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Massachusetts Institute of Technology

 
 

Magnetic Reconnection experiments on vtf

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Experiments at VTF

 

The main focus of the experiment is magnetic reconnection:

But we have also conducted experiments on

 

There are two different magnetic configurations that we use for studying reconnection: an open cusp magnetic field and a closed cusp. A cusp is simply a point where the in-plane magnetic field is 0. Both configurations give an in-plane x-line configuration; both have toroidal (into the figure) magnetic field, also called a guide field; and both are azimuthally symmetric.

open and closed configurations

 

 

Fast Magnetic Reconnection Mediated by Orbit Effects (Open Configuration)

 

The open cusp magnetic configuration is created by four external coils, seen at the right of the following figure. The reconnection is driven in our case by an electric field induced by a solenoid on the inner wall of the machine. This electric field combines with the in-plane magnetic field to give ExB flows into the x-line. This electric field drives reconnection.

 

 

reconnection drive

 

 

 

We measure the magnetic field, the current density, the plasma density and the floating potential, and the results can be seen in the following movie (10 MB, mpeg). (The color scale in the movie increases from blue to red.)

Open configuration plasma response

A few things to notice: the magnetic field lines are seen to reconnect, but moreover plasma density (at left) flows from the lower-right quadrant to the upper-right quadrant; this can only happen if there is reconnection, since the plasma is frozen to the field away from the reconnection region. The current density increases when the reconnection drive is switched on, and then fades away as the electrostatic potential structure builds up. The total current (~60 A) is about 3 orders of magnitude lower than the value $E/\eta_s$, where
$\eta_s$ is the Spitzer resistivity, calculated using the measured electron temperature.

The potential structure can be understood as the plasma's effort at satisfying the ideal Ohm's law (E+v x B = 0). If we take the dot product of B with this equation, we get

E\cdot B=0

where $\phi$ is refers to the toroidal (into-plane) component, and 'poloidal' and 'cusp' refer to the in-plane components. The magnetic fields and the toroidal electric field (the reconnection drive) are set externally by the experiment, while the poloidal electric field is freely determined by the plasma. It can be shown that the this measured potential structure satisfies the ideal Ohm's law almost everywhere in the plane.

electrostatic structure

 

Ohm's law can be solved for the electron velocity by taking the cross product of the equation with B. If we further take E electrostatic ${\bf E} = \nabla\phi$ then

v_{E\times B} = \nabla(\phi)\times B/B^2 so electrons flow along contours of constant color in the potential figure above.

 

 

The ideal Ohm's law is not satisfied everywhere; near the x-line it is violated, and this region of non-ideal behavior is shown in the following figure (at left):

diffusion region width is electron orbit width

 

The region where ${\bf E}\cdot{\bf B}$ is nonzero defines the diffusion region in which magnetic reconnection is taking place. The size of the diffusion region $\delta$ is found to scale with the toroidal magnetic field divided by the gradient of the in-plane field (see middle of figure above). It turns out that the diffusion layer width is also exactly the electron orbit width $\rho_c$, which can be shown analytically to be $\rho_c=$, where $\rho_e$ is the electron gyroradius. (The orbit width derivation assumes that the canonical angular momentum in the toroidal direction is constant (because of toroidal symmetry) and that the magnetic moment is conserved.) Delta was confirmed experimentally to be independent of ion mass and plasma density.

 

For more information, see J. Egedal et al., Phys. Rev. Lett. 90, 135003 (2003)

 

To further investigate the importance of electron orbit effects in reconnection, particle simulations were done. Using conservation of phase space we can follow f along the electron orbits in the externally imposed electric and magnetic fields. Assuming a maxwellian distribution far from the x-line, we can find the distribution near the x-line.

kinetic modeling

(J. Egedal et al., Computer Physics Communications 164, 29 (2004))

 

Once the distribution is found, it can be integrated to find the current. The theoretical current profile agrees with the measured current profile if we take into account the finite spatial resolution of the measurements.

 

current comparison

 

 

Results from the Wind Satellite in the Deep Magnetotail

 

The orbit effects in reconnection experiments on VTF would prove useful in understanding reconnection in the earth's magnetotail. The Wind satellite was launched in 1994, and in April 1999 (see Øieroset et al., Nature 412, 414 (2001)), it crossed an active diffusion region in the distant magnetotail (60 Re). Shown here is the reconstructed path of the satellite (see Egedal et al., PRL 94, 025006 (2005)).

wind trajectory

 

 

Electron distribution function measurements showed strong anisotropy in conjunction with a change in direction of a component of the plasma flow speed and magnetic field. There tended to be less lower-energy electrons moving perpendicular to the magnetic field (pitch angle = 90°) at this particular location. Higher energy electrons are less affected (green).

