Competing X-lines During Magnetic Reconnection

OUTLINE 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 Observations o What leads to one X-line winningout over others? o Momentum Plots o Current Sheet Shapes

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?

Driving from the solar wind leads to magnetic reconnection in 2 distinct areas of the Earth’s magnetosphere.

Why should we study magnetic reconnection? Magnetic reconnection can cause problems in plasma containment devices.

Resistive Term Hall Term Electron Pressure Term Electron Inertia Term Ideal vs. Resistive MHD

Upstream Magnetic Energy Density Downstream Kinetic Energy Incoming Magnetic Energy Per Unit Time Outgoing Kinetic Energy Per Unit Time Basic Sweet-Parker Model

Assumptions: 1.Steady-state 2.Ignores kinetic effects 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-lines  Spatial grid is 501 x 101 (mesh-packing)  Time goes until 1 or 2 dominate X-lines remain.  Information on: J y V x ηJ y B x V z V x B y B z PE y n Poloidal Flux d10a d11a Simulations

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. 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. 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?

Perturbations are given different spacing and different initial amplitudes. 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 3 rd largest amplitude and is ranked 2 nd for its proximity to other X-lines. They are ranked 1 st and 2 nd 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).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 J y, 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

CONCLUSIONS & OPEN QUESTIONS o When multiple X-lines interact in a current sheet,an individual’s survival is dependent on the initialamplitude of the X-line and its proximity to otherstrong X-lines. o X-lines on the edges have an advantage. o Winning X-lines are always supported by plasmapressure. o In a dynamic current sheet, the following order isalways observed from the center of the currentsheet 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 neareach other. o What conditions lead to these points moving toone side of the current sheet? o A w-shaped current sheet is observed more oftenthan a wedge-shaped one. o Is the “w” a necessary condition for formation ofnew X-lines?