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Aspects of three-dimensional magnetic reconnection
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10.1063/1.1857912
/content/aip/journal/pop/12/3/10.1063/1.1857912
http://aip.metastore.ingenta.com/content/aip/journal/pop/12/3/10.1063/1.1857912
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Comparison between the position of the point as a function of time (crosses) and the displacement calculated by integrating in time the velocity . Note the very good agreement, especially in the nonlinear phase.

Image of FIG. 2.
FIG. 2.

Perturbed magnetic flux and current density profiles at and for two different simulation times. Note the asymmetry of these functions with respect to the rational surfaces located at , in the linear phase, and the nonlinear drift of the current density peaks.

Image of FIG. 3.
FIG. 3.

Left frame, for different modes. Right frame, normalized to the growth rate of the (1, 1) mode. Note that the time interval has been selected in such a way that all the represented modes have a significant amplitude.

Image of FIG. 4.
FIG. 4.

Contour plots of the current density and vorticity on the plane, at different simulation times. Superimposed is the magnetic island separatrix (black solid line). Note that the plots have been shifted by in the direction so that the cross structure appears in the middle of the box.

Image of FIG. 5.
FIG. 5.

Contour plots of on the plane, at different simulation times. Superimposed is the magnetic island separatrix (black solid line).

Image of FIG. 6.
FIG. 6.

Left frame, for different modes. Right frame, normalized to the growth rate of the (1, 1) mode. Note that the time interval has been selected in such a way that all the represented modes have a significant amplitude.

Image of FIG. 7.
FIG. 7.

Perturbed magnetic flux (top panel) and current density (bottom panel) profiles as function of , on the plane , at different simulation times: .

Image of FIG. 8.
FIG. 8.

Isosurfaces and contour plots of the current density field at two different simulation times. The values of the isosurfaces have been chosen close to the value of the maximum of the current density at the corresponding time.

Image of FIG. 9.
FIG. 9.

Difference between each term of the energy, as defined in Eq. (6), and the corresponding value at the initial time, divided by the total initial energy plotted time.

Image of FIG. 10.
FIG. 10.

Conservation properties of a single-helicity case and of a double-helicity case. The data of the single-helicity case refer to the case presented in Sec. III, while the data of the double-helicity case refer to the case I presented in this section. denotes the difference between the final and the initial values. Note that both integrals are Casimir invariants for a single helicity case in which case they are numerically conserved within the same percentage range. On the contrary, for a double-helicity case is not invariant and its variation grows in time as the nonlinear interactions become important.

Image of FIG. 11.
FIG. 11.

In the first column are the contour plots of the current density in the plane. In the second column are the sections of for on the same plane. Note how the presence of a smaller perturbation on the (1, 1) mode significantly alters the structure of the (1, 0) mode when the merging between the two corresponding peaks has occurred.

Image of FIG. 12.
FIG. 12.

Left frame: current density isosurface corresponding to a value close to the maximum of the current density. Right frame: isosurface at a lower value.

Image of FIG. 13.
FIG. 13.

(Color). Poincarè maps for case I at different evolution times. The maps have been computed by integrating the field line equations vs the variable using the Hamiltonian obtained from the MHD code. Stochasticity starts to develop near the separatrices of the magnetic islands, corresponding to the two initially excited modes. Subsequently, it grows to such a level that in the Poincarè map corresponding to the last Hamiltonian output of the MHD simulation (last frame), only a few KAM magnetic surfaces are preserved. The curves drawn in red represent the KAM surfaces utilized in Sec. VI to define the reconnected flux.

Image of FIG. 14.
FIG. 14.

Plot of the average Lyapunov exponent vs the number of periods along , , for the Hamiltonians corresponding to different times. The average has been performed over field lines with initial conditions taken in the stochastic region.

Image of FIG. 15.
FIG. 15.

Plot of the first-order, , and second-order moments, , vs the number of periods along , , at . Each moment oscillates around its mean value represented by the superimposed horizontal line. After a few periods the value of , averaged over different initial conditions, becomes of the order of the maximum width of the stochastic region.

Image of FIG. 16.
FIG. 16.

(Color). Contour plots and profiles of the current density on the plane, corresponding to the last two frames of Poincarè maps of Fig. 13.

Image of FIG. 17.
FIG. 17.

(Color). Poincarè maps for case II at different evolution times. The curves drawn in red represent the KAM surfaces utilized in Sec. VI to define the reconnected flux.

Image of FIG. 18.
FIG. 18.

Logarithmic plot of the toroidal magnetic flux for case I and case II. The time has been normalized to the linear growth rate for , . The two curves have been shifted to highlight their similar behavior when the transition to the global stochasticity is encountered.

Image of FIG. 19.
FIG. 19.

Logarithmic plot of the magnetic energy variation, , dashed line, and of the reconnected magnetic flux , solid line, vs the normalized time . The data refer to case I.

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2005-02-18
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Aspects of three-dimensional magnetic reconnection
http://aip.metastore.ingenta.com/content/aip/journal/pop/12/3/10.1063/1.1857912
10.1063/1.1857912
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