The Solar Wind – Magnetosphere Interaction
Alternate models for planetary processes, part3
This post is the third of seven articles in support of the PROM article “An integrated physical model characterizing planetary magnetism and heat”, which proposes an alternate origin for the geomagnetic field versus the consensus geodynamo theory.
Each PSI post documents an alternate model to the existing scientific consensus on planetary processes. Post 3 deals with the solar wind-magnetosphere interactions and how the incident solar wind energy is transferred to a planet.
The importance of solar wind energy in planetary processes
The PROM paper presents the Solar Wind Induced Electromagnet (SWIEM) model, whereby the solar wind powers the magnetic fields of the planets, and generates their heat anomalies as a by-product. PSI Post 1 shows that the 5 TW of power required for Saturn’s 200-400 K higher temperature represents roughly 18% of the 28 TW of incident solar wind power, while the PROM article demonstrates that the 5-6 TW of Earth-incident solar wind power is sufficient to generate both the 3.6-10 TW geomagnetic field as well as the 4 TW of heat lost by the Core to the Mantle. The solar wind is therefore a credible power source for Saturn’s energy crisis and Earth’s magnetic field.
The solar wind consists of a stream of charged particles (mainly protons and electrons) that is ejected from the Sun’s corona at supersonic speeds and is accompanied by stream-embedded magnetic energy[1]. The solar wind continually deforms the planetary magnetospheres, compressing their windward, dayside direction into a bow lobe, and extending their leeward, nightside into a tail lobe [1] (Fig. 1). The solar wind energy hereby applies a force/pressure to the magnetic field lines and displaces them, and therefore does positive work that transfers energy to the magnetosphere.
Figure 1: Schematic of how the Solar Wind deforms the geomagnetic field lines. C: Core; M: crust + mantle; Black ellipses in the Northern Hemisphere represent magnetic flux patches. Not to scale.
The prevailing theories on what happens to Earth-incident solar wind energy
Most articles on solar wind focus on describing its effect on deforming the magnetosphere (e.g. [1]) or its energetic interactions with ionospheric ring currents (e.g. [2]). Yet only a small fraction of the solar wind energy is directly transferred to the ionosphere via charged particles that enter the magnetosphere via its cusps (Fig. 1): this transmitted power is routinely estimated to be less than 1% of the total solar wind power [3,4].
There is currently no prevailing theory on where the remaining 99+% of the 5-6 TW [PROM article] of Earth-incident solar wind power goes. Most authors [3,4], the IPCC [5], and the PROM article agree that the power is not transferred to the Earth’s atmosphere: even though it’s significantly smaller than the solar irradiation power, the 5-6 TW of Earth-incident solar wind power is large enough to be noticeable as a climate forcing [3,4], as its power can achieve the same amount of work as a 25 megaton thermonuclear warhead exploding every 5 hours.
This PSI post, therefore, follows the Earth-incident solar wind energy, from the magnetopause – where it deforms the Earth’s magnetosphere (performs work) and generates geomagnetic flux energy – to the Outer Core where it powers the geomagnetic field via induced currents.
The Maxwell Equations
Electromagnetic energy interactions are governed by the Maxwell equations [6]:
Whereby ∇. is the divergence operator, E is the electric field, ρV is the electric charge density, B is the magnetic flux density, ∇× is the curl operator, FE is the electromotive force, FM is the magnetomotive force, t time, and µ (magnetic permeability), 𝛜 (electric permittivity), and σ (electric conductivity) are material constants.
These equations can be intimidatingly difficult to algebraically solve, even for physicists, so their physical meaning will be used to qualitatively explain the solar-wind magnetosphere interactions.
Figure 2: Schematic used to explain the physical meaning of the Maxwell equations. Arrows represent the direction and magnitude of either the electric or magnetic field. Dashed circles represent spherical cross-sections. Circled “+” positive and “-“ negative charges. The circled “x” represents either an electric current or a magnetic flux change entering the page.
Eqns. 1 and 2 deal with field divergence, which is how electric and magnetic fields can diverge. Eqn. 1 – Gauss’ Law – states that when an electric field diverges that it does so due to an electric charge (units ρV are Coulomb/m3). This means that in Fig. 2 that a and b are possible for an electric field, but c and d are not. Eqn. 2 is Gauss’ Law for magnetic fields and states that magnetic fields never diverge away from a point, and that the magnetic flux into a volume equals the magnetic flux out. In contrast to the electric domain, magnetic charges and magnetic monopoles do not exist. This means that Figs. 2 a-d are not possible for magnetic fields.
Eqns. 3 and 4 deal with the curls of electric and magnetic fields, that is how these fields circuit (Fig. 2 e). Eqn. 3 – Faraday’s law – indicates that a magnetic field that changes in time induces a circuiting electric field. Note that the negative sign in Eqn. 3 symbolizes a direction: a temporal change in magnetic flux density (number of magnetic field lines per unit area) induces a circuiting electric field that is able to move charges, i.e. that is able to induce a current, whose magnetic field in turn opposes the initially varying magnetic field (Lenz law).
