The Myth Of Powerful Ring Currents
Alternate models for planetary processes, part 5
This is the fifth of seven posts 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. This post (#5) is a follow-up of PSI Post 3 (The Solar Wind-Magnetosphere Interaction) and deals with the origins of the “solar quiet” daily geomagnetic variations measured at Earth’s surface.
A recap of PSI Post 3
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).
Fig. 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 geomagnetic field lines are compressed (Fig.1) as a result of the solar wind energy: the kinetic and magnetic energies of the particles are converted to magnetic flux energy. Magnetic flux is defined as the surface integral of the normal component of the magnetic field (number of field lines through field-perpendicular surfaces such as F1 and F2 in Fig. 2), so Fig. 2 demonstrates that the solar wind compression increases the magnetic flux in F2 at time t1 relative to time t0.
Also note that the solar wind incidence locally causes the geomagnetic field strength to decrease on Earth’s dayside: geomagnetic energy is consumed, and the (lower strength) sunward geomagnetic field lines are displaced towards Earth, locally reducing the geomagnetic field strength on Earth’s windward side.
Fig. 2: Schematic of how the solar wind compresses magnetic field lines on the bow side of the magnetosphere. SW: solar wind; B: magnetic field (B1 and B4 are magnetic field lines; B1 < B4); 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.
Note that this summary also represents the current, uncontroversial consensus view.
The prevailing theories on the origins of the “Solar Quiet” daily disturbance
The Earth experiences daily geomagnetic field variations of around 30 nT that are termed Solar Quiet (Sq) disturbances. These disturbances are commonly thought to be created by a complex system of ionospheric currents that are powered by ionosphere-magnetosphere (solar wind) interactions as well as ionospheric dynamos.
The consensus view on the highly complex interactions of solar wind particles, ring currents, Birkeland and Pedersen currents, Electrojet currents, magnetosphere currents, etc. goes well beyond the intent of this Post; a comprehensive overview is presented by Daglis et al. [5]
Fig. 3: Schematic of how the ring current is generated (circled “+” are protons, circled “-” are electrons), and how solar wind particles can become trapped in Earth’s magnetotail (after [5])
Most of these ring current particles eventually enter the magnetotail (Fig. 3), thereby increasing the magnetotail’s charge and generating magnetic flux [5]. The magnetic flux energy in the tail is released when the Earth rotates this flux back to the windward side [5]. Consensus theory states it is this energy that generates the horizontal (Pedersen) current system that induces the Solar Quiet deformation.
The Solar Quiet observations
A large number of satellites and ground-based geomagnetic observatories are used to regularly monitor the geomagnetic field strength variations. The solar wind strength varies with time, so only variations during the 5 days of lowest (quiet) monthly geomagnetic activity are averaged when determining the Solar Quiet (Sq) disturbance (Fig. 4).
Fig. 4: magnetic daily variation contours of the Sq total intensity (in nT) above the ionosphere at 16:30 UT (left) and 20:30 UT (right) derived from CHAMP satellite data (after: [6]). Colored Arctic blobs represent high positive (red) and negative (blue) magnetic flux areas. Yellow circle is the solar direction; the green line is the daylight boundary.
Powerful Ring Currents are possible, yet extremely unlikely
Ring current theory uses the horizontal component of the observed daily magnetic Sq variations to calculate the current intensities of a hypothesized ionospheric sheet current that is theorized to be responsible for these variations. Often a distinction is made [6] between the external Sq disturbance produced by the ionospheric sheet currents and the internal Sq disturbance that is caused by Earth-induced magnetic currents that are roughly one-third in size and opposite in direction to the external variations [9]. Numerous articles document the proposed powerful ionospheric current sheets operating on Earth [5,6,7,9] and other planets such as Saturn [8].
All of these articles assume the daily magnetic disturbance is fully caused by ionospheric current sheets (e.g. Fig. 5). These articles use the Sq magnitude to back-calculate current sheet strengths under the assumption that the solar wind and ionospheric dynamos supply sufficient energy to power the system, though a back of the envelope calculation demonstrates that such an assumption is unrealistic.
Consider the northern hemisphere 100 kA current contour in Fig. 5. It is part of a 3D current sheet that consensus theory deems responsible for the e.g. 35 nT northern hemisphere’s external daily disturbance (Fig. 4). For reference, a lightning bolt is roughly 30 kA, so the consensus theory claims continuous ionospheric current sheets more than 25 times (5 squared) more powerful than lightning are permanently circuiting over Earth’s dayside.
