(Color online). (a) SSPX flux-conserver geometry showing bias magnetic flux. The radius of the inner electrode (cathode) at the insulating boundary is and the outer electrode is . The NIMROD domain includes an insulating boundary which approximates the experimental insulator which is at the top of the flux conserver. (b) Time history of the plasma startup in SSPX (left) and in NIMROD (right). The current history in NIMROD is programmed to duplicate that in the experiment. To make this comparison, the initial mode amplitudes in the code were as large as convergence would permit, about 1% of the energy of the component. The initial rise in voltage, azimuthally averaged toroidal flux, and magnetic field are due to the “bubble burst” from the gun; the subsequent drops in toroidal flux are accompanied by step increases in poloidal magnetic field and azimuthally averaged poloidal flux (not shown). (Adapted from Ref. 11.)
Magnetic energy in the axisymmetric and nonaxisymmetric modes in the analyzed simulation run. The reconnection event starts at about , and the energy in the axisymmetric component is converted into nonaxisymmetric modes and thermal energy. Linear scale (top). Logarithmic scale (middle) showing the mode growth. Also shown (bottom) is the gun voltage showing the voltage spike occurring during the reconnection event; compare to Fig. 1.
Simulation results: (top) toroidally averaged poloidal flux and (bottom) field line Poincaré plots early in the reconnection event . The puncture point structure arises because the magnetic field is primarily toroidal in the volume “inside” the poloidal flux contours, so field lines puncture the plane many times before leaving the flux conserver. In the code the flux conserver is inverted from the experiment.
(a) Toroidally averaged poloidal flux and (b) field line Poincaré plots late in the reconnection event .
(Color online). (a) Vacuum field lines. (b) Poloidal position on the cathode. Half the lines are shown, with the line which starts closest to the geometric axis on the flux conserver.
(Color online). Traces of a bundle of five field lines within the spheromak flux conserver, initially spaced 1 cm apart in a cross on the flux-conserver surface. (a) The initial flux balloon from the gun pushes the field lines up against the flux conserver, . (b) As current diffuses to radii inside the field line, the resulting toroidal field causes the lines to rotate around the geometric axis, . (c) As the reconnection proceeds, the field line geometries become quite complex, and the five lines behave differently, . (d) The field line topology change sometime generates knots, .
(Color online). Four of the five fieldlines shown in Fig. 6 at . The lines go to very different locations on the cathode. Four form complex knots; the fifth does not. Color changes along the field lines are used to clarify how the lines loop around themselves.
(Color online). Spatial structure of . As the toroidal angle is changed in steps of , the pattern shifts in response to the magnetic oscillation, dominated by . The eigenvalue of the flux conserver is , so the local departure from the Taylor state is very large.
(Color online). Velocity component perpendicular to the magnetic field at and . Plasma rotation is applied to bring the mode frequencies into approximate agreement with experiment; this corresponds to at .
(Color online) Contours of (a) azimuthally averaged poloidal flux and (b) azimuthally averaged .
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