Laboratory Observation of Electron Phase-Space Holes during Magnetic Reconnection

We report the observation of large-amplitude, nonlinear electrostatic structures, identified as electron phase-space holes, during magnetic reconnection experiments on the Versatile Toroidal Facility at MIT. The holes are positive electric potential spikes, observed on high-bandwidth ($\sim 2\mathrm{GHz}$) Langmuir probes. Investigations with multiple probes establish that the holes travel at or above the electron thermal speed and have a three-dimensional, approximately spherical shape, with a scale size $\sim 2\mathrm{mm}$. This corresponds to a few electron gyroradii, or many tens of Debye lengths, which is large compared to holes considered in simulations and observed by satellites, whose length scale is typically only a few Debye lengths. Finally, a statistical study over many discharges confirms that the holes appear in conjunction with the large inductive electric fields and the creation of energetic electrons associated with the magnetic energy release.

Figure 1

(a) A schematic of the experiment at one poloidal cross section. (b) Total plasma current, (c) toroidal-averaged toroidal electric field, and (d) fluctuation trace for the time period $1300–1500\mu \mathrm{s}$. (e) Zoom-in on the fluctuation trace from 1418 to $1426\mu \mathrm{s}$. (f) Log-histogram of voltages measured by fluctuation probe over this time period. The black curve indicates a best Gaussian fit to the central portion of the data; it is parabolic on the log scale.

Figure 2

(a) A pair of fluctuation traces over a 200 ns window and (b) a 10 ns window. The probes are separated by 4.6 mm parallel to the magnetic field. (c) Histogram of probe-probe delays for the spikes. (d) Histogram of measured spike temporal widths (FWHM).

Figure 3

Probe-probe correlation histograms and corresponding single-probe log-histograms at zero time delay. The probe separations range from 0.8 to 4.6 mm perpendicular to the magnetic field.

Figure 4

(a) Reconnection electric fields for 80 discharges aligned to have peak $E_{\varphi }$ at $\Delta t=0$. (b) Histogram of observed spike events, the fraction out of all discharges which observed a given rate of spikes versus time relative to the peak $E_{\varphi }$. (c) Mean spike rate versus electric field, i.e., the total spikes observed given at particular electric field, divided by the total time elapsed with that electric field, divided by 4 probes. (d) Mean spike rate versus tail temperature.