Entangled Dynamos and Joule Heating in the Earth's Ionosphere
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Ann. Geophys., 38, 1019–1030, 2020 https://doi.org/10.5194/angeo-38-1019-2020 © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License. Entangled dynamos and Joule heating in the Earth’s ionosphere Stephan C. Buchert Swedish Institute of Space Physics, Uppsala, Sweden Correspondence: Stephan C. Buchert ([email protected]) Received: 9 May 2019 – Discussion started: 21 May 2019 Revised: 2 June 2020 – Accepted: 5 August 2020 – Published: 24 September 2020 Abstract. The Earth’s neutral atmosphere is the driver of the cently by Yamazaki and Maute(2017). Sq is driven by a well-known solar quiet (Sq) and other magnetic variations neutral dynamo. Vasyliunas¯ (2012) has summarized the fun- observed for more than 100 years. Yet the understanding of damental equations for a neutral dynamo and his critical view how the neutral wind can accomplish a dynamo effect has of the understanding within the community. The conceptual been incomplete. A new viable model is presented where a difficulty of the author’s interpretation of the neutral dynamo dynamo effect is obtained only in the case of winds perpen- can be phrased less mathematically as follows: in the frame dicular to the magnetic field B that do not map along B. of the neutral gas the product j · E∗, j the electric current, Winds where u × B is constant have no effect. We identify and E∗ the electric field is in the steady state zero or pos- Sq as being driven by wind differences at magnetically con- itive, because of the well-known Ohm’s law for the iono- jugate points and not by a neutral wind per se. The view of sphere. This indicates that Joule heating takes place (which, two different but entangled dynamos is favoured, with some however, has not been addressed yet in works specifically on conceptual analogy to quantum mechanical states. Because Sq, as far as we are aware of). A common comprehension of the large preponderance of the neutral gas mass over the seems to be that the dynamo effect occurs in the Earth-fixed ionized component in the Earth’s ionosphere, the dominant frame where j · E∗ − u × B, u the neutral wind, can be effect of the plasma adjusting to the winds is Joule heating. negative as required for a dynamo. However, a clear justifi- The amount of global Joule heating power from Sq is esti- cation for choosing this Earth-fixed frame over any other of mated, with uncertainties, to be much lower than Joule heat- the infinitely many possible frames, for example, Sun-fixed ing from ionosphere–magnetosphere coupling at high lati- or star-fixed inertial frames, seems to be lacking. Undoubt- tudes in periods of strong geomagnetic activity. However, on edly Sq variations have to do with neutral motion, but a neu- average both contributions could be relatively comparable. tral wind u and associated motional field u × B are frame The global contribution of heating by ionizing solar radiation dependent. In the frame of the neutral gas both are zero. So in the same height range should be 2–3 orders of magnitude what exactly drives the Sq currents and fields? larger. We will first present a new viable steady-state model of the neutral dynamo in the Earth’s ionosphere. As the title suggests, it actually involves (at least) two dynamos. A dis- cussion of various aspects of the new model follows, with 1 Introduction further references to other works on the subject. The interaction between the ionospheric plasma and neutral wind in the Earth’s atmosphere has been described in schol- 2 Preliminaries arly textbooks (e.g. Kelley, 2009) and numerous research ar- ticles. Still, for a long time the author has felt that his un- A scenario is considered where the lower thermosphere derstanding of the subject is incomplete. In this work we within two circles of latitude in each hemisphere is connected describe progress that has been finally made when thinking by the dipolar geomagnetic field, as sketched in Fig.1. In about the solar quiet (Sq) magnetic variations at mid lati- the Northern Hemisphere branch an easterly (westerly) zonal tudes. A praiseworthy review of Sq has been published re- wind flows, with a westerly (easterly) wind in the Southern Published by Copernicus Publications on behalf of the European Geosciences Union. 