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I've often thought that rather than doing some pointwise fitting of the MXH coefficients, we should just optimize directly on the fit of the coefficients with the cost as the Ψ at the points. This has been quite slow because Ψ(R, Z) is expensive in TEQUILA and this will be high dimensional. It's possible that a good initial guess might make it worth while. A possible way to do this is to use shifted surfaces that move the old flux surfaces to be centered at the new magnetic axis, while keeping the rest of the coefficients fixed (not concentric with the boundary). To do this, you need to find where the vector between the old axis and new axis intersects the boundary, then shift the surfaces so they keep the same fractional difference to that intersecting point. This prevents any overlapping of surfaces. Then these shifted surfaces serve as your initial guess for the optimize. This might be a little slow for the first few steps, but could wind up converging very rapidly. Needs testing.
The text was updated successfully, but these errors were encountered:
I've often thought that rather than doing some pointwise fitting of the MXH coefficients, we should just optimize directly on the fit of the coefficients with the cost as the Ψ at the points. This has been quite slow because Ψ(R, Z) is expensive in TEQUILA and this will be high dimensional. It's possible that a good initial guess might make it worth while. A possible way to do this is to use shifted surfaces that move the old flux surfaces to be centered at the new magnetic axis, while keeping the rest of the coefficients fixed (not concentric with the boundary). To do this, you need to find where the vector between the old axis and new axis intersects the boundary, then shift the surfaces so they keep the same fractional difference to that intersecting point. This prevents any overlapping of surfaces. Then these shifted surfaces serve as your initial guess for the optimize. This might be a little slow for the first few steps, but could wind up converging very rapidly. Needs testing.
The text was updated successfully, but these errors were encountered: