Plasmoids Formation During Simulations of Coaxial Helicity Injection in the National Spherical Torus Experiment

The formation of an elongated Sweet-Parker current sheet and a transition to plasmoid instability has for the first time been predicted by simulations in a large-scale toroidal fusion plasma in the absence of any preexisting instability. Plasmoid instability is demonstrated through resistive MHD simulations of transient coaxial helicity injection experiments in the National Spherical Torus Experiment (NSTX). Consistent with the theory, fundamental characteristics of the plasmoid instability, including fast reconnection rate, have been observed in these realistic simulations. Motivated by the simulations, experimental camera images have been revisited and suggest the existence of reconnecting plasmoids in NSTX. Global, system-size plasmoid formation observed here should also have strong implications for astrophysical reconnection, such as rapid eruptive solar events.

Figure 1

(a) Line drawing showing the main components in NSTX required for plasma start-up using CHI. The initial poloidal field, the injector flux (shown by the blue ellipse), connecting the inner and outer divertor plates in the injector region is produced using the lower divertor coils (shown with numbers 1, 2, and 3). In the presence of an external toroidal field ($B_T$), and after gas injection, voltage ($V$) is applied to the divertor plates at $t=6\mathrm{ms}$ (as in the simulations) to initiate the discharge [24]. The path of $I_{\text{inj}}$ from the voltage source to the outer divertor plate, then through the upper part of the injector flux, and back to the voltage source, is shown by the three red arrows. (b)–(d) Poloidal flux evolution during simulations with one plasmoid. After the discharge fills the vessel (c), the voltage is rapidly reduced to zero at $t=9\mathrm{ms}$. This induces reconnection in the injector region to form closed flux surfaces (d). The arrows show oppositely directed field lines in the injector region where the S-P current sheet forms (c).

Figure 2

(a) and (b) Poloidal R-Z cut of toroidal currents during magnetic reconnection and (c) and (d) Poincaré plots at two times. (a),(c) An unstable elongated current sheet formed (shown in yellow-green $L\approx 1.4\mathrm{m}$) and multiple small scale transient plasmoids formed at the same time ($t=9.044\mathrm{ms}$). (b) and (d) A large scale breaking of a current sheet to form three larger scale islands is clearly seen, the current sheets between islands is S-P like ($t=9.174\mathrm{ms}$). (e),(f) Poincaré plots during the evolution of large-scale plasmoids (system-size) into one plasmoid at (e) $t=9.645\mathrm{ms}$, (f) $t=10.2\mathrm{ms}$, $S=39000$. The points in the Poincaré plots are the intersections of a field line with a poloidal plane, as the field line is followed around the torus.

Figure 3

(a) Number of plasmoids vs $S$. Blue: small sized transient plasmoids during the early phase of discharge (Fig. 2). Red: large scale and persistent plasmoids during the later phase of discharge. The solid line is the linear theoretical $S$ scaling. (b) The reconnection rate, $1/{\tau }_{\text{rec}}$ vs $S$. The transition to plasmoid instability is shown at $S\sim 3000$. The solid line is the S-P scaling.

Figure 4

Camera image during CHI discharge in NSTX shows the formation of two discrete plasma bubble plasmoids.

Figure 5

Plasmoid formation in MHD simulations of NSTX-U with ${\mathrm{\Psi }}_{\text{inj}}=0.065\mathrm{Wb}$ and strong poloidal flux shaping ($t=7.93\mathrm{ms}$). Poloidal R-Z cut of toroidal currents (a) for the whole device (b) zoom around the injector region.