# NLFFF Solar and Model Results - PowerPoint PPT Presentation

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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

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NLFFF Solar and Model Results

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## 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.

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.

385x385x71 array, variable grid spacing in Z

only.

Fortran -- 4.5 hours on 2.4 GHz 32 bit

machine , IDL --11 hours on 3.2 GHz 64

bit machine.

### Magnetofrictional (cont.)

JxB/(B2Δx)

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/(B2Δx)

vs. z

divB/(BΔx)

vs. z

Nlfff vs. pfield

vector-cauchy

(0.60 at z=0)

Nlfff vs. pfield

vector-mean-error

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!)

### Solar (cont.)

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…)