 

anisotropy in f

To understand this anisotropy, we need to consider electron orbit dynamics, including magnetic trapping and electrostatic trapping. An electron can be followed numerically in externally prescribed fields and it it found to cool as it moves towards the x-line, because it moves against the force of the electric field. The bounce motion (4 MB, mpg) is due to conservation of magnetic moment and requires that v_te>>v_flow (the electrons are moving fast enough to complete many bounce cycles before flowing into and out of the x-line). Note that the in-plane component of B and the into-the-plane component of B are roughly equal (in contrast to VTF's experiments, in which the in-plane B is weaker).

 

orbit movie bounce motion

 

 

There are two types of orbits in this configuration: trapped and passing, depending on the pitch angle. Trapped electrons will lose perpendicular velocity as they move into the x-line (by conservation of magnetic moment µ, since B decreases). But, at the same time, the parallel electron velocity will increase due to conservation of the second adiabatic invariant, J, since the bounce length of the orbit decreases. The energy will therefore decrease or increase depending on the relative strength of parallel and perpendicular velocity. An electron with large parallel velocity will gain energy as it moves into the x-line, while an electron with large perpendicular velocity will lose energy, by moving against the force of the reconnection electric field. But it is the trapped electrons (with larger perpendicular velocity) that spend more time in the diffusion region, so at a given energy there will be fewer electrons in the diffusion region with large perpendicular velocity. This explains the dip in f at perpendicular pitch angles. The affected range of pitch angles is determined by the trapped-passing boundary. Since Bmin~Bmax/2, this angle range is roughly 45°.

 

magnetic trapping

 

 

 

It turns out that magnetic trapping effects are not sufficient to explain the behavior of f at low energies; low energy electrons are all affected, even at near parallel pitch angle (0° and 180°). The explanation is that there must be a trapping potential; the diffusion region is positively charged relative to the background plasma. When such a potential is added (-1150 V in this case), there is perfect agreement with the measured distribution.

trapping potential

 

 

 

 

Observation of Spontaneous Reconnection (Closed Configuration)

 

J. Egedal et al., Phys. Rev. Lett., 98, 015003 (2007)

 

 

closed configuration

 

A new magnetic configuration has been implemented in VTF, which has very different boundary conditions than the previous configuration. The field lines no longer intersect the machine walls, so that electrostatic trapping is no longer significant. The new configuration is achieved by moving the current-carrying coils inside the chamber. Incidentally, the plasma density is two orders of magnitude higher (10^18 m^-3) than the open-field-line configuration. The mean-free-path for collisions is long compared to the size of the machine so that the plasma can be considered collisionless.

 

The reconnection drive is also modified. As can be seen in this animation (3 MB, mpeg), current ramps up in all four coils to create the x-line configuration. Then the current in the inner two coils is suddenly decreased while the current in the outer two is increased. Effectively, the current is pulled away from the x-line, adding magnetic stress to the system. A toroidal electric field is induced according to Faraday's law since the in-plane magnetic field is changing in time.

 

The plasma current builds up in response to this electric field for about 80 µs, and then it spontaneously drops by about a factor of 2 within about 20 µs. The current build-up can be understood by considering the plasma to be an inductor in the shape of a conducting loop; as the current in the 4 internal coils is effectively pulled away from this inductor it acts to maintain the current. During the sudden decrease in current, the reconnection rate spikes and magnetic field line reconnection is measured (3 MB, mpeg).

magnetics

 

 

This spontaneous reconnection is definitely not Sweet-Parker-like. For one thing it is much faster, and for another, the reconnection electric field and current are not even proportional to each other:

Not Sweet-Parker

 

 

The size of the reconnection region, measured by the width of the expelled current filament, is on the order of the ion-sound gyroradius:

 

delta J

 

The expulsion of current means that the magnetic energy stored in that current loop/inductor must have gone somewhere, and indeed we sometimes observe bulk plasma flows after reconnection (3 MB, mpeg).

spontaneous reconnection movie

 

The movie shows plasma density in the upper left (ion saturation current measured by an array of Langmuir probes), and just after the sharp decrease in current (bottom plot), a filament of plasma is ejected downwards. At the same time, a potential structure (center plot) develops that suggests a downwards ExB velocity consistent with the density motion. A rough energy balance shows that the energy in the Alfvénic outflow is a significant (~60%) fraction of the released magnetic energy.

 

The sharp decrease in plasma current and the burst of fast reconnection do not occur every time the experiment is run. More work is needed to map out the parameter regime that yields spontaneous reconnection and to investigate possible 3D effects at the onset of reconnection.

 

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