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Competing X-lines During Magnetic Reconnection
Aleida YoungMentor: Dr. Nick Murphy
Harvard-Smithsonian Center for Astrophysics
Solar REU Summer 2010
OU
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o What is magnetic reconnection?
o Why should we study it?
o Ideal MHD vs. Resistive MHD
o Basic Sweet-Parker Model
o Simulations
o Observationso What leads to one X-line winning
out over others?
o Momentum Plots
o Current Sheet Shapes
http://en.wikipedia.org/wiki/File:Reconnection.gif
What is magnetic reconnection?
Image from LASCO
Magnetic reconnection is the probable source of energy for coronal mass ejections.It is a leading proposed mechanism for the heating of the sun’s corona.Many flare models also involve magnetic reconnection.
Why should we study magnetic reconnection?
Why should we study magnetic reconnection?
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http://galacticfool.com/uploads/galacticfool.com/2009/09/tokamak.jpg
Driving from the solar wind leads to magnetic reconnection in 2 distinct areas of the Earth’s magnetosphere.
http://galacticfool.com/uploads/galacticfool.com/2009/09/tokamak.jpg
Why should we study magnetic reconnection?
Magnetic reconnection can cause problems in plasma containment devices.
Resistive MHD:Ideal MHD:
Resistive
TermHall Term
Electron
Pressure
Term
Electron
Inertia Term
Ideal vs. Resistive MHD
http://www.psfc.mit.edu/research/physics_research/vtf/introduction.html#sp
Upstream Magnetic Energy Density
Downstream Kinetic Energy
Incoming
Magnetic
Energy Per Unit
Time
Outgoing
KineticEnergyPer Unit
Time
Basic Sweet-Parker Model
http://www.psfc.mit.edu/research/physics_research/vtf/introduction.html#sp
Assumptions: 1. Steady-state2. Ignores kinetic
effects.3. 2 Dimensional
Problems: 1. Predicted time scale is
weeks. Observed time scale is seconds.2. Long thin current sheets are likely to be unstable in highly conducting plasmas.
Basic Sweet-Parker Model
Occurrences of multiple X-lines have been observed in Earth’s magnetotail. Although it is hard to observe, it is probable that they occur in CME’s.
Start with quiet, unperturbed Harris sheet.Introduce between 5 and 20 initial X-linesSpatial grid is 501 x 101 (mesh-packing)Time goes until 1 or 2 dominate X-lines remain.Information on: Jy Vx ηJy
Bx Vz Vx By
Bz P Ey
n Poloidal Flux
https://nimrodteam.org/
d10a
d11aSimulations
What leads to one X-line winning out over others?Nakamura et al. (2010) AGU
All perturbations were evenly spaced. When all X-lines were given the same
initial perturbation amplitude, X-lines on the edges of the current sheet win out over other X-lines.
When all X-lines were given varying initial perturbation amplitudes, the X-lines on the edges of the current sheet had an advantage but this could be overcome if the amplitude of another X- line was sufficient.
What leads to one X-line winning out over others?
Perturbations are all given the same spacing and the same initial amplitude.
X-lines on the edges win.Confirmation of Nakamura et al.
Perturbations are all given the same spacing but with varying initial amplitudes.
The X-lines with the largest initial amplitudes win, even though one is in the middle.Also suggests confirmation of Nakamura et al.A possible explanation could be that the X-lines on the edges have one side with completely unobstructed outflow.
Hypothesized the initial amplitude must be large enough so that the outflows are strong enough to force away the neighboring X-lines.
Nakamura et al. (2010) AGU All perturbations were evenly spaced. When all X-lines were given the same initial
perturbation amplitude, X-lines on the edges of the current sheet won out over other X-lines.
When all X-lines were given varying initial perturbation amplitudes, the X-lines on the edges of the current sheet had an advantage but this could be overcome if the amplitude of another X-line was sufficient.
Going Further Varied amplitudes and spacing of different numbers of perturbations. Performed analysis to determine the importance of spacing as
well as amplitude of initial X-lines.
What leads to one X-line winning out over others?
What leads to one X-line winning out over others?
Perturbations are given different spacing and different initial amplitudes.Winner!
Winner!
Winning X-line from the middle has the strongest amplitude, but is ranked 7 out of 10 for its proximity to other X-lines.
Winning X-line from the top is the 3rd largest amplitude and is ranked 2nd for its proximity to other X-lines.
They are ranked 1st and 2nd when the amplitude and distance-to-closest-neighbor are multiplied together.
Nakamura et al. (2010) AGU All perturbations were evenly spaced. When all X-lines were given the same initial
perturbation amplitude, X-lines on the edges of the current sheet won out over other X-lines.
When all X-lines were given varying initial perturbation amplitudes, the X-lines on the edges of the current sheet had an advantage but this could be overcome if the amplitude of another X-line was sufficient.
Going Further Varied amplitudes and spacing of different numbers of perturbations. Performed the same analysis previously seen to confirm
Nakamura et al. Results
Observed widely varying interactions. Winning X-lines are ranked at 3 or above in
(Amplitude)*(Proximity) index, or are on the edges (with 1 exception).
What leads to one X-line winning out over others?
A negative value is a force acting towards the left.
A positive value is a force acting towards the right.
The winning X-line is the only X-line supported by the plasma pressure. The X-line moves to one side of the current sheet. The X-point, max Jy, and local max ηJ all move together and always stay close together. In long current sheets, the area of max pressure is closer to the center, the diverging flow point is farther out, and then the X-point is closest to the edge.
VERY small along z=0
Force Plots
Contours are drawn at the point where the current density has dropped by a factor of 4.
The graph is stretched for emphasis.
The X-point will always occur at a minimum in current sheet thickness. Two shapes have been observed: the “w” shape and the wedge shape. In almost every simulation the wedge shape turns into a “w” shape. Frequently, “w” shaped current sheets develop new X-lines at the second minimum thickness point. The number of X-lines can change only through resistive diffusion.
Current Sheet Shapes
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o When multiple X-lines interact in a current sheet, an individual’s survival is dependent on the initial amplitude of the X-line and its proximity to other strong X-lines.
o X-lines on the edges have an advantage.
o Winning X-lines are always supported by plasma pressure.
o In a dynamic current sheet, the following order is always observed from the center of the current sheet outwards: max pressure, diverging flow, X-point.
o The X-line, local max of the resistive electric field, and the max current sheet density are always near each other.
o What conditions lead to these points moving to one side of the current sheet?
o A w-shaped current sheet is observed more often than a wedge-shaped one.
o Is the “w” a necessary condition for formation of new X-lines?
