Experimental Evidence of Plasmoids in High-$\beta$ Magnetic Reconnection

Magnetic reconnection is a ubiquitous and fundamental process in plasmas by which magnetic fields change their topology and release magnetic energy. Despite decades of research, the physics governing the reconnection process in many parameter regimes remains controversial. Contemporary reconnection theories predict that long, narrow current sheets are susceptible to the tearing instability and split into isolated magnetic islands (or plasmoids), resulting in an enhanced reconnection rate. While several experimental observations of plasmoids in the regime of low-to-intermediate $\beta$ (where $\beta$ is the ratio of plasma thermal pressure to magnetic pressure) have been made, there is a relative lack of experimental evidence for plasmoids in the high-$\beta$ reconnection environments which are typical in many space and astrophysical contexts. Here, we report strong experimental evidence for plasmoid formation in laser-driven high-$\beta$ reconnection experiments.

Figure 1

Experimental design. A plastic (CH) foil illuminated by two interaction laser beams, producing plasma bubbles. A proton backlighter consisting of a gold foil driven by a high-power, short-pulse laser beam produces energetic protons, which generate proton images after passing through the subject configuration. The collision between two antiparallel magnetic fields driven by the bubble expansion leads to the changing of the field topology and reconnection, as indicated in the reconstructed fields shown in the inset.

Figure 2

Raw radiography data. Proton radiographs show the spatial structure and temporal evolution of magnetic fields associated with the expanding plasma bubbles and interaction regions. These radiographs were formed by protons with energies between 11 and 36 MeV. The dashed cyan line in the second image represents approximately where lineouts for Figs. 5 and 5 were taken, though each image had a slightly different location for the lineout to ensure sampling of the correct current sheet structure (between apparent plasmoids). The dashed cyan circle denotes the position of edge of the Biermann bubble along the lineout. In these images, image contrast has been artificially increased to render the structure in the center of the radiograph more visible to the naked eye.

Figure 3

Reconstructed path-integrated fields and currents. (a) The reconstructed magnetic fields from the radiography data. All of these reconstructions are of different films from the same experimental shot. The black curves in the magnetic field strength plots denote contours of the path-integrated magnetic vector potential $\overrightarrow{A}$, while the black arrows denote the approximate direction of the magnetic field at their locations. The presence of isolated magnetic islands is evident in all of the radiographs. The third panel in this column additionally has labeled $\mathsf{O}$ and $\mathsf{X}$ points in the magnetic field topology, corresponding to the lineout in Fig. 4. (b) The inferred path-integrated parallel current, obtained from Ampére’s law by taking the curl of the path-integrated magnetic field: $\nabla \times {\overrightarrow{B}}_p={\mu }_0{\overrightarrow{j}}_p$, where the $p$ subscript denotes a path-integrated quantity.

Figure 4

Lineout along the current sheet. The lineout of the vertical path-integrated magnetic field along the direction of the current sheet, with error bars indicating the approximate uncertainty in the path-integrated field information. The labeled $\mathsf{X}$ and $\mathsf{O}$ points on the plot correspond to those labeled on the third panel of Fig. 3. The data here have been spatially down sampled for visual clarity, so the placement of individual data points does not correspond to the spatial resolution of the system. The inset at top right is a reproduction of the path-integrated parallel current from the third panel Fig. 3 showing where the lineout along the current sheet is located.

Figure 5

Lineouts through the current sheet. (a) Lineouts of the path-integrated $x$-directed magnetic field at each time step, showing the piling up of magnetic flux on either side of the reconnection layer. The blue arrow denotes the approximate location of the edge of a Biermann bubble (referred to later as “far from the current sheet”), demonstrating that the field strength is considerably higher in the reconnection layer than outside of it. (b) Lineouts of the path integrated parallel current at each time step (enlarged to show detail—note restricted horizontal length scale).

Figure 6

Time evolution of various quantities. (a) The width of the current sheet, inferred from the lineouts in Fig. 5, over time. The left axis shows the width in microns, while the right axis shows the ratio of the measured width to the calculated ion skin depth. (b) The measured width of the various plasmoids, perpendicular to the “horizontal” direction of the current sheet, as inferred from the largest closed contours of the path-integrated magnetic vector potential (located by selecting the potential at an adjacent $\mathsf{X}$ point). (c) The peak magnetic field near the center of the current sheet plotted alongside the representative magnetic field near the edge of an expanding bubble [“far from CS,” see Figs. 2 and 5].