Alternatively, Eqn. 3 states that a circuiting electric field induces a change in magnetic flux density that will counteract the circuiting field. This illustrates the yin/yang behavior of the electric and magnetic fields: a disturbance in one gives rise to a perturbation in the other that will try to undo the original disturbance. The word “induces” – whereby one disturbance creates the other – may therefore be somewhat inappropriate. “Co-exist” or “accompany” may actually describe the situation better: either both or neither are observed (Fig. 2 e). Eqn. 4 indicates that both a time-variant electric flux as well as an electric current induce a circuiting magnetic field.
The origin of planetary magnetic fields
Eqns. 3 & 4 explain the origin of all steady-state planetary magnetic fields: planet-interior currents are continually generating their (circuiting not diverging) magnetic fields. In a steady-state magnetic field, the magnetogenic electric currents must also circuit, as a non-circuiting current would cause local charge build-up, which over time would reverse the current. A circuiting electrical field causes the free electrons in a good conductor to follow its circuit, which the Biot-Savart law indicates generates a magnetic field, B:
Whereby µ is the magnetic permeability of the conductor, I the current, and r the radius of the circuit. Ohm’s law can be used to determine the power, P, required to move the current around – that is the power dissipated in – such a circuit:
Whereby R is the resistance of the conductor, and σ its conductivity. Eqns. 5 & 6 demonstrate there must be a spatial and temporal relationship between a planet’s magnetic field and the waste heat generated during magnetogenesis. Note that significant magnetic fields are more likely generated in conductors with high conductivity (lower power requirement) and high magnetic permeability.
Also, note that all of the above is fairly uncontroversial: planet-internal electrical circuits are inducing circuiting planetary magnetic fields. However, the origin of these currents is the main subject of the PROM paper. Geodynamo theory suggests these electric circuits are generated by the complex convections of Outer Core fluids moving through a magnetic field. A far simpler, alternative explanation (see also PSI Post 6) is that these electric circuits are induced by the daily geomagnetic flux variations caused by the solar wind, as is predicted by the Maxwell equations.
Solar Wind – Magnetosphere energy exchange mechanism
The solar wind continually deforms the Earth’s magnetosphere, compressing its windward, dayside direction into a bow lobe, and extending its leeward, nightside into a tail lobe (Fig. 2), thereby transferring its kinetic and magnetic energy to the magnetosphere as geomagnetic flux.
The most commonly-used approach to calculating the energy exchange between the solar wind and a planet’s magnetosphere is to use the work-energy principle, that is to consider the solar wind as tiny particle masses that collide with and transfer their kinetic and magnetic energy to the magnetosphere [3,4, PROM].
While numerically correct such an approach masks the physical mechanisms underlying the actual energy exchange, and as a result makes it more difficult to track where solar wind energy goes. A better approach is therefore to use Poynting’s theorem [6], which describes the conservation of energy for electromagnetic (EM) fields. The Poynting vector, S, describes the directional energy flux (the flow of energy per time per area):
Note that the magnetic permeability of space (also referred to as the vacuum permeability) is not 0: µ0 = 1.256.10−6N⋅A−2.
Poynting’s theorem is a restatement of the conservation of energy: it describes the power flow in EM fields. For a specified volume, the rate of energy transfer, ∂U/∂t, equals the rate at which fields do work on the charges in the volume, J.E, plus the energy flow leaving the volume (divergence of S) [6]:
Whereby J is the current density. The charged solar wind particles’ movement into the geomagnetic field results in a force acting on the particles that are perpendicular to their direction and the geomagnetic field, and therefore in their deflection (Eqn. 7; Fig. 3).
Ambient geomagnetic field energy is hereby converted into deflected particle kinetic energy, while incident particle kinetic and magnetic energy is transferred to the magnetosphere as geomagnetic flux (Eqn. 8; Fig. 3). Magnetic flux is defined as the surface integral of the normal component of the magnetic field, so Fig. 3 demonstrates that the solar wind compression of the magnetosphere conceptually increases the magnetic flux density in F2 at time t1 relative to time t0. Eqn. 3 indicates this change in magnetic flux density must be accompanied by (“induces”) an electric current, which the PROM article demonstrates circuits in the Outer Core.
Note that the solar wind deformation of the magnetosphere causes both positive (F2) and negative (F1) fluxes, whose distributions determine the location and direction of the induced Outer Core electric currents. Also note that the solar wind incidence causes the geomagnetic field strength to drop on the windward side of the planet: geomagnetic energy is consumed, and the (lower strength) sunward geomagnetic field lines, such as B1 (Fig. 3) are displaced towards Earth, locally reducing the windward geomagnetic field strength, e.g. at F1.
Fig. 3: Schematic of how the solar wind compresses the bow side of the magnetosphere. SW: solar wind; B: magnetic field (B1 and B4 are magnetic field lines); E: electric field. S: Poynting vector. F1 and F2 space-stationary flux patches. Left: time=t0, before solar wind impact; Right: time=t1, after solar wind impact.
