UCLA BPPL - Magnetic Field Anhilation

Reconnection of 1-D antiparallel field lines is called magnetic annihilation since the opposing fields completely cancel. The lost magnetic energy is converted into kinetic energy of the plasma. For fields with two components, approximately antiparallel field lines exist in highly elongated X, Y, or O-type magnetic null regions carrying current sheets. In the latter case closed field lines vanish when the current flows through nonideal plasmas. This has been studied in a controlled laboratory experiment described below. The topic of O-point annihilation is as important as for X-point reconnection yet has received little attention in theory or experiments. To our knowledge no other laboratory experiment has explored this process. It is observed that the stored magnetic energy produced by plasma currents is lost anomalously fast.


Fig. 1 (a) Experimental setup to create a large field-reversed configuration with a Helmholtz coil inserted into a magnetized plasma column. (b) Picture of the Helmholtz coil inside the plasma device. Other loop antennas were retracted in the reconnection experiments.

As shown in Fig. 1 the field topology is that of an elongated field-reversed configuration (FRC). The magnetic field is embedded in the plasma and subsequently switched off rapidly. The embedded magnetic field decays without external drive or boundary effects by a process called "spontaneous" reconnection. The plasma physics is characterized by electron magnetohydrodynamics (EMHD) with a high electron beta value (1012 cm-3, 4 eV, 5 G). The FRC is produced with a pulsed Helmholtz coil (30 cm diam) whose field (25 G) opposes the weaker uniform dc magnetic field.

A magnetic field is embedded in the plasma and subsequently switched off rapidly. The embedded magnetic field decays without external drive or boundary effects. This process is called "spontaneous" reconnection.

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Fig. 2. (a) Time waveform of the coil current. The field line annihilation occurs after the coil current is switched off. (b,c) Magnetic field lines at early and later times of the relaxation, showing a stretching of the FRC. Tearing of the elongated neutral sheet forms small magnetic islands.

Figure 2 shows that after the Helmholtz coil field has penetrated the plasma, the coil current is rapidly switched off and the FRC, now only supported by plasma currents, relaxes freely. The FRC is embedded in a larger background plasma (100 cm diam) and the conducting chamber walls are too far away (150 cm diam) to stabilize it. The FRC is subject to small tilting and precessing motions, but predominantly it elongates. The toroidal electron current sheet is driven by the decay of the poloidal magnetic field. The field topology exhibits two 3-D null points on axis and a toroidal O-type null layer with toroidal separator. The elongated null layer exhibits tearing during its decay. The elongation is characteristic for whistler mode propagation along the ambient magnetic field B0.


Fig. 3 (a,b) Field lines embedded by the Helmholtz coil in the plasma. To see the growth and decay of the field topology click on the



The time evolution of the magnetic field topology has been displayed in two short movies. The field lines are defined by contours of constant flux. During the current growth the field lines around the two individual Helmholtz coils reconnect at a toroidal X-line to form new lines enclosing both coils. The latter are separated from the deformed B0 lines by an outer separatrix Which passes through the two 3D null points on axis. When the coil current is turnedd off the plasma current continues to flow in an axially elongated sheet. It decays and the FRC vanishes. Without null line the residual magnetic energy propagates away in the whistler mode.

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Fig. 4. Field components in the y-z plane (left picture) and normal to the plane (right contour map). The quadrupole field topology is characteristic for EMHD physics. It is caused by the toroidal (out-of-plane) electron flow which rotates the frozen-in field lines out and into the plane. The resultant field lines are a short flux rope.

Figure 4 describes the field topology in 3D produced by plasma currents. The in-plane field components are dipolar as in an FRC. The out-of-plane field is not a single toroidal field as in a spheromak or vortex. It forms a quadrupole field common in EMHD physics. It is formed by the toroidal electron flow which convects the frozen-in field lines out of the y-z plane. The toroidal twist produces opposite signs of Bx with respect to the center of the FRC. The twist produces helicity which is positive in the direction along B0 and negative in the direction against B0. It is the beginning of shedding two propagating whistler spheromaks.

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Fig. 5. Electron heating during the relaxation of the FRC. (a) Langmuir probe traces at different times during the field decay, showing electron heating by almost an order of magnitude. (b) Space-time evolution of the hot electrons. They originate near the coil where the largest currents flow, then gradually shift toward the axis where the FRC collapses.

