniform viscosity profile without self-consistent time evolution was considered in the previous modelling activity, reducing it to a constant scalar of the model. On the contrary, in this work, we study the impact of non-uniform and time dependent viscosity. Firstly, we test the effect of different time-independent viscosity profiles, including the one derived according to the Braginskii formula of perpendicular viscosity [7], on both 2D and 3D numerical simulations. While not displaying important qualitative differences, such modification quantitatively modifies the tearing modes MHD activity and the plasma flow, suggesting a slight reduction of the magnetic field chaos for viscosities increasing towards the plasma edge. Secondly, we introduce (limited to the uniform profile case) a preliminary self-consistent time evolution of the Hartmann number. We express the latter as a function of the dominant mode magnetic energy: this allows mimicking the effect of increased magnetic order and plasma temperature, resulting in reduced visco-resistive dissipation and thus increased reconnection period in the RFP sawtooth activity. The results motivate further development of self-consistent viscosity and resistivity studies in 3D nonlinear MHD.