Where the Solar Wind generated magnetic flux energy goes
As discussed above, it is commonly accepted that most of the solar wind-generated magnetic flux energy is not absorbed by the atmosphere: it is justifiably not a recognized IPCC climate forcing [3,4,5]. The compression of the field lines represents a temporal change in magnetic flux density which Eqn. 3 predicts must induce an electric current that will attempt to undo the deformation, that is generate opposing magnetic flux that will return the geomagnetic field to its t0 position in Fig. 3.
The Earth is therefore actively generating magnetic counter-flux that opposes the solar wind deformation of its magnetosphere via an induced current (Eqn. 3), which therefore must be circuiting on a planetary scale. Such a current cannot be induced in the low conductivity atmosphere or Mantle, as it would be readily converted to heat (Eqn. 6), therefore, circuits in the ferromagnetic Outer Core, whose magnetic permeability and electric conductivity are numerous orders of magnitude larger than the non-ferromagnetic atmosphere and Mantle materials.
This counter-flux in turn is driven – via the magnetomotive force – back to the magnetopause in order to maintain the magnetic pressure balance, which is what is predicted by Eqn. 4: at the edge of the magnetosphere – the magnetopause – the magnetic pressure caused by the solar wind’s magnetic energy and momentum is countered in real-time by the magnetic counterpressure exerted by the geomagnetic field [7], resulting in a dynamic balance.
The compression of the Earth’s magnetosphere is therefore analogous to the traditional grade school experiment whereby one magnet (A) is used to push a same-pole magnet (B) around a table without touching it. The movement of magnet A into the vicinity of magnet B causes the compression of magnet B’s (and A’s) field, which generates magnetic flux that induces currents in the magnets (Eqn. 3) that will attempt to generate a magnetic field that counterbalances/cancels the deformation, thereby creating counter-pressure at the A-B magnetic interface, which pushes magnets A and B away from each other and restores their original magnetic fields.
Figure 4: Schematic of a counterclockwise (as seen from the north) Solar Wind-Induced Current circuit pair generating a “reverse” polarity magnetic field (top) and a clockwise SWIC circuit pair generating a “normal” polarity field. Black lines are magnetic field lines; black ovals present flux patches(C=Core, M=Mantle, NH=Northern Hemisphere, SH=Southern Hemisphere). Red loops represent solar wind-induced current (SWIC) circuits. Thick red arrows represent poloidal magnetic moments. Combined NH and SH SWIC circuit magnetic moments plotted at the geographical equator. Not to scale.
The Solar Wind Induced Current (SWIC)
The induced currents attempt to re-establish the steady-state geomagnetic field. The PROM article demonstrates that the solar wind deformation of the magnetosphere induces two synchronous currents, one in the northern hemisphere and one in the southern hemisphere (Fig. 4), that circuit in the outermost shell of the Outer Core.
These currents – termed Solar Wind Induced Currents or SWICs – result in tilted magnetic moments (perpendicular to the circuits) whose N-S components combine to form the geomagnetic dipole, and whose E-W and radial components largely cancel each other out at the magnetic equator. Note that Fig. 4 displays conceptual currents: the three-dimensional deformation of the magnetosphere likely results in three-dimensional current sheets.
Alternate model 3: The solar wind compression of the Earth’s magnetosphere causes induction currents – termed Solar Wind Induced Currents or SWICs – in the Earth’s Outer Core. These SWICs generate counter-balancing magnetic flux that attempts to restore the geomagnetic field to its steady state.
[1] Kivelson, M.G., Bagenal, F., 2014, Planetary Magnetospheres In Encyclopedia of the Solar System (Third Edition), Academic Press; ISBN: 978-0-12-415845-0, p. 137-157
[2] Cowley, S. W. H., Bunce, E. J., and O’Rourke, J. M.: A simple quantitative model of plasma flows and currents in Saturn’s polar ionosphere, J. Geophys. Res., 109, A05212, doi:10.1029/2003JA010375, 2004b.
[3] Dessler A., 1974, Some Problems in Coupling Solar Activity to Meteorological Phenomena. Symp. Possible Relationships between Solar Activity and Meteorological Phenomena, Nov. 1973, NASA., 187-197
[4] Baker, D., Pulkkinen, T., Hesse, M., McPherron, R., 1997, A quantitative assessment of energy storage and release in the Earth’s magnetotail. JGR, 102, 7159-7168, doi: 10.1029/96JA03961.
[5] Bindoff, N.L., Stott, P.A., AchutaRao, K.M. et al., 2013: Detection and Attribution of Climate Change from Global to Regional. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., et al. (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.
[6] Purcell, E.M., Morin D., 2013, Electricity and Magnetism, 3rd Edition, Cambridge University Press, ISBN 978-1-107-01402-2
[7] Schultz M., 1991, The magnetosphere. Geomagnetism, 4, 87-293, ISBN 0-12-378674-6
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