2007ApJ...670..841S

A technique is described for measuring electrical currents in the solar corona. It uses radioastronomical polarization measurements of a spatially extended radio source viewed through the corona. The observations yield the difference in the Faraday rotation measure between two closely spaced lines of sight through the corona, a measurement referred to as differential Faraday rotation. It is shown that the expression for differential Faraday rotation is proportional to the path integral {conint}nB⋅ds, where n is the plasma density, and B is the coronal magnetic field. The integral is around a closed loop (Amperian loop) in the corona. If the plasma density is assumed roughly constant, the differential Faraday rotation is proportional to the current within the loop, via Ampere's Law. The validity of the constant density approximation is discussed, and two test cases are presented in which the associated error in the inferred current is small, of the order of tens of percent or less. The method is illustrated with observations of the radio source 3C 228 with the Very Large Array (VLA) in 2003 August. A measurement of a differential Faraday rotation ``event'' on 2003 August 16, yields an estimate of 2.5x10⁹ A in the Amperian loop. A smaller event on August 18 yields an enclosed current of 2.3x10⁸ A. The implications of these currents for coronal heating are briefly discussed.