1. Non-linear FFF Model J.McTiernan 17-May-2004

3. 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 + F*dt (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.

4. 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 18:46 UT.

6. Potential Field AR 10486

7. NLFFF field, AR 10486

8. 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