Wednesday, August 7, 2013

The Sweet-Parker Reconnection Model or Theory

As I read about Magnetic Reconnection the Sweet-Parker Model or Theory it somehow made a lot of sense to me because it explained how "Time-independent magnetic reconnection" can happen seemingly very fast and much faster than one would think logically without considering changes to the time space continuum during this process of magnetic reconnection.

The Sweet-Parker Model

At a conference in 1956, Peter Sweet pointed out that by pushing two plasmas with oppositely directed magnetic fields together, resistive diffusion is able to occur on a length scale much shorter than a typical equilibrium length scale.[1] Eugene Parker was in attendance at this conference and developed scaling relations for this model during his return travel.[2]
The Sweet-Parker model describes time-independent magnetic reconnection in the resistive MHD framework when the reconnecting magnetic fields are antiparallel (oppositely directed) and effects related to viscosity and compressibility are unimportant. The ideal Ohm's law then yields the relation
E_y = V_{in} B_{in}
where E_y is the out-of-plane electric field, V_{in} is the characteristic inflow velocity, and B_{in} is the characteristic upstream magnetic field strength. By neglecting displacement current, the low-frequency Ampere's law, \mathbf{J} = \frac{\nabla\times\mathbf{B}}{\mu_0}, gives the relation
J_y \sim \frac{B_{in}}{\mu_0\delta},
where \delta is the current sheet half-thickness. This relation uses that the magnetic field reverses over a distance of \sim2\delta. By matching the ideal electric field outside of the layer with the resistive electric field, \mathbf{E}=\eta\mathbf{J}, inside the layer, we find that
V_{in} \sim \frac{\eta}{\mu_0\delta},
where \eta is the plasma resistivity. When the inflow density is comparable to the outflow density, conservation of mass yields the relationship
V_{in}L \sim V_{out}\delta,
where L is the half-length of the current sheet and V_{out} is the outflow velocity. The left and right hand sides of the above relation represent the mass flux into the layer and out of the layer, respectively. Equating the upstream magnetic pressure with the downstream dynamic pressure gives
\frac{B_{in}^2}{2\mu_0} \sim \frac{\rho V_{out}^2}{2}
where \rho is the mass density of the plasma. Solving for the outflow velocity then gives
V_{out} \sim V_A \equiv \frac{B_{in}}{\sqrt{\mu_0 \rho}}
where V_A is the Alfvén velocity. The dimensionless reconnection rate can then be written as
\frac{V_{in}}{V_A} \sim \frac{1}{S^{1/2}}
where the dimensionless Lundquist number S is given by
S \equiv \frac{\mu_0 L V_A}{\eta}.
Sweet-Parker reconnection allows for reconnection rates much faster than global diffusion, but is not able to explain the fast reconnection rates observed in solar flares, the Earth's magnetosphere, and laboratory plasmas. Additionally, Sweet-Parker reconnection neglects three-dimensional effects, collisionless physics, time-dependent effects, viscosity, compressibility, and downstream pressure. Numerical simulations of two-dimensional magnetic reconnection typically show agreement with this model.[3] Results from the Magnetic Reconnection Experiment (MRX) of collisional reconnection show agreement with a generalized Sweet-Parker model which incorporates compressibility, downstream pressure, and anomalous resistivity.[4]

end quote from wikipedia under the heading: Magnetic Reconnection and subheading "The Sweet Parker model".

So, even though some factors are not represented in this theory, still it addresses more why reconnection rates are not time dependent and to a little degree why the changes are not directly related to the time space continuum (at least the way most of us that are not paid researchers in the field might view it). 

So, my thought is: "If Magnetic reconnections are not directly relatable to the time space continuum, could extreme events occur without any warning here on earth regarding our magnetosphere? My thought is that potentially unfortunately the answer likely is: Yes! However, then you might have to go to probabilities. And I'm not entirely sure how you would even begin to go about that.

If I look at this as an intuitive only and not in a scientific way it is my thought that we are in for it in a way not seen in the last century on earth. What does that mean? It likely means that in addition to extreme weather events we may also see extreme Cosmic Ray events. But because we all don't have cosmic ray detectors in whatever area we live in on earth (maybe we should), we will only notice when the sun is out or above the clouds that our eyes might hurt even with sunglasses on. (Which is something I have noticed lately while traveling). However, this isn't something I can scientifically prove. 
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