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Astron. Astrophys. 364, 785-792 (2000)

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3. Numerical results

We have solved numerically Eq. (29) and Eq. (30) in two dimensions with three field components using a fast Fourier transform method. The problem with a periodic boundary-condition with respect to y is considered. The initial conditions which is satisfied to [FORMULA] is chosen as

[EQUATION]

where [FORMULA] is a period and [FORMULA] is the width of the electromagnetic envelope. Evolution of the solution of Eq. (29) and Eq. (30) with the initial condition (31) is given in Figs. 2-4. These parameters are chosen as

[EQUATION]

[EQUATION]

[EQUATION]

[FIGURE] Fig. 1. The distribution of initial electric field

[FIGURE] Fig. 2. Collapse development of self-generated magnetic field when [FORMULA]

[FIGURE] Fig. 2. (continued)

[FIGURE] Fig. 2. (continued)

[FIGURE] Fig. 3. Collapse development of self-generated magnetic field when[FORMULA]

[FIGURE] Fig. 3. (continued)

[FIGURE] Fig. 3. (continued)

[FIGURE] Fig. 4. Collapse development of self-generated magnetic field when[FORMULA]

[FIGURE] Fig. 4. (continued)

[FIGURE] Fig. 4. (continued)

The distribution of the initial electric field is shown in Fig. 1. For coronal active regions, the numerical solution for Eqs. (29) and (30) show that the magnetic field self-generated by transverse plasmons with frequency [FORMULA] would collapse (see Figs. 2-4). The level contours of [FORMULA] at successive times are shown in Figs. 2-4 for two dimensional geometry. In other words, due to self-compressing, a stronger magnetic field could be produced in a small region.Quantities in Figs. 1-4 are dimensionless. For coronal active regions, their relations to dimensional ones are(taking [FORMULA] [FORMULA])

[EQUATION]

[EQUATION]

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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