Non-linear FFF Model

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Non-linear FFF Model

• J.McTiernan
• 17-May-2004

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Optimization method (cont)

• Iterative process, start with Potential field,
  extrapolated from magnetogram.
• Be sure that B does not change on the boundary
• Calculate F, set new B B Fdt (typical dt
  1.0e-4)
• Objective function, L, is guaranteed to
  decrease, but the change in L (dL) becomes
  smaller as you go.
• Keep going until dL approaches 0.

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Optimization method (cont)

• At the start, the field is only non-potential at
  the bottom boundary. Non-potentiality propagates
  outward as the iterations increase.
• Iterations end long before non-potentiality
  reaches upper boundary the non-potentiality in
  the final field is concentrated near the lower
  boundary. Is this an effect of finite grid size?
  Not sure, but decreasing the grid size to ½ of
  original has no effect.
• This comparison of potential, NLFFF field is for
  AR 10486. Chromospheric magnetogram 29-oct-2003
  1846 UT.

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Potential Field AR 10486
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NLFFF field, AR 10486
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Conclusions

• NLFFF Optimization model seems to give reasonable
  results near the lower boundary.
• Non-potentiality in the solution is concentrated
  near the lower boundary. This may be an effect
  of finite grid size.
• NLFFF field has 1.66 times the energy of the
  potential field