Magnetic Field Line Reconnection Experiment

Magnetic field line reconnection was and is an unsolved problem. It was originally proposed by Giovanelli to explain solar flares. The only free energy for plasma heating was the magnetic field, but in ideal MHD there is no dissipation of magnetic energy possible except near magnetic null points where MHD breaks down. The time was right to investigate the models in a controlled laboratory plasma. This had started in small, fast pinch-type plasmas. We developed a large diameter laboratory plasma which allowed detailed diagnostics of the reconnection physics. However, reconnection encompasses many scales and global effects. The parameter regime of our laboratory plasma did not address the MHD physics but explored the EMHD effects near the null line. It was before the time where EMHD became a fashionable topic. Furthermore, reconnection was usually treated in 2D geometries with no concern about the current closure at some boundaries. The present experiment was done in a linear device which has end boundaries. Current sources and sinks are vital to understand the current sheet and energy conversion. Toroidal plasma devices have been used to avoid boundary problems, but solar flares encounter boundaries at footpoints on the sun. Many problems still remain unsolved. The present attention deals with current sheet and its instabilities which can produce anomalous resistivity and dissipation.

We start with a brief description of the plasma device. Fig. 1a shows a picture of the device which is also shown schematically in Fig. 1b. The heart of the device is a 1m diam hot cathode which produces a dense (1012 cm-3), uniform plasma in a weak axial guide field (10 G) and provides for a large emission current to produce a strong current sheet. The plasma is diagnosed with various probes to measure magnetic fields in 3D, electric fields, particle distributions in 3D velocity space, rf probes for correlation measurements to identify wave turbulence. The experiment is pulsed at a fast rate (1 Hz) which permits detailed measurements in a relatively short time. X, Y, or O-type magnetic null points. The latter has been established in a laboratory plasma with a field-reversed configuration (FRC). The plasma physics is described by electron magnetohydrodynamics (EMHD) with a high electron beta value (1012 cm-3, 4 eV, 5 G). The FRC is induced with a pulsed Helmholtz coil (30 cm diam) whose field (25 G) opposes the weaker uniform dc magnetic field.

Schematic

Fig. 1. Facility for studying magnetic reconnection in a large laboratory plasma. (a) Picture of the machine. (b) Schematic drawing of the device. (c) Picture of the 1m diam cathode which produces a uniform dense magnetoplasma.

Schematic

Fig. 2. Schematic of the reconnection experiment. (a) Side view of the device showing the discharge source at the right, the parallel plate electrodes with current flow along the axial ambient magnetic field B0 in y-direction, and a multitude of diagnostic probes. The induced axial plasma current is carried by electrons supplied by the oxide coated hot cathode. Note that the applied inductive electric field is opposed by a space charge electric field so as to produce a reduced electric field which satisfies Ohm's law. Most of the inductive voltage drops off at the cathode sheath where electrons are energized. Shows that the global current path has to be investigated, not just a 2D current sheet. (b) End view of the chamber with two plate conductors carrying parallel currents axially with return currents through the chamber wall. Field lines form an X-type null point on axis. (c) Picture of the discharge between the two axial sheet electrodes.

An electrical schematic is shown in Fig. 2a. Two parallel plates carry pulsed currents Is in the same axial direction. The current is pulsed which induces axial currents in the plasma which fills the space between the plates. In vacuum the field topology is sketched in the cross sectional x-y plane of Fig. 2b. The induced current is supplied by the emission current of the cathode and collected by the end plate and returned through the conducting chamber walls. The metal plates are insulated from the plasma such that plate and plasma currents are independent of each other.

FRC

Fig. 3. Classic reconnection topologies. (a) Classical neutral sheet for 2D reconnection. (b) Classical fluid flow showing vertical ion inflow and fast horizontal ion outflow (ion jetting). The ions are accelerated by space charge electric fields set up by faster electron ExB drifts in Hall/EMHD.

