Magnetospheric electric convection field

The collision of solar wind with the earth's magnetic field creates an electric field in the inner magnetosphere ( , with a being the earth's radius), the magnetospheric electric convection field . It is essentially oriented from the morning to the evening side. The co-rotating plasma of the inner magnetosphere drifts perpendicular to this field and perpendicular to the lines of force of the earth's magnetic field B _o . The process of creating this field is not yet fully understood. One possibility would be a friction process between solar wind and the boundary layer of the magnetosphere - the magnetopause . Reconnection of the magnetic field lines is another possibility. Finally, a hydromagnetic dynamo process in the polar regions of the magnetosphere is conceivable. Today satellite measurements give a pretty good picture of the structure of this field. There are a number of models in this field. ${\displaystyle r<10~{\text{a}}}$

A model that is often used in literature is the Volland-Stern-Modell (Engl. Volland-Stern model ).

Model description

The model is based on two simplifying conditions:

The real earth's magnetic field is replaced by a coaxial dipole field . Its magnetic field lines can be determined by the shell parameter ${\displaystyle B}$

${\displaystyle L={\frac {r}{a\sin ^{2}\theta }}}$

(1)

being represented. It is the equation of a field line, the distance from the earth, the earth's radius and the pole distance . For is the pole distance of the base point of the magnetic field line on the earth's surface, and is the radial distance of the line in the equatorial plane (θ = 90 °) ${\displaystyle L={\text{const.}}}$ ${\displaystyle r}$ ${\displaystyle a}$ ${\displaystyle \theta }$ ${\displaystyle r=a}$ ${\displaystyle \theta }$ ${\displaystyle r=aL}$

It is assumed that the electric field can be derived from an electrostatic potential Φ _c . Because of the great electrical conductivity in the magnetosphere, the electrical fields can only be aligned perpendicular to the electrical potential and perpendicular to the magnetic field. Therefore the electrical potential has to be parallel to the magnetic field. The relationship

${\displaystyle \Phi _{\text{c}}={\frac {\Phi _{\text{co}}}{2}}\left({\frac {L}{L_{\text{m}}}}\right)^{q}\sin(\tau -\tau _{\text{co}})}$

(2)

fulfills this condition. It is L _m = 1 / sin ² θ _m, the so-called separatrix, which covers the area of ​​magnetospheric middle and low latitudes (θ ≥ θ _m ) with closed magnetic field lines from the polar area (θ ≥ θ _m ) with open magnetic field lines (the only one Own base point on the earth's surface), separates. τ is the local time, θ _m ≈ 20 ° the polar border of the aurora borealis and Φ _co the total potential difference between the morning and the evening side. q, Φ _co , and τ _co are empirical parameters that are determined from the observations. Eq. (2) applies to a fixed coordinate system oriented away from the sun. The geomagnetic equator in this model is identical to the geographic equator. Since the electrical potential is symmetrical with respect to the equator, it is sufficient to restrict yourself to the northern hemisphere. For a transformation from a non-rotating to a rotating coordinate system, the local time τ must be replaced by the geographical longitude λ.

Inner magnetosphere

With the numerical values ​​q ≈ 2, and Φ _co and τ _co , depending on the geomagnetic activity (e.g. Φ _co ≈ 17 and 65 kV, and τ _co ≈ 0 and 1 h during calm or geomagnetically disturbed conditions), is Eq. (2) the Volland star model, valid outside the polar regions (θ> θ _m ) in the inner magnetosphere (r ≤ 10 a) (see Fig. 1a).

Figure 1: Equipotential lines of the global magnetospheric convection field within the equatorial plane of the magnetosphere (left), and the sum of the convection field and the co-rotation field (right) during geomagnetically calm conditions

The use of an electrostatic potential assumes that this model can only be used for very slow changes over time (periods greater than about half a day). Because of the assumption of a coaxial magnetic dipole field, only global structures can be simulated.

The electric field components are determined from

E = - degree Φ

(3)

as

E _r = - (q / r) Φ _c

E _θ = (2q / r) cotθ Φ _c

E _λ = 1 / (r sinθ) cot (τ - τ _co ) Φ _co

It is known from electrodynamics that the following relationship exists between an electric field in a rotating system E _{ro and} the field in a non-rotating system E _nr :

E _ro = E _nr + U x B

U x B is the Lorentz force with U = R Ω the rotational speed, R the axis distance and Ω the angular frequency of the rotation. The Lorentz force therefore acts on the co-rotating plasma in the inner magnetosphere in the non-rotating coordinate system

Φ _r = - Φ _ro / L

(4)

with Φ _ro = 90 kV. This is the potential of the so-called electric co-rotation field. In the non-rotating coordinate system, the thermal plasma in the inner magnetosphere reacts to the two potentials in Eq. (2) and Eq. (4):

Φ _c + Φ _r

(5)

The potential Φ _r decreases with distance from the earth, while the potential Φ _{c increases} . The sum of both potentials has a torus-like structure with closed potential surfaces, called the plasma sphere (Fig. 1b), in which the thermal plasma is captured. Whistler observations actually show that the plasma inside the plasma sphere is several orders of magnitude larger than outside the plasma pause, the last closed potential surface (Fig. 1b)). From the configuration of the plasma pause, the exponent q = 2 in Eq. (2) derive, while the extent of the plasma pause determines the size Φ _co .

Origin of the convection field

The interaction of the solar wind with the earth's magnetic field causes the creation of an electric field in the magnetosphere . In the polar regions of the magnetosphere, the field lines of the interplanetary magnetic field can combine with those of the earth’s magnetic field, so that these lines only have one base point on the earth's surface. In the polar regions of the inner magnetosphere these are practically perpendicular. The solar wind flowing through the polar regions induces an electric field (hydromagnetic dynamo effect) that is directed from the morning to the evening side. There is an electrical charge separation at the boundary layer of the magnetosphere, the magnetopause. Electric discharge currents can flow along the last closed magnetic field lines (L _m ) as field-parallel currents (Birkeland current) into the ionospheric dynamo layer , within this electrically very good conductive layer in two parallel currents on the day and on the night side (polar electric jets or DP1 - currents) to the evening side and from there back to the magnetosphere. The fluctuations in the earth's magnetic field on the ground are a measure of the variability of such electrical currents in the ionosphere and magnetosphere.

Polar magnetosphere

The electric convection field in the near-Earth polar regions of the magnetosphere can be determined by the exponent in Eq. (2) can be simulated. At the separatrix (L _m ), the potential Φ _c connects continuously to the potential in middle and low latitudes (Eq. (2)). There is, however, a field reversal associated with the Birkeland currents mentioned above. This is confirmed by the observations. ${\displaystyle q=-1/2}$

In a more precise model, the polar light zone between about 15 ^o and 20 ^o pole spacing, again simplified by a coaxial magnetic field, is introduced as a transition layer. The ionospheric dynamo layer between about 100 and 200 km altitude is an area in which ions and electrons have different mobility. Due to the influence of the earth's magnetic field, there are two types of flows: the Pedersen current, parallel to the electric field E , and the Hall stream perpendicular to E and B .

In the polar light zone, the electrical conductivity is significantly increased depending on the geomagnetic activity. This is taken into account in the model by the parameter τ _co in Eq. (2). The electric convection field also drives electric currents in the polar regions of the ionospheric dynamo layer (DP2), which can also be simulated by the model.

The electrical currents derived from the earth's magnetic fluctuations on the ground apply only to horizontal surface currents in the ionosphere. However, the real flows are usually three-dimensional. The Birkeland currents have hardly any magnetic effect on the earth's surface. Direct magnetic field measurements in the ionosphere and magnetosphere are therefore necessary to clearly determine the actual current configuration.

The model allows the separation of Pedersen and Hall currents. DP2 consists e.g. B. almost only from reverb currents. The polar electric jets (DP1) have both power components. The jets have currents of several hundred kiloamps. Dissipation of the Pedersen currents ( Joule heating) is passed on to the neutral gas of the thermal atmosphere . This creates thermospheric and ionospheric disturbances. Long-lasting disturbances combined with strong geomagnetic variations develop into global thermosphere and ionospheric storms.

Individual evidence

1. ↑ I. Pukkinen and others (eds.): The Inner Magnetosphere: Physics and Modeling. Geophysical Monograph AGU, Washington, DC, 2000.
2. ↑ ^{a b} J.P. Heppner In: ER Dyer (Ed.): Critical Problems of Magnetospheric Physics. Nat.Akad. Sci., Washington DC 107, 1972.
3. ^ ^{A b} T. Iijima, TA Potemra: Large-Scale Characteristics of Field-Aligned Currents Associated with Substorms . In: Journal of Geophysical Research . tape 83 , A2, 1978, pp. 599-615 , doi : 10.1029 / JA083iA02p00599 .
4. ^ CE McIlwain: A Kp dependent equatorial electric field model . In: Advances in Space Research . tape 6 , no. 3 , 1986, pp. 187-197 , doi : 10.1016 / 0273-1177 (86) 90331-5 .
5. ^ AD Richmond et al. a .: Mapping Electrodynamic Features of the High-Latitude Ionosphere from Localized Observations: Combined Incoherent-Scatter Radar and Magnetometer Measurements for January 18-19, 1984 . In: Journal of Geophysical Research . tape 93 , A6, 1988, pp. 5760-5776 , doi : 10.1029 / JA093iA06p05760 .
6. ^ DR Weimer: A flexible, IMF dependent model of high ‐ latitude electric potentials having “Space Weather” applications . In: Geophysical Research Letters . tape 23 , no. 18 , 1996, p. 2549-2552 , doi : 10.1029 / 96GL02255 .
7. ↑ ^{a b} H. Volland: A Semiempirical Model of Large-Scale Magnetospheric Electric Fields . In: Journal of Geophysical Research . tape 78 , no. 1 , 1973, p. 171-180 , doi : 10.1029 / JA078i001p00171 .
8. ↑ David P. Stern: The Motion of a Proton in the Equatorial Magnetosphere . In: Journal of Geophysical Research . tape 80 , no. 4 , 1975, p. 595-599 , doi : 10.1029 / JA080i004p00595 .
9. ↑ Burke, WJ, The Physics of Space Plasmas , Boston College, ISR, Boston, 2012
10. ↑ VM Vasyliunas: Mathematical models of magnetospheric convection and its coupling to the ionosphere . In: BM McCormac (Ed.): Particles and fields in the magnetosphere . D. Reidel, Dordrecht 1970, p. 60-71 .
11. ^ Atsuhiro Nishida: Formation of Plasmapause, or Magnetospheric Plasma Knee, by the Combined Action of Magnetospheric Convection and Plasma Escape from the Tail . In: Journal of Geophysical Research . tape 71 , no. 23 , 1966, pp. 5669-5679 , doi : 10.1029 / JZ071i023p05669 .
12. ^ DL Carpenter: Whistler Studies of the Plasmapause in the Magnetosphere 1. Temporal Variations in the Position of the Knee and Some Evidence on Plasma Motions near the Knee . In: Journal of Geophysical Research . tape 71 , no. 3 , 1966, pp. 693-709 , doi : 10.1029 / JZ071i003p00693 .
13. ^ ^{A b} Hans Volland: A Model of the Magnetospheric Electric Convection Field . In: Journal of Geophysical Research . tape 83 , A6, 1978, pp. 2695-2699 , doi : 10.1029 / JA083iA06p02695 .
14. ^ Naoshi Fukushima: Electric Current Systems for Polar Substorms and Their Magnetic Effect Below and Above the Ionosphere . In: Radio Science . tape 6 , no. 2 , 1971, p. 269-275 , doi : 10.1029 / RS006i002p00269 .
15. ^ Gerd Prölss, Michael Keith Bird: Physics of the Earth's Space Environment: An Introduction . Springer, Heidelberg 2010, ISBN 978-3-642-05979-7 (reprint).