The decay of the embedded magnetic field creates inductive electric fields which freely accelerates the electrons along the toroidal null line. This results in very energetic electrons as seen in Langmuir probe traces shown in Fig. 5 a. The hottest electrons are seen during switch-off near the coils where the largest electric field is located. Figure 5b shows the radial spread of the hot (>15 eV) electron flux which follow the toroidal current layer. At late times the hot electrons fill the center of the decaying FRC.

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Fig. 6. Light emission due to the conversion of magnetic field energy into electron heating. (a) Light for two different directions of the Helmholtz coil field. Light emission arises only when the topology forms a null line where runaway electrons are produced. (b) Space-time dependence of the light which starts near the coil and gradually shifts toward the center following the decaying current layer.

The hot electrons produce light emission which is detected with a collimated photomultiplier system. First, it is established that the light is produced only by fast electrons in a null layer. Figure 6a shows that no light arises when the Helmholtz coil current is reversed, yet producing the same B-field and inductive electric fields. Figure 6b shows the light emission vs radius and time. The light originates where the fast electrons are located, i.e. in the shrinking current layer.

The toroidal electron drift through stationary ions produces current-driven instabilities. Figure 7a shows large rf fluctuations on probes in the current layer well after the end of the coil current (bottom trace). A Fast Fourier Transform (Fig. 7b) shows that the spectrum falls into the range of ion acoustic waves. Anomalous resistivity from current-driven sound turbulence is well known and may explain the rapid loss of magnetic energy shown in Fig. 7c. If the decay was due to classical Coulomb collisions the decay rate should be 200 times slower than observed. For the observed fluctuation levels (deltan/n approx 10%), the predicted resistivity is at least one order of magnitude larger than the classical value, consistent with direct resistivity measurements in the neutral sheet, Etheta/Jtheta 10 (Omega cm)-1.

Noise spectrum

Fig. 7 (a). Density fluctuations observed in the FRC off axis where the peak current flows. The dominant fluctuations are observed after the coil current (bottom trace) has been switched off and a toroidal electron current is maintained by the decaying magnetic field. The short noise burst during the coil current pulse is due to an ion burst created at current turn-on. (b) Frequency spectrum of the dominant fluctuations. The noise falls into the ion acoustic branch and is thought to be current-driven ion sound turbulence. (c) Decay of the magnetic energy which is two orders of magnitude faster than the resistive decay rate. The scattering of electrons by turbulent fields is a cause for the anomalous resistivity.

There is also evidence for kinetic effects due to runaway electrons in the current layer. Figure 8a shows that microwaves are emitted during the decay of the FRC. These can be detected in situ with rf probes or externally with microwave antennas. The high frequency emissions can be produced by electron beams which excite electron plasma waves and these in turn scatter from ion waves or mode-convert at the critical layer to produce electromagnetic waves. Lower level microwave emissions are also observed from the discharge plasma where energetic primary electrons from the cathode excite whistlers and electron plasma waves. They have also been observed in the linear reconnection experiment where the 3D velocity distribution with fast electron tails have been measured. Figure 8b shows the spectra of the emissions which are close to the electron pasma frequency. The beam-plasma instability mainly heats the beam electrons which in turn transport energy to the bulk electrons.

Noise spectrum

Fig. 8 (a). Microwave emissions during magnetic field annihilation. (a) Probe-detected microwave signal showing peak emissions after the end of the Helmholtz coil current. (b) Frequency spectrum of the microwave signal detected externally with microwave horn antennas. The high frequency signal is thought to be produced by beam-plasma instabilities and mode conversion or scattering from ion sound turbulence.

In conclusion, the present simple experiment gives a self-consistent picture of energy conversion from magnetic fields to particles which is the essence of magnetic field line reconnection/annihilation. In X-points only partial field conversion is possible, in O-points the conversion is total. Irrespective of classical collisions the drift of electrons through ions creates instabilities and anomalous resistivity, which dissipates magnetic energy and heats particles, mainly electrons. Hall physics controls the vicinity of the null region which in MHD theories was simply described by a black box of non-ideal plasma.