Magnetically Driven Flows in Arched Plasma Structures

Laboratory experiments demonstrate high-speed plasma flows from both footpoints of arched magnetic flux tubes, resulting in bulk plasma transport into the flux tube and persistent axial collimation even as the flux tube lengthens and kinks. The measured flows are in agreement with the predictions of hoop force and collimation models involving fundamental MHD forces. These forces are expected to drive plasma acceleration in other open flux configurations with arched geometries, such as those found on the solar surface.

Figure 1

(a) Two sets of vacuum magnetic field lines link a pair of solenoids (only the last few coils of which are drawn). Dashed lines show the projection of the magnetic field lines onto the three orthogonal planes; arrows indicate lines’ separation, which is 5 to 8 times greater at the top of the arch than at the footpoints. (b) A hydrogen flux tube (shown with a red temperature color table) exhibits a comparatively narrow, uniform cross section both shortly after its formation ($0.05\mu \mathrm{s}$) and even as its axis lengthens and kinks at later times ($0.75,1.45,2.15\mu \mathrm{s}$).

Figure 2

(a) A nitrogen-hydrogen plasma loop at four consecutive times. Color pictures were produced by combining images from three different shots; two of the images were taken through optical filters, then used to color the third, unfiltered image. Nitrogen sections of the plasma (originating from the left footpoint) are tinted blue and hydrogen sections of the plasma (originating from the right footpoint) are tinted red. (b) Locus of the loop axis at 14 different times, all overlaid on top of the $3.30\mu \mathrm{s}$ frame. Thin green (left) and white (right) contours indicate the nitrogen and hydrogen sections of the loop, respectively.

Figure 3

(a)–(c) Collections of curve traces for three different dual-gas plasma combinations, displayed in the same manner as 2b. In the case of the N-Ar combination (b), appropriate optical filters for color coding were not available, so the boundary between the two species is chosen based on the “cusp” that forms there. (d) Curve length measurements from a number of different dual-gas plasma shots (each shot denoted with a different symbol), including those in (a)–(c).

Figure 4

(a) Loop length versus time for six different hydrogen plasmas, fired from five different capacitor charge voltages. (b) Total capacitor output currents $I_{\mathrm{cap}}$ versus time for the same set of shots. Magnetic probe measurements indicate current through the flux tube $I(t)\approx I_{\mathrm{cap}}(t)/10$. (c) Time derivatives of the quadratic fits shown in (a) versus the simultaneous current values shown in (b), demonstrating a single proportionality constant at early times. The legend for all three plots is given in the lower right hand corner of the figure.

Figure 5

Dependence of $\kappa$ on ion mass; error bars indicate variation in $\kappa$ within each species. Inset: numerical solutions (curves) for the hydrogen data (points) from Fig. 4. Solutions $s_{\mathrm{num}}(t)$ were calculated from the simplified hoop force model via the fourth order Runge-Kutta method, using expressions for $I(t)$ matched to experimental measurements, with $\kappa$ for each determined by the best fit to the data.