Abstract
Abstract. Maxwell's equations allow the magnetic field B to be calculated if the electric current density J is assumed to be completely known as a function of space and time. The charged particles that constitute the current, however, are subject to Newton's laws as well, and J can be changed by forces acting on charged particles. Particularly in plasmas, where the concentration of charged particles is high, the effect of the electromagnetic field calculated from a given J on J itself cannot be ignored. Whereas in ordinary laboratory physics one is accustomed to take J as primary and B as derived from J, it is often asserted that in plasmas B should be viewed as primary and J as derived from B simply as (c/4π)∇×B. Here I investigate the relation between ∇×B and J in the same terms and by the same method as previously applied to the MHD relation between the electric field and the plasma bulk flow vmv2001: assume that one but not the other is present initially, and calculate what happens. The result is that, for configurations with spatial scales much larger than the electron inertial length λe, a given ∇×B produces the corresponding J, while a given J does not produce any ∇×B but disappears instead. The reason for this can be understood by noting that ∇×B≠4π/c)J implies a time-varying electric field (displacement current) which acts to change both terms (in order to bring them toward equality); the changes in the two terms, however, proceed on different time scales, light travel time for B and electron plasma period for J, and clearly the term changing much more slowly is the one that survives. (By definition, the two time scales are equal at λe.) On larger scales, the evolution of B (and hence also of ∇×B) is governed by ∇×E, with E determined by plasma dynamics via the generalized Ohm's law; as illustrative simple examples, I discuss the formation of magnetic drift currents in the magnetosphere and of Pedersen and Hall currents in the ionosphere. Keywords. Ionosphere (Electric fields and currents) – Magnetospheric physics (Magnetosphere-ionosphere interactions) – Space plasma physics (Kinetic and MHD theory)
Highlights
Starting with elementary courses in electromagnetism, one becomes accustomed to think of the magnetic field B as determined by the given distribution of electric current density J
In magnetospheric physics, continue to apply this mode of thinking when investigating problems of large-scale plasma physics, for which the converse view – that J is derived from B as (c/4π)∇×B – has been proposed by Cowling (1957) and Dungey (1958) and in recent years strongly argued by Parker (1996, 2000)
The first point to note is that the electric field by itself does almost nothing: in the ionosphere, νin ωp and the result derived by Vasyliunas (2001), that V produces E but E does not produce V, applies – his calculation did not include the effect of collisions, the adjustments he describes occur on a time scale of electron plasma frequency, so the presence or absence of ion-neutral collisions makes no difference
Summary
Starting with elementary courses in electromagnetism, one becomes accustomed to think of the magnetic field B as determined by the given distribution of electric current density J. This paper attempts to determine whether and under what conditions a definite physical answer to the above question can be given. It is the third paper in a series dealing with some fundamental questions, motivated in part by the controversy (Parker, 1996, 1997, 2000; Heikkila, 1997; Lui, 2000) on whether B and V or, instead, J and E are to be treated as the primary variables. The first paper (Vasyliunas, 2001) considered an analogous question: given that V and E are connected by the MHD approximation, which one can be regarded as producing the other? In this paper I show that this subordination of J to (c/4π )∇×B holds not just for the time derivatives and for the quantities themselves
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