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This paper presents the Pseudo-Current Method for resolving the 180-degree ambiguity in vector magnetic fields. The method employs a non-linear least-squares multi-dimensional minimization algorithm to minimize the vertical electric current distribution, leading to more accurate interpretations of magnetic field data. By defining the current density in terms of an ambiguity parameter, our approach effectively reduces ambiguity in solar active regions. References to existing algorithms and quantitative tests with synthetic data are provided to evaluate the efficacy of this novel approach.
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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. 274. (Powell Method) 2nd Azimuth Ambiguity Resolution Workshop, SDO/HMI-CSAC Boulder, CO October 4-6, 2006
Pseudo-Current MethodF[jz2] The Pseudo-Current Method of analysis minimizes the vertical electric current distribution using a non-linear least-square multi-dimensional minimization algorithm: F [jz2] /p = [ jz2(x,y) dx dy] /p where jz= By/x - Bx/y Acute Angle Rule wrt New Direction 212
Generation of the Reference Field Potential Field + Pseudo Currents: Wires with cosine function profiles of variable width, location, and maximum current density as parameters - Pi=P[xi,yi,widthi,Jzimax] (xi,yi) Reference Field
The Approach-Minimize F[jz2] Define the jz in terms of an ambiguity parameter i,j: F[jz2] = 2/4 j=2N-1 j= 2N-1 [ i+1,j yi+1,j |Byi+1,j| - i-1,j yi-1,j |Byi-1,j| - i,j+1 yi,j+1 |Bxi,j+1| + i,j-1 yi,j-1 |Bxi,j-1| ]2 i j Where is the quadrant parameter =(1,1) or (1,-1): i,j = Bxi, j Byi,j / ( |Bxi,j | |Byi,j | ) Bxi, j = i,j yi,j |Bxi,j| Byi, j = i,j yi,j |Byi,j| i,j = Ambiguity Parameter i,j i+1,j II I IV III
