4.5 Derived quantities, electric currents, and α

The well-known large uncertainties in the horizontal magnetic field component, in particular in weak field regions (see Section 4.1), cause large errors when computing the electric current density with finite differences via Equation (13View Equation). Even more critical is the computation of α with Equation (14View Equation) in weak field regions and in particular along polarity inversion lines (see, e.g., Cuperman et al., 1991Jump To The Next Citation Point). The nonlinear force-free coronal magnetic field extrapolation is a boundary value problem. As we will see later, some of the NLFFF codes make use of Equation (14View Equation) to specify the boundary conditions while other methods use the photospheric magnetic field vector more directly to extrapolate the field into the corona.
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