Resolving the 180-degree Ambiguity via Pseudo-Current Method G. Allen Gary MSFC/NSSTC REFERENCES on the Pseudo-Jz Method: T. R. Metcalf, K. D. Leka, Graham Barnes, Bruce W. Lites, Manolis K. Georgoulis, A. A. Pevtsov, K. S. Balasubramaniam, G. Allen Gary, Ju Jing, Jing Li, Y. Liu, H. Wang, Valentyna, Vasyl Yurchyshyn,and Y.-J. Moon, An Overiew of Existing Algorithms for Resolving the 180-degree Ambiguity in Vector Magnetic Fields: Quantiitative Tests with Synthetic Data, Solar Phys., 2006, 237, 267 G. Allen Gary and Pascal Démoulin, Reduction, Analysis, and Properties of Electric Current Systems in Solar Active Regions, Ap. J., 1995, v445, p982. G. Allen Gary and Pascal Démoulin, Electric Current Systems in Solar Active Regions ASP Conf. Series, 1994,v 68, 171 Sac Peak Workshop/NSO, 1993,'Solar Active Region Evolution- Comparing Models with Observations', eds. K. S. Balasubramaniam and George Simon. Section 10 in Numerical Recipes by W. H.Press, B. P. Flannery, S. A. Teukosky, and W. T. Vetterling (New York: Cambridge University Press), 1986, pp (Powell Method) 2 nd Azimuth Ambiguity Resolution Workshop, SDO/HMI-CSAC Boulder, CO October 4-6, 2006

Pseudo-Current Method F[j z 2 ] The Pseudo-Current Method of analysis minimizes the vertical electric current distribution using a non-linear least-square multi-dimensional minimization algorithm :  F [j z 2 ] /  p =  [   j z 2 (x,y) dx dy] /  p where  j z =  By/  x -  Bx/  y 2 12 Acute Angle Rule wrt New Direction

Generation of the Reference Field Pseudo Currents : Wires with cosine function profiles of variable width, location, and maximum current density as parameters - P i =P[x i,y i,width i,Jz i max ] Potential Field + Reference Field (x i,y i )

Define the j z in terms of an ambiguity parameter  i,j : F[j z 2 ] =  2 /4  j=2 N-1  j= 2 N-1 [  i+1,j  y i+1,j |B y i+1,j | -  i-1,j  y i-1,j |B y i-1,j | -  i,j+1  y i,j+1 |B x i,j+1 | +  i,j-1  y i,j-1 |B x i,j-1 | ] 2  i  j Where  is the quadrant parameter  =(1,1) or (1,-1):  i,j = B x i, j B y i,j / ( |B x i,j | | B y i,j | ) B x i, j =  i,j  y i,j |B x i,j | B y i, j =  i,j  y i,j |B y i,j |  i,j = Ambiguity Parameter IV III III i,j i+1,j The Approach-Minimize F[j z 2 ]

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