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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