Figure 3 shows the classical 2D reconnection geometry. The plasma current modifies the vacuum field and generates a flat neutral sheet (Bperp=0) between the plates shown in the vector field of Fig. 3a. It should be pointed out that there is also a comparably strong axial field Bz. The axial inductive electric field creates a vertical electron ExB drift which produces a space charge separation and an electric field Eperp which accelerates the ions. This creates a delayed ion inflow and an accelerated horizontal outflow as seen in Fig. 3b. This is the ion jetting effect in MHD theory which energizes the plasma on expense of magnetic field energy. The basic idea in reconnection is to couple electrical power into a fluid conductor which can be accelerated. The current is vital for the acceleration. Furthermore, if a large current makes the plasma resistive electrons and ions will also be heated.

FRC

Fig. 4. Time varying currents and field topologies. (a) Waveforms of the applied plate current and the induced plasma current. Contour plots of the transverse field strength shows a horizontal neutral sheet (b) at the current rise of Is and (c) a vertical sheet when Is falls. (d) An O-type null point is produced when the applied current vanishes while the plasma current still flows.

Since the plasma current is induced it varies in time which is shown in Fig. 4. The plate current performs a damped oscillation. The induced plasma current is phase shifted such that the field of both currents varies in time. Contours of the perpendicular magnetic field, shown in Fig. 4b,c show a horizontal neutral sheet during the initial current rise of Is, then a vertical sheet during the current fall. When the plate current goes through zero the field of the plasma current produces an O-type null point geometry in 2D or a flux rope in 3D. The field topologies are interesting but their importance lies in producing large currents in thin layers where plasma energization can occur.

FRC

Fig. 5. Electric field diagnostics and measurement results. (a) A loop probe is used to measure the axial inductive electric field. (b) A dipole Langmuir probe measures the sum of the inductive and space charge electric field in plasma. (c) The axial electric field is found to be much smaller than the applied electric field. (d) Schematic picture showing the profiles of the induced voltage/field and the opposing axial space charge potential/field. Most of the reconnection voltage drops off at the cathode where it accelerates electrons to high (100 eV) energies. This shows that reconnection (energy conversion to particles) can occur at other locations of the global current system than the neutral sheet.

Particles are accelerated by electric fields, not magnetic fields. Thus it is important to measure E. In plasmas there are two sources for electric fields, space charges and induction. The inductive electric field can be obtained from the induced voltage in a wire loop as shown in Fig. 5a. The loop has two radial legs and an axial wire which is parallel to the axial inductive electric field and produces the loop voltage. In plasma one can use two Langmuir probes in a dipole configuration along B0. The shift in the plasma potential is due to the total electric field which includes space charge fields and the induced field on the parallel wire sections. Sweeping this probe through the transverse x-z plane one obtains a field strength map as shown in Fig. 5c. The result shows that the axial electric field in plasma is much smaller than the applied inductive electric field measured in vacuum. Thus the space charge field opposed the inductive field. Since the latter is irrotational it cannot oppose it everywhere. The large potential drop occurs at one end of the device, i.e. at the cathode, as displayed in Fig. 5d. Nearly the entire inductive voltage drops off at the cathode sheath. At this location the energization takes place and produces fast electrons and ions. This shows the importance of the global current circuit. The current sheet in the bulk of the plasma is not the location of energization but it occurs at a different place where the current I-V dependence differs from the plasma resistivity.

FRC

Fig. 6. Wave turbulence observed in a current sheet. (a) Current-driven ion sound turbulence identified by its spectrum and dispersion obtained from cross correlation measurements. (b) Magnetic fluctuations in the frequency regime of whistler waves and with a (kx, kz)-spectrum near the dispersion surfaces of oblique whistler modes. (c) Enhanced microwave emission at the electron plasma frequency indicating electron beam-plasma instabilities and mode conversion/scattering.