1020 S. C. Buchert: Entangled dynamos and Joule heating practically instantaneously, with only small amplitudes in the transients. We use the jargon and paradigms of the iono- sphere community. Astrophysical dynamos (usually without a neutral gas) are typically rather described in terms of a mechanical magnetohydrodynamics (MHD) approach. Dif- ferences between the two approaches have been discussed by Parker(1996) for the high latitudes and by Vasyli unas¯ (2012) for specifically the Earth’s neutral wind dynamo. Both authors acknowledged that for the steady state both ap- proaches give equivalent results and that for highly symmet- ric cases, such as this one, the “traditional” ionospheric E and j paradigm is efficient and mathematically simpler. The electrodynamics of the ionosphere particularly in the steady state and with a neutral gas is treated in a scholarly manner by Kelley(2009). For completeness we rephrase the most important points relevant for this work: in the reference frame of the neutral gas in the dynamo region, roughly at altitudes 90–200 km, where collisions are significant, an electric field E∗ drives Pedersen and Hall currents J P and J H according to Ohm’s law for the ionosphere: ∗ ∗ J P D 6PE ; J H D −6HE × B=B: (1) Figure 1. 3-D sketch of a scenario where regions between L D 2:5 6P and 6H are the Pedersen and Hall conductances and B and 3 are magnetically connected by a dipole magnetic field. The the magnetic field. The electric field E in other reference Supplement includes this figure in html format which, when opened frames with the neutral gas velocity u 6D 0 is in a browser supporting JavaScript, allows one to change the camera ∗ view point. E D E − u × B: (2) Please note that in many publications this equation is written with the Cu × B term on the E side, which is the standard Hemisphere. A zero tilt between geodetic directions (west- form of the Lorentz transformation for non-relativistic veloc- erly, easterly) and magnetic field-aligned Cartesian coordi- ities u. Often E is measured in some frame (for example the nates is assumed. An ionosphere with a dynamo region ex- Earth-fixed one), and the task is to estimate E∗. In this work ists, as well as magnetized plasma in a plasmasphere (not we prefer to write the relation as in Eq. (2). It is here im- sketched in Fig.1). The plasma adjusts to the conditions portant to note that E∗ is a frame-independent field driving imposed by the neutral winds but does not interfere oth- currents according to Eq. (1). The frame-dependent motional erwise, meaning that neither plasma pressure gradients nor u × B does not drive any currents; it is not a real field. electric fields penetrating from outside, etc., play any role. In the topside ionosphere and plasmasphere collisions are Zero meridional wind is assumed, and the deviation of the rare and the plasma drifts such that E C v × B D 0, and v is magnetic field B from a vertical inclination in the latitude the ion or electron drift. This means that the electric field in range of the zonal wind is ignored. The latitude range is the frame of the plasma is zero. The conductivity along B small, such that gradients of u, B, and the height-integrated is very high compared to the Pedersen and Hall conductivi- Pedersen conductivity 6P across the range are neglected. In ties, and in the steady state Ek D 0. For constant B, E .z/ is other words, u, B, and 6P are assumed constant across the also constant (where z is the coordinate along B). This justi- latitudes of the zonal jets. u and B are also assumed constant fies using height-integrated quantities in Eq. (1). When com- over the altitude range where there is significant collisional paring electric fields between the magnetosphere and iono- interaction with the plasma. In other words, the ionosphere sphere, B is not constant and E is said to “map” between is assumed to be thin. The scenario is highly simplified com- positions along z (Kelley, 2009, Chapter 2.4). For the sce- pared to any realistic one, in order to achieve a good physical nario in Fig.1 we also require such mapping of E between understanding of the situation. hemispheres. Owing to the highly symmetric preconditions We strive only for a steady-state description. The neutral the mapping is simply that a northward E in the Northern wind in the Earth’s ionosphere at mid latitudes changes only Hemisphere maps to southward in the Southern Hemisphere slowly over timescales of several hours, and the plasma be- with equal magnitudes and analogously for reversed direc- tween hemispheres would be able to adjust within seconds, tions of E. Ann. Geophys., 38, 1019–1030, 2020 https://doi.org/10.5194/angeo-38-1019-2020 S. C. Buchert: Entangled dynamos and Joule heating 1021 ∗ × · ∗ The Pedersen current driven by E is associated with Joule EN 1B/µ0 matching the Joule heating JN EN in the N or frictional heating (Vasyliunas¯ and Song, 2005) with power dynamo. −2 ∗ DQ ∗ ∗ in Wm : In SES uB is also northward; i.e. EN and ES do not map to each other along the magnetic field.