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Magnetic Reconnection experiments on vtf

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Introduction

 

Magnetic reconnection is a change in the topology of magnetic fields that can release

magnetically stored energy. This energy release can be quite dramatic as, for example, in solar flares and coronal mass ejections. Reconnection is also important in the generation of aurora phenomena (northern lights), and in sawtooth crashes in magnetic fusion devices.

 

Here is a sampling of movies from the Solar and Heliospheric Observatory (SOHO). The flare and coronal mass ejection in these movies are the results of magnetic reconnection:

 

the sun image from SOHO (NASA & ESA)
Plasma along magnetic field lines on the sun. The motion of these giant loops builds up magnetic stress that is often released through magnetic reconnection. EIT 19.5 mm (495 KB, mpeg), solar flare LASCO (23.5 MB, mpeg), giant coronal mass ejection with proton showers (white streaks on screen); sun is white circle in the center.(courtesy of SOHO, a collaboration between ESA & NASA)

 

 

 

This animation from the THEMIS mission website at NASA shows how a solar flare interacts with the earth's magnetic field. The field shields the earth from the full effects of the flare, but magnetic reconnection allows some of the solar plasma to flow along the field towards the earth's poles to produce aurora (northern lights).

 

Magnetic reconnection releases stored magnetic energy; the process is explained in this short powerpoint presentation (90 KB).

 

 

 

The two best known models of reconection

While many models have been devised to explain the process of magnetic reconnection, the phenomenon remains an open question. The two best known models of magnetic reconnection are the Sweet-Parker model and the Petschek model.

The predicted reconnection rate in the Sweet-Parker model is found to be too slow to explain the sudden release of energy in flares, for example, but its relative simplicity makes it a useful reference for more complicated models.

The Petschek model is useful as another reference because it gives a reconnection region geometry that is consistent with fast reconnection. The Petschek model was found to be unstable in numerical simulations (for uniform resistivity), but it also serves as a useful reference.

 

 

The Sweet-Parker model, separately proposed by A. Sweet in 1958 and E. N. Parker in 1957, was the first quantitative model of magnetic reconnection in two-dimensional geometry. It centered on the role of resistivity in the conversion of magnetic field energy into plasma thermal energy.

Sweet and Parker assumed the plasma to be an incompressible fluid within a steady-state system in which the reconnecting magnetic fields are anti-parallel and of equal strength.

These magnetic fields are pushed together by some external agency, causing a current sheet of thickness delta and length L to form along the entire boundary between the two fields, where delta and L are related by

equation

 

By the generalized Ohm's law, the magnetic field can diffuse with respect to the plasma when the plasma has a nonzero resistivity:

equation

Plasma flows into the current layer at some relatively small inflow velocity Vo. It then accelerates along the layer and shoots from the ends of the magnetic diffusion layer with a relatively large exit velocity VA.

The Sweet-Parker model was the first model to show how localized "reconnection" of field lines can cause the observed macroscopic changes. Its validity has been confirmed by many numerical simulations and by the recent Magnetic Reconnection Experiment (MRX) operated by the Princeton Plasma Physics Library. It was far too slow, however, to account for the rapidity of reconnection observed in the solar system. The energy release in solar flares, for instance, is observed to occur in minutes as opposed to the tens of days the model predicts.

 

image
Sweet, 1958 and Parker, 1957

The Petschek model, proposed by H.E. Petschek in 1964, aimed to solve the slowness of the Sweet-Parker model with a few modifications.

Petschek suggested a much smaller diffusion region (smaller L), reaching over only a portion of the boundary between the opposing magnetic fields. Because delta and L are still related by

equation

 

the decrease in L means a decrease in thickness delta, making the diffusion and therefore the reconnection process faster.

 

Put another way, because what flows in must flow out, the inflow speed (reconnection rate) will be roughly the outflow speed times the aspect ratio. Since the outflow speed is fixed (on the order of the Alfvén speed), the inflow speed is limited only by the geometric aspect ratio of the diffusion region. A very wide and short diffusion region (Sweet-Parker) gives very small inflow speed, while a more square region gives faster reconnection (Petschek).

 

Petschek proposed the concept of two collisionless, slow-mode shock waves which, too, convert magnetic energy into plasma themal energy, and serve as the main sites of such conversion. The waves propogate outward from the diffusion region and stand in the flow, making it possible for a great quantity of plasma to flow into the boundary region without going through the tiny diffusion region.

 

While Petschek's model gives reconnection rates that match observations, it remains highly controversial. Many physicists take issue with the notion of two shockwaves that can be sustained for the entirety of the time needed to allow for the steady state process of reconnection.

image
Petschek, 1964

It is still unknown exactly how fast reconnection is maintained or triggered, although much progress has been made in 2d numerical simulations. Experiments on VTF have helped clarify one mechanism of fast reconnection, by investigating the role of particle orbits in reconnection electric and magnetic fields. Further experiments on VTF will address what triggers fast reconnection and what happens when you no longer have a 2d system, and 3d effects become important.

 

 

 

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