Measurements of the Canonical Helicity of a Gyrating Kink

Conversions between magnetic and kinetic energy occur over a range of plasma scales in astrophysical and solar dynamos and reconnection in the solar corona and the laboratory. Canonical flux tubes reconcile all plasma regimes with concepts of twists, writhes, and linkages. We present measurements of canonical flux tubes, their helicity, and their helicity transport in a gyrating plasma kink. The helicity gauge is removed with general techniques valid even if only a limited section of the plasma is measured. Temporal asymmetries in the helicities confirm irreducible 3D fields in the kink.

Figure 1

(a) Schematic of the RSX experiment. The flux rope (purple) is produced by a plasma gun 50 cm away from the anode. Axial flow and applied magnetic field are directed towards the anode. The current flows in the opposite direction and is chosen so that the flux rope is kink unstable, displaces helically, and gyrates. Measurement planes (Fig. 2) and visualization volume (Fig. 3) are drawn in pink. (b) Visible emission from the RSX experiment together with schematics of plasma gun and anode.

Figure 2

Axial current density $j_z$ profiles in the $z=24.9\mathrm{cm}$ plane at (a) $t=7.34\mu \mathrm{s}$ and (b) $t=15.84\mu \mathrm{s}$, and $j_z$ isosurfaces in the visualization volume at $t=7.34\mu \mathrm{s}$ [36]. While the driven current forms a current channel, the reverse current is diffuse. Here, $j_z$ contours are shown where measurements of $B_x$ and $B_y$ were made. The hatched plane is the $x–y$ cross section of the visualization volume. The field null positions over one gyration period of $17\mu \mathrm{s}$ are plotted as dots with time progression corresponding to change in color from white to black and a circle fit (dashed red). Error bars (yellow) are plotted on every 6th field null. A blue arrow marks the field null position at plot time. The isosurfaces (c) enclose $j_z\le -10\mathrm{A}/{\mathrm{cm}}^2$ (green) and $j_z\ge 10\mathrm{A}/{\mathrm{cm}}^2$ (purple).

Figure 3

Gyrating electron (a) and ion canonical (b) flux tubes in the visualization volume shown in Figs. 1 and 2 at $t=7.34\mu \mathrm{s}$ [36]. (a) $n\overrightarrow{B}$ ($n{\overrightarrow{\mathrm{\Omega }}}_e$) field lines trace two electron canonical flux tubes (orange and red). (b) $n{\overrightarrow{\mathrm{\Omega }}}_i$ field lines trace two ion canonical flux tubes (black and gray) in the visualization volume. The field lines are launched from circles of 1 mm (orange and black) and 5 mm (red and gray) radii centered at the null of $B_x$ and $B_y$ in the $z=24.9\mathrm{cm}$ plane. The field line null gyration path is shown in black (compare Fig. 2). In (a), a single yellow magnetic field line on the outer flux tube helps visualize the twist of the electron canonical flux tubes. Contours of $j_z$ are plotted in the $z=24.9\mathrm{cm}$ plane.

Figure 4

(a) Measured (solid) and model (dashed) relative magnetic (red), cross (green), flow (blue), and total ion canonical (black) helicity in the visualization volume from Fig. 2. The helicities are boxcar filtered ($1.02\mu \mathrm{s}$ width) and normalized to the peak cross helicity. The raw data is plotted with transparency. (b) Time integrated static injection (orange), time-dependent injection (yellow), sources and sinks (pink), change in relative canonical helicity (purple) terms, and their sum, total change in relative canonical ion helicity (black). The mean value of each transport term is subtracted before integration. The white area in (a) marks the time the $z=24.9\mathrm{cm}$ plane field null is inside the visualization volume.