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Structure and stability of the magnetic solar tachocline
Rather weak fossil magnetic fields in the radiative core can produce the solar tachocline if the field is almost horizontal in the tachocline region, i.e. if the field is confined within the core. This particular field geometry is shown to result from a shallow (≲1 Mm) penetration of the meridional flow existing in the convection zone into the radiative core. Two conditions are thus crucial for a magnetic tachocline theory: (i) the presence of meridional flow of a few metres per second at the base of the convection zone, and (ii) a magnetic diffusivity inside the tachocline smaller than 108 cm 2 s-1. Numerical solutions for the confined poloidal fields and the resulting tachocline structures are presented. We find that the tachocline thickness runs as Bp-1/2 with the poloidal field amplitude falling below 5% of the solar radius for Bp > 5 mG. The resulting toroidal field amplitude inside the tachocline of about 100 G does not depend on the Bp. The hydromagnetic stability of the tachocline is only briefly discussed. For the hydrodynamic stability of latitudinal differential rotation we found that the critical 29% of the 2D theory of Watson (1981 Geophys. Astrophys. Fluid Dyn. 16 285) are reduced to only 21% in 3D for marginal modes of about 6 Mm radial scale. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
On the fundamental relation of laser schlieren deflectometry for temperature measurements in filamentary plasmas
Recently, laser schlieren deflectometry (LSD) had been successfully employed as a temperature measurement method to reveal the heat convection generated by micro filaments of a self-organized non-thermal atmospheric plasma jet. Based on the theory of the temperature measurements using LSD, in this work, three approaches for an application of the method are introduced: (i) a hyperbolic-like model of refractive index is applied which allows an analytical theory for the evaluation of the deflection angle to be developed, (ii) a Gaussian shape model for the filament temperature is implemented which is analyzed numerically and (iii) an experimental calibration of the laser deflection with a gas mixture of helium and argon is performed. Thus, these approaches demonstrate that a universal relation between the relative maximum temperature of the filament core (T1/T0) and a the maximum deflection angle δ1 of the laser beam can be written as T1/T0=(1 − δ1/δ0)−1, where δ0 is a parameter that is defined by the configuration of the experiment and by the assumed model for the shape of the temperature profile.