A neutral sheet carries current which is a source of current-driven instabilities. It starts when the drift velocity between electrons and ions exceeds the sound velocity. When Te > Ti ion sound turbulence is created which scatters electrons, produces anomalous resistivity which in turn heats the electrons. Figure 6a shows the evidence for this instability. A broad spectrum of waves up to the ion plasma frequency is observed. By filtering a single frequency and cross-correlating the signals from two probes the dispersion relation of ion sound waves is identified. On magnetic probes fluctuations are observed in a broadband fluctuations up to the electron cyclotron frequency are seen. Cross correlations are performed between 3 vector components from two movable magnetic probes. The signals are Fourier transformed in time and space and the modes are observed to fall near the dispersion surface of oblique whistlers. The source of the waves has not been identified but suspected to lie in anisotropic electron distributions. Finally, at higher frequencies near the electron plasma frequency a greatly enhanced microwave signal is produced during reconnection. This signal is also observed external to the plasma implying that electron plasma waves are mode converted either through scattering off ion sound turbulence or by mode conversion on density gradients.

FRC

Fig. 7. Advanced diagnostics of particle distribution functions in 3D velocity space. (a) Directional electron velocity analyzer which measures the particle distribution in one direction only. By scanning the collection direction over all angles the complete velocity distribution is obtained. (b) Example of the distribution function in a current sheet, showing non-Maxwellian tails and drifts. Such measurements can address kinetic instabilities and transport processes.

In order to identify the mechanism of a microinstability one has to know the particle distribution functions, particularly the electron distribution. Since ordinary Langmuir probes integrate the particle flux from all directions they cannot resolve an unknown distribution function. We have developed and used probe which collects particles from one direction only. Sweeping its I-V characteristics for a multitude of polar angles the 3D distribution function has been resolved. It is time consuming but theoretically possible to extend these measurements to 3D space and time to obtain the full distribution f(vx, vy, vz,x,y,z,t), which could provide data for comparison with kinetic plasma theory. But to our knowledge, nobody has followed up with this possibility.

Figure 7a shows a schematic of the directional probe. It is a plane retarding potential energy analyzer which collects particles through a microchannel plate. The plate has long, thin, parallel holes which passes particles only within a narrow cone of angles. For magnetized particles the holes must be smaller than the Larmor radius. With this velocity analyzer the electron distribution function has been measured in the neutral sheet during reconnection. Since a function of 3 variables cannot be displayed Fig. 7b shows f(vparallel, vperp) at a fixed position and time. One can see that there are tails of energetic electrons in one direction away from the cathode. These tails can produce beam-plasma instabilities the observed electron plasma waves. The moments of the distribution functions yield drifts which readily explain the sound turbulence. Heat transport could also be investigated.

FRC

Fig. 8. Current disruptions with formation of a double layer. (a) Schematic diagram showing enhanced current collection to a smaller electrode on axis of the current sheet. The result of the large current concentration is a sponteneous current disruption by plasma expulsion with formation of a strong double layer. Its potential is given by the inductive voltage of the return current system. Again, stored magnetic energy is converted to produce accelerated particles at a localized region of a global current flow. (b) Waveforms of the plasma current and plasma potential showing spontaneous disruption events.

Since reconnection is more efficient with increasing current densities we attempted to narrow the current layer by collecting the induced current on a smaller endplate. It was biased slightly (10 V) above ground so as to attract the collection of electrons. As the reconnection started the current rose as expected but then disrupted spontaneously by several 100 A/micro s. Simultaneously, the electrode voltage increased to several 10s of V which is due to LdI/dt where L is the inductance of the current closure path. The positive voltage on the collector raised the plasma potential but only over a short distance where a sudden steep potential drop arises in the form of a double layer. The current disruption with double layer formation is found to be due to ion expulsion by radial electric fields of the a current-carrying plasma channel. The loss of density in a current carrying plasma channel can lead to a runaway current disruption. The inductive voltage accelerates the density loss and current drop. The stored magnetic energy is released in the particle acceleration at the double layer. Such events may also occur in magnetospheric current channels where current disruptions trigger substorms.

References