3-DIMENSIONAL CHROMOSPHERIC MAGNETIC-FIELD CONFIGURATIONS BASED ON PHOTOSPHERIC-VECTOR AND CHROMOSPHERIC-MULTI-LEVEL LONGITUDINAL-MAGNETIC FIELD OBSERVATIONS

The three-dimensional (3D) reconstruction of magnetic configurations a bove the photosphere is considered within the framework of the nonline ar force-free-field (FFF) model. The physical- computational algorithm proposed and tested incorporates, for the first time, the following b asic features: 1) Both photospheric vector field, B(x, y, O) and chrom ospheric line of sight field component, B-z(x, y, z) data are utilized ; this reduces significantly the degree of ill-posedness characterizin g the Cauchy problem corresponding to the case when only B(x, y, O) - values are used as boundary conditions. 2) A high-order, very efficien t computational algorithm is developed and used: horizontal derivative s are evaluated by 14 - terms formulas in 14 different forms, selected such as to provide optimal computational accuracy; the vertical integ ration is achieved by the use of ''moving'' 10 - term formulas express ed in terms of 10 derivatives and the first B-i(x, y, z) values (i = x ,y,z). 3) At neutral points, where inherent computational singularitie s in the values of the FFF-function alpha arise, rather than using smo othing techniques based on four-neighbouring- values averages, suitabl e procedures ensuring continuity are developed and used. The overall r esult of the incorporation of these novel features is an improvement b y orders of magnitude of the accuracy with which the chromospheric fie lds are reconstructed in the case in which one uses (i) only B(x, y, O ) - values as boundary conditions and (ii) relative simple computation al formulas and smoothing techniques; at (z) over bar = 20, Delta B-i/ B-i < 10(-3) ! The elimination/minimization of measurement errors as w ell as the fitting of the corrected date to FFF-model-states is also d iscussed.