Collisionless simulation with . Shown is an isosurface of constant density on the low-β side of the current sheet, colored by the magnitude of current density . Instabilities of the central current sheet and very strong LHDI activity along low-β separatrices are clearly visible. Simulation parameters are specified in the text.
Geometry of the MRX simulations: (a) 3D extension of the geometry used to conduct previous 2D simulations; 16,17 (b) reduced geometry utilized in this study. The shaded surfaces represent conducting boundary conditions for fields and reflecting boundary conditions for the particles. Periodic boundary conditions are imposed on unshaded surfaces. The reconnection is driven by ramping down y-current in prescribed regions of the simulation domain that mimic PF coils in MRX. The poloidal field coils are enclosed by flux cores (F.C.), which are modeled through absorbing particle boundary conditions.
Weakly collisional simulation performed in MRX geometry with . Shown is an isosurface of current density colored by the x-component of the electron flow velocity in order to highlight multiple instabilities of the central current sheet. The back panel shows ion outflow velocity . Sample magnetic field lines and the flux core surfaces are also shown. Simulation parameters are specified in the text.
Radial profile of the magnetic fluctuation frequency spectrum across the reconnection layer in the experiment (experiment), collisionless simulation (collisionless), and weakly collisional simulation in MRX geometry (collisional). Here, z 0 refers to the average z-coordinate of the X-line. In all cases, the X-line is located close to (within the resolution of the diagnostics). The quantity plotted in each panel is , where is the maximum of the respective spectrum.
Comparison of a typical spectrum observed in MRX deuterium discharges (bottom panel) with the spectra measured in the collisionless (top) and weakly collisional (middle) simulations. All spectra are normalized to their respective peak value . In each panel, the thin black line corresponds to . Note that with the normalizations utilized here, . In order to compute the slope of the curve for the experimental plot, was assumed. The normalizations for simulation data are computed as follows: , stress tensor , and particle density ne are measured at the center of the reconnection layer, while is computed with the magnetic field measured at the edge of the reconnection layer. The value of vs in the experiment is computed using temperature measured by a Langmuir probe.
Average current density in the 3D weakly collisional case (top) and in its 2D equivalent (bottom). In the top two panels, jy is normalized to its peak value in 2D case. The bottom panel shows x-profile of at z = 0.
Correlation of the fluctuation amplitude with the collisionality regime, as measured by ratio of reconnection electric field E to the critical Dreicer field ED . Qualitatively similar dependence can be observed dynamically within a single discharge. The error bars are from an average over a 1.2 μs window around the time at which the current sheet passes by a fixed array of Langmuir probes at R = 37.5 cm.
Left: the width of the reconnection layer δ vs collisionality regime . Experimental discharges are grouped into those with small fluctuation amplitude (○, ) and those with significant fluctuations (*, ). Simulations are represented by symbols (2D cases with ), (3D weakly collisional), and (3D collisionless with formally infinite ). Right: fluctuation amplitude vs the width of the reconnection layer. The error bars on the experimental data points are from an average over a 1.2 μs window around the time at which the current sheet passes by the probes. Layer thickness δ is defined as the half-width of the current profile at 40% of its maximum value as measured at the z location of the layer center. To compute electron gyro-radius and , the temperature and density were measured at the center of the electron layer, while Bz was measured at one δ upstream. The reconnection electric field E in the experimental data is the inductive field at the X-point obtained through magnetic flux integration.
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