Fig. 5: Equivalent ionospheric current contours (in kA) associated with the external portion of Sq variations for March (after [7]).
whereby µ0 is the magnetic permeability of the ionosphere. The calculated number is indeed a reasonable match for the observed values in Fig. 4.
However, Ohm’s law indicates the power required to move the current around – that is the power dissipated in – such a circuit is enormous:
P = I2R = I2(2π * r * ⍴) = (100 103 )2 A2 * (2π * 2000 103 m * 0.02 Ω.m) ≈ 2500 TW
whereby ⍴ is the electric resistivity of the ionosphere, here (very generously) assumed to be as low as 0.02 Ω.m.
This calculated power represents only a fraction of the power required (only the 100 kA current): adding the 50 kA loop (r = 4000 km; P=1250 TW) and the 150 kA loop (r=1000 km; P=2850 TW), and multiplying by 2 (2 hemispheres) yields a rough power requirement well in excess of 13,000 TW to continuously fuel the proposed ring current.
This power is roughly equal to 8% of the total Earth-incident solar radiation power (~170 103 TW), yet is purportedly supplied by 1% of the 5-6 TW solar wind, as well as friction generated by an ionospheric dynamo, two power sources that are multiple orders of magnitude too small.
In addition, the continuous Ohmic dissipation of the 13,000 TW would be noticeable as a significant heat source – such power is the equivalent of a 25-megaton thermonuclear warhead exploding every eight seconds – yet one that is unrecognized by the IPCC as a major climate forcing. Such a powerful ring current system is therefore extremely unlikely.
An alternate Solar Quiet theory
That ring currents exist has been adequately documented, and is not disputed by the PROM article: the deflection of the solar wind’s protons and electrons by the magnetosphere (Fig. 3) is an integral part of the Solar Wind Induced Electromagnetic (SWIEM) model. That such ring currents cause the Solar Quiet disturbance is highly doubtful. The alternate theory is much simpler: the solar wind deforms the geomagnetic field (Fig. 1), which causes the Earth-surface observable Sq geomagnetic variations (Fig. 2).
The solar wind compresses the geomagnetic field lines on Earth’s dayside (Fig. 2) and displaces them towards the poles (Fig. 1), that is its pressure “pushes” them away from the Sun. This is evidenced by the daily path of the North Magnetic Pole (NMP) position – the intersection of the Earth’s surface with the geomagnetic field line that vertically penetrates it – which follows an ellipse with axes of up to 80 km (Fig. 6b [10]).
A space observer will witness a stationary magnetospheric compression on the windward, dayside of the Earth, but an observer rotating with the Earth will notice local geomagnetic field variations that roughly follow a wave (Fig. 4, 6a). The maximum compression – and greatest negative geomagnetic field variation – occurs roughly at LT 12:00 (local time noon), when the Sun is directly overhead, while the minimum compression – and greatest positive variation – occurs at LT 24:00 (local midnight) when the Sun is directly on the opposite side of the Earth (Fig. 4).
Fig. 4 represents the daily Sq magnetic variations near the top of the atmosphere, which represent the geomagnetic variation caused by the solar wind deformation of the magnetosphere (pressure) and the geomagnetic field’s response (counter-pressure). The direct-incident solar wind particles consume the most geomagnetic energy and therefore affect the largest negative daily geomagnetic field strength variation: the largest negative contours occur at the Local Time (LT) 12:00 meridian (Fig. 4 left: ~308°; right: ~248°) when the sun is directly overhead.
Magnetic flux is defined as the surface integral of the normal component of the magnetic field, so geomagnetic field lines that penetrate the Earth’s surface at a high angle (Fig. 1), that is the polar regions (geomagnetic inclination > 70°), deliver more geomagnetic flux to Earth than the low incidence angle field lines in the equatorial regions (geomagnetic inclination ≈ 0°).
The maximum magnetic flux density generated by the solar wind, therefore, occurs in a high-latitude LT 12:00 meridian “sweet-spot”. As the Earth rotates, the direct-incidence location moves relatively westwards, while locally this maximum magnetic flux density will start to decrease as its location is displaced relatively eastwards: the maximum rate of flux density change (dB/dt) occurs at the polar LT 12:00 positions, where an increasing magnetic flux density trend switches to decreasing (Fig. 6a).
Due to the Earth’s rotation during the course of the day, the direct-incidence location moves relative to the west, while the locally deformed field moves relative to the east (Fig. 6c). As the deformed field rotates eastwards from the LT 12:00 position the solar wind pressure and its transferred magnetic flux start to decrease, the solar wind deformation becomes less, and the geomagnetic field starts to “recover”.
