The correct application of Poynting's theorem to the time-dependent magnetosphere: reply to Heikkila

In his comment, Heikkila (1998) raises a number of objections to the concept of time-varying magnetic reconnection, and magnetic reconnection in general, which was obviously the basis of our paper on the longitudinal extent of magnetopause reconnection pulses (Lockwood and Davis, 1996). These objections are invalid. Much of the problem arises because Heikkila relies heavily on a simple electrical circuit analogy for the magnetosphere. As an analogy, this can be useful but it remains only an analogy. Thus, for example, Heikkila continues to inappropriately and erroneously invoke Lenz's law. However, the most serious e€ect in his comment is on how he applies Poynting's theorem. He refers to the reconnecting dayside magnetopause as a load (valid in the sense that J á E > 0) and his analogy demands that this be connected to a dynamo (by which he means a region in which J á E < 0) in a current loop. This can be valuable for the steady-state magnetosphere, with allowance for the fact that there are a number of complex current loops (Cowley, 1991). However, the rise and fall of magnetic energy density must be added in the non-steady situation we discuss. Because Heikkila does not do this, his simple load-and-dynamo analogy is invalid and inappropriate, as are his objections to our paper. Let us brie ̄y derive and apply Poynting's theorem. If we compress a magnetic ®eld B by ds in volume, we do work against the Maxwell magnetic pressure of @WB ˆ …B=2lo†ds. Thus the rate at which energy is stored in the magnetic ®eld in a volume s is: