NLFFF Solar and Model Results J.McTiernan NLFFF workshop 5-jun-2006

Optimization method: Wheatland, Roumeliotis & Sturrock, Apj, 540, 1150 Objective: minimize the “Objective Function” We can write: If we vary B, such that dB/dt = F, and dB/dt = 0 on the boundary, then L will decrease.

Optimization method (cont): Start with a box. The bottom boundary is the magnetogram, the upper and side boundaries are the initial field. Typically start with potential field or linear FFF, extrapolated from magnetogram. Calculate F, set new B = B + F*dt (typical dt =1.0e-5). B is fixed on all boundaries. “Objective function”, L, is guaranteed to decrease, but the change in L (ΔL) becomes smaller as iterations continue. Iterate until ΔL approaches 0. The final extrapolation is dependent on all boundary conditions and therefore on the initial conditions. Requires a vector magnetogram, with 180 degree ambiguity resolved.

Magnetofrictional (Aad_model) Potential NLFFF

Vertical field lines? I am not so sure and think that this is due to not setting /flux_balance in fff.pro. If this slide is here on 5-jun, then the new extrapolation hasn’t finished.

Magnetofrictional (cont.) 385x385x71 array, variable grid spacing in Z only. Fortran hours on 2.4 GHz 32 bit machine, IDL --11 hours on 3.2 GHz 64 bit machine.

JxB/(B 2 Δx) vs. z divB/(BΔx) vs. z Nlfff vs. pfield vector-cauchy (0.8 at z=0) Nlfff vs. pfield vector-mean-error

Solar Model Potential (Green’s function) NLFFF

Solar Model closer view Potential (Green’s function) NLFFF

Solar Model even closer view Potential (Green’s function) NLFFF

JxB/(B 2 Δx) vs. z divB/(BΔx) vs. z Nlfff vs. pfield vector-cauchy (0.60 at z=0) Nlfff vs. pfield vector-mean-error

Solar (cont.) 231x245x61 array, variable grid spacing in Z only. Fortran – 15 minutes on 3.2 GHz 64 bit IDL – 2 hours on 3.2 GHz 64 bit 231x245x231 array, with uniform grid took 36 minutes on 3.2 GHz 64 bit (Fortran version, the IDL version ran out of memory…) (Greens function potential field took 10 hours!)

The solar model only is non-potential for a short distance from the bottom boundary, this is typical for real data But not necessarily for model data. For model data, the non-potentiality reaches much higher. This is true even if noise is added. (still testing this…)