Full recovery occurs near the LT 18:00 position (Fig. 4 left: 38°; right: 338°), whereby the solar wind-generated magnetic flux density returns to 0, and the negative magnetic flux of the recovering geomagnetic field (Fig. 4 blue blobs) reaches a maximum (Fig. 4, 6a). As these locations rotate further relatively eastwards, they will enter the magnetotail, where geomagnetic field extension (negative compression) occurs, with a maximum negative magnetic flux density occurring at LT 24:00.
The further rotation of these locations from LT 24:00 to LT 12:00 then follows the mirror sequence: the geomagnetic field recovers from its extension near the LT 06:00 position (Fig. 4 left: 218°; right: 158°), where the deformation contours return to 0 (Fig. 4) and the positive magnetic flux of the recovering geomagnetic field (Fig. 4 red blobs) reaches a maximum (Fig. 6a).
Note that Fig. 4 roughly represents the NH summer solstice (Sun roughly over the Tropic of Cancer) so the solar wind-generated magnetic flux at the north pole is at its yearly maximum, while the south pole is at its yearly minimum.
Figure 6: a) Normalized solar wind generated magnetic flux density during idealized local diurnal compression of the geomagnetic field as viewed by an observer on Earth; b) daily path of the North Magnetic Pole (NMP) in 1991 (after Geological Survey of Canada 2008): small solid ellipse represents “quiet” days of low solar wind; large dashed ellipse represents the path during more active days. Numbers reflect LT at the position. c) Daily compression and extension of the geomagnetic field by the solar wind represented as a coiled spring.
The deformation process is conceptually similar to a rotating spring: the spring is compressed (stores flux energy) at LT 12:00, but releases this energy by LT 18:00; the spring is extended at LT 24:00 but releases this energy by LT 06:00 (Fig. 6c).
The diurnal geomagnetic flux energy generated by the solar wind propagates as a three-dimensional electromagnetic wave (Fig. 4 & 6), a geomagnetic flux pulse with an extremely low frequency roughly equal to (1/24 h * 3600 s.h-1)-1 ≈ 10-5 Hz (Fig. 6a).
The solar wind-induced currents (SWIC’s)
The solar wind stores the bulk of its Earth-incident 5-6 TW power as geomagnetic flux, which travels relatively unimpeded through the Mantle (PSI Post 4) and induces a ±250 kA current in the Outer Core (see PROM article) toward the LT 06:00 direction which loops around Outer Core circuits that are defined by their peripheral heat anomalies (see PSI Post 2).
Note that the calculated current strength is the same order of magnitude as the proposed ring currents (Fig. 5), but that the Outer Core is a highly-conductive ferromagnetic medium that can generate larger magnetic fields with much smaller heat losses when compared to ionized gas molecules. A quick back of the envelope indicates (assuming a northern and south circuit, each of 3,000 km radius, core resistivity of 1.67 x 10-6 Ω.m; PROM article)
P = I2 (2π * r * ⍴) = (250 103 )2 A2 * (2π * 6000 103 m * 1.67 x 10-6 Ω.m) ≈ 4.0 TW
This amount is equal to the estimated 4 TW of heat lost by the core to the mantle via the Core-Mantle Boundary (CMB): in contrast to Ring Current theory, there is a good match between the observed and the theoretically predicted heat power.
Alternate model 5: The solar quiet daily geomagnetic field variations are caused by the daily, rotating solar wind deformation (compression/extension) of the magnetosphere.
[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] Purcell, E.M., Morin D., 2013, Electricity and Magnetism, 3rd Edition, Cambridge University Press, ISBN 978-1-107-01402-2
[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.N., 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] Daglis, I. A., Thorne, R. M., Baumjohann, W., Orsini, S., 1999, The terrestrial ring current: Origin, formation, and decay, Rev. Geophys., 37, 407– 438, doi:10.1029/1999RG900009.
[6] Turner, J., Winch, D., Ivers, D., Stening, R., 2007, Regular daily variations in satellite magnetic total intensity data. Annales Geophysicae, 25, 2167-2174.
[7] Yamazaki, Y., Yumoto, K., Uozumi, T., Cardina M., et al., 2011, Intensity variations of the equivalent Sq current system along the 210° magnetic meridian. Journal of Geophysical Research, 116, doi:10.1029/2011JA016487
[8] 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.
[9] Matsushita, S. Maeda H., 1965, On the geomagnetic solar quiet daily variation field during the IGY. JGR. 70, 2535–2558, doi: 10.1029/JZ070i011p02535
[10] Geological Survey of Canada, 2008, Tracking the North Magnetic Pole. Retrieved 11 January 2021.
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