(Color online) Multiple helicity-single helicity transition diagram. The sketch represents a synthesis of numerical results from extended sets of nonlinear 3D MHD numerical simulations (Refs. 2 and 18). The continuous transition between turbulent (multiple helicity) and laminar (single helicity) helical solutions is observed as a function of the Hartmann number (related to the strength of dissipative forces). An intermediate region displaying intermittent quasihelical solutions (quasi single helicity) connects the two extreme multiple and single helicity regimes.
(Color online) 3D representation, over one-fifth of the entire periodical cylinder, of the helical magnetic structure in the single helicity steady state. Contour plot for the helical flux function ; grey surface for a flux surface of shown as a reference; blue lines for some of its magnetic field lines, as reconstructed by means of a Runge-Kutta algorithm. Red arrows represent the projection of the total plasma flow on a poloidal cross section.
(Color online) Electrostatic potential and the related electrostatic field in the single helicity steady state, over one-fifth of the entire periodical cylinder. (a) Toroidal cross section of the isosurfaces of . Red arrows represent the electrostatic field. Contour levels of the helical magnetic flux, , are also shown. (b) 3D representation of the same structure. Red and blue surfaces are the isosurfaces corresponding to 75% of the maximum and minimum of , respectively. The yellow surface is an example of constant magnetic surface. Red lines are a representation of the electrostatic field lines, directed upwards, between the plates of the “core helical capacitor.”
(Color online) Projection on a poloidal cross section of the total plasma flow and its contributions, in the single helicity steady state. Fields are shown only over half of the disk without loss of information, since the configuration is symmetric for reflection about the horizontal diameter of the circular cross section. (a) Total plasma flow (blue arrows, top half) and perpendicular flow (red arrows, bottom half). (b) Paramagnetic pinch velocity (blue arrows, top half) and electrostatic drift (red arrows, bottom half).
(Color online) Radial profiles of mean parallel Ohm’s law components, in the single helicity steady-state. (a) Ohm’s law parallel to the total magnetic field. (b) Ohm’s law parallel to the mean magnetic field.
(Color online) Temporal average of the radial profiles of mean parallel Ohm’s law components, in a multiple helicity simulation (case with , , and ).
(Color online) Temporal evolution of the reversal parameter (dotted line) and the rms of the electrostatic potential (solid line), during a multiple helicity simulation (case with , , and ).
(Color online) Electrostatic potential and the related electrostatic field in a multiple helicity simulation during and just after a dynamo relaxation event. (a–c) Toroidal cross section of the isosurfaces of . (b–d) 3D representation of the same structure. Red and blue surfaces are the isosurfaces corresponding to 50% of the maximum and minimum of , respectively.
(Color online) Temporal evolution of the main modes by external measurements in the RFX-mod experiment. Two examples are shown from the present early operation stage with . (a) Quasi single helicity (QSH) regime obtained in passive operation. The preferred helicity is associated with the mode during the whole discharge. (b) QSH regime obtained in “virtual shell” first feedback operation; a highly oscillating behavior of the dominant mode shows up. In this case a clear correlation with plasma temperature oscillations has been reported. (c) Blow up of the temporal window with intermittent QSH of case (b).
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