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# MHD Equilibrium Structures

A magnetic arcade in the corona, in equilibrium with no flow, may be modelled by solving,

which satisfies (4.1) when and . Thus, is a solution to . This is equivalent to
 (4.12)

In addition, and so, taking the curl of (4.12) we obtain

Using a vector identity we obtain

Thus, as the first term in the middle expression is zero, we have
 (4.13)

For , (4.12) and (4.13) become
 (4.14)

and
 (4.15)

respectively. To solve these equations we note that they are linear equations and that the coefficients are constants and so we look for seperable solutions of the form

Substituting into (4.15) gives

Dividing by and rearranging gives

Taking the constant as we obtain equations for and as

These are easily solved in terms of trigonometric functions and expontential functions respectively to give one possible solution as

and

The field lines are shown in Figure 4.5.

Subsections

Next: Potential Problems leading to Up: Magnetohydrodynamics MHD Previous: Effect of on
Prof. Alan Hood
2000-11-06