Nonequilibrium Alfve ´nic Plasma Jets Associated with Spheromak Formation Deepak Kumar and Paul M. Bellan California Institute of Technology, Pasadena, California 91125, USA (Received 6 February 2009; published 4 September 2009) Nonequilibrium Alfve ´nic flows have been observed in plasma jets during the helicity injection stage of the Caltech spheromak experiment. Density and time of flight measurements of these jets show that the flows convect dense plasma (  1) because of the axial gradient in the current channel profile. A simplified MHD theory is derived to model the flow. DOI: 10.1103/PhysRevLett.103.105003 PACS numbers: 52.30.Cv, 52.55.Ip, 52.55.Wq, 52.72.+v MHD-driven flows have been observed over a wide range of scales from terrestrial experiments (coaxial gun accelerators [1,2], plasma thrusters [3], high-current arcs [4], Z-pinch formation [5], spheromak formation [6,7], and sustainment [8]) to extraterrestrial phenomenon (solar co- ronal mass ejections [9] and astrophysical jets [10]). Various mechanisms and scalings for these flows have been proposed. For example, Reed [4] proposed a mecha- nism whereby the axial flow velocity u should scale as I 1=2 in flared high-current arcs, where I is the arc current. As another example, Barnes et al. [8] used a zero-pressure plasma model to predict that the flow of plasma from the electrodes in a steady-state driven spheromak should scale as I 3 . This Letter presents quantitative measurements of MHD-driven flow velocity and shows that u  I. A model is presented showing that flow results from a process whereby the radial magnetic pinch force associated with I produces a large on-axis plasma pressure. Axial nonun- iformity of the current channel results in a plasma pressure that is largest near the electrodes. The axial gradient of the pressure drives plasma jet flow away from the electrodes. This Letter also has important implications regarding the classic Taylor relaxation theory [11] conventionally used to model spheromaks, reversed field pinches, and aspects of solar coronal loops [12]. Our experimental results show that evolution of the magnetized plasma is not via a se- quence of zero-pressure gradient static equilibria [6] as presumed in the Taylor model, but rather involves large pressure gradients and fast flows. The Caltech spheromak experiment [13,14] has a cylin- drical geometry with coaxial planar electrodes for helicity injection (see Fig. 1). A vacuum magnetic field created by a coil behind the electrodes links an inner disk cathode and outer annular anode. Just before the discharge, neutral gas is puffed near the electrodes using 16 orifices, eight each on the two electrodes. A capacitor bank (59 F, 6–8 kV) is switched across the electrode by an ignitron to create the discharge. The experiment normally uses two 59 F ca- pacitors in parallel, but only one capacitor was used for the measurements reported in this Letter. This was done to eliminate jitter associated with firing two ignitrons and also to limit the current below the plasma kinking threshold [13]. As seen from typical current and voltage traces (Fig. 2), the current and voltage across the electrodes are approximately out of phase. This implies that the plasma can be considered an inductive load. Figure 1 shows a series of plasma images which elucidate the sequence of plasma evolution leading to a changing inductance. Ini- tially (0:5 s after breakdown) eight ‘‘spider legs’’ are formed linking the gas nozzles on the two electrodes. Previous work [14] has primarily focused on the collima- tion and flow of plasma in these spider legs. As the current ramps up, the spider legs expand due to hoop force and then merge to form a central column jet because of the pinch force (3 s after breakdown). This results in a slightly flaring plasma jet which drives plasma from near the electrodes to the vacuum. As the jet evolves outward, it increases the plasma inductance and thus acts as a helicity injection mechanism. This Letter shows that MHD-driven flows act as the mechanism to drive the change in the in- ductance of the plasma jet. As the jet expands towards vac- uum, it eventually overcomes the Kruskal-Shafranov kink FIG. 1 (color online). False colored images depicting the formation of a hydrogen plasma jet from shot numbers 9920 and 9923. The green vertical line represents the path of the laser beam used to measure plasma density. PRL 103, 105003 (2009) PHYSICAL REVIEW LETTERS week ending 4 SEPTEMBER 2009 0031-9007= 09=103(10)=105003(4) 105003-1 Ó 2009 The American Physical Society