Revista Brasileira de Ensino de Fısica, v. 36, n. 1, 1305 (2014)www.sbfisica.org.br

Ionosphere-magnetosphere coupling and field-aligned currents(Acoplamento ionosfera-magnetosfera e correntes alinhadas aos campos)

D. Oliveira1

EOS Space Science Center, University of New Hampshire, Durham, NH, USARecebido em 2/5/2013; Aceito em 13/5/2013; Publicado em 6/2/2014

It is presented in this paper a review of one of several interactions between the magnetosphere and theionosphere through the field-aligned currents (FACs). Some characteristics and physical implications of the cur-rents flowing in a plane perpendicular to the magnetic field at high latitudes are discussed. The behavior of thissystem as an electric circuit is explained, where momentum and energy are transferred via Poynting flux fromthe magnetosphere into the ionosphere.Keywords: space physics, ionosphere-magnetosphere interaction, plasma physics.

E apresentada nesse artigo uma revisao de uma entre diversas interacoes entre a magnetosfera e a ionosferaatraves de correntes alinhadas aos campos. Algumas caracterısticas das correntes fluindo em plano perpendicularao campo magnetico em altas latitudes sao discutidas. O comportamento desse sistema como um circuito eletricoe explicado; momento e energia sao transferidos via o fluxo de Poynting direcionado da magnetosfera a ionosfera.Palavras-chave: fısica espacial, interacao ionosfera-magnetosfera, fısica de plasmas.

1. Introduction

The existence of the Earth’s magnetic field was well-established long ago by the alignment of a compass ne-edle in a particular direction. Near the Earth’s surfacethis field behaves like a dipole field, and its existenceis believed to be due to motion of electrically chargedmaterial inside the core [1]. In the regions further awayfrom the surface of the Earth, this field interacts withcharged particles that originate on the sun, which to-gether are known as plasma or solar wind [2, 3]. Thesolar wind has its own magnetic field attached to it,called interplanetary magnetic field (IMF), which in-teracts with the Earth’s dipole field. The presence ofthis dipole field immersed in the solar particle flow gi-ves rise to a cavity called the magnetosphere, whichis shown with some of its current systems in Fig. 1.The existence of the magnetosphere in the space en-vironment close to the Earth is important because itshields the Earth from particles coming from differentregions of space, mainly those coming from the sun. Asone of the first attempts to explain such environment,in two sequential papers from 1931 about geomagnetic

storms, Chapman and Ferraro [4] came up with a the-ory of currents and compression of the magnetosphere,which was the first idea of a magnetopause-boundarybetween the magnetosphere and the ambient medium.The bow shock is formed due to the fact that the so-lar wind [5] is super-alfvenic,2 and the region betweenthe bow shock and the magnetopause is called magne-tosheath. Plasma from this region has access to the io-nosphere via the dayside cusps and the magnetosphericboundary layer. Descriptions of other magnetospheres,such of planets, their satellites, and even comets, canbe found in Refs. [7] and [8].

The “Chapman-Ferraro cavity”, as the magne-tosphere was referred to initially, generated interest bysome researchers in the middle of the twentieth century.It was Dungey in 1961 [9] who first proposed a modelof open magnetic field lines for the magnetosphere. Inthis model, IMF lines reconnect with Earth’s magne-tic field lines, and this coupling can generate severalimplications in the ionosphere, such as transfer of mo-mentum and energy from the magnetosphere into theionosphere. In this work we review some of these im-plications, starting off in the ionosphere considering a

1E-mail: dennymauricio@gmail.com.

2The solar wind has origin on the sun in a region called exosphere. This region is basically made up of protons ( 95%) and alphaparticles ( 5%). Since the plasma there behaves like a fluid, a theory called magnetohydrodynamics (MHD) [6] is used to study thisplasma. MHD waves are generated due to oscillations of the magnetic field and ions within that region. This theory also provides aquantity to measure the propagation velocity, known as Alfven speed. This plasma is then called super-alfvenic because its speed isgreater than the Alfven speed.

Copyright by the Sociedade Brasileira de Fısica. Printed in Brazil.

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partially ionized plasma. In all discussions and argu-ments that follow, only the open field line model of themagnetosphere will be considered.

Figura 1 - The magnetosphere and some of its current systems,as seen in Ref. [7]. Our interest is centered in the implicati-ons generated by the field-aligned currents in the magnetosphere-ionosphere coupling.

2. Current flow and conductivity in theionosphere

Plasmas are characterized by two classes: collisionaland collisioness plasmas. In the latter, collisions are sounlikely to happen that they can be neglected in anyanalysis of the plasma dynamics. Collisional plasmasare generally divided in fully ionized plasma, where ithas only electrons and ions, and partially ionized plas-mas, which means that some neutral atoms or mole-cules can be found in the plasma. In this case directcollisions between charged and neutral particles domi-nate, while in the fully ionized case Coulomb collisionsdominate [10]. The plasma flowing in the ionosphereis a collisional, partially ionized plasma, which can beseen in the Dungey cycle-convection scheme represen-ted in Fig. 2. This flow drags the plasma and heats theneutral gas, connecting the E region3 of the ionospherewith the magnetosphere.

It is important to know how often a collision maytake place in a partially ionized collisional gas, i.e.,how frequent collisions between neutrals and chargeshappen. Assuming that neutrals, atoms or molecules,behave like heavy obstacles to the charged particles,frontal collisions may be considered with a molecularcross-section given by σn = πr20, where r0 is the ra-dius of the target. If ⟨v⟩ represents the average ve-locity, the ion-neutral collision frequency is given byνin = nnσn⟨v⟩, with the neutral particle density repre-sented by nn. Assuming that the gas is stationary in

the Earth’s frame, the Lorentz equation for ions withdrift velocity vi is written as

miνinvi = e(E+ vi ×B) , (1)

where E and B represent the electric and magnetic fi-elds, mi is the ion mass, and e the ion charge. In orderto understand the dynamics of the ionosphere at thispoint, Eq. (1) must be solved. Magnetic field linesin high latitudes are almost parallel to each other, soB = B ez will be used for simplicity and the electricfield will be assumed with components in the plane per-pendicular to the magnetic field. Thus, using the iongyrofrequency defined by Ωi = eB/mi, the solutions forthis equation are

vx =1

1 +

(Ωi

νin

)2

[(Ωi

νin

)Ex

B+

(Ωi

νin

)2Ey

B

],

vy =1

1 +

(Ωi

νin

)2

[(Ωi

νin

)Ey

B−(Ωi

νin

)2Ex

B

].

These solutions can be written in a compact, vecto-rial form that represents the velocity perpendicular tothe magnetic field

v⊥ =1

1 +

(νinΩi

)2

[(νinΩi

)E

B+

E×B

B2

]. (2)

Figura 2 - Schematic representation of Dungey’s cycle flow in theionosphere in a noon-midnight diagram. Figure extracted fromCowley [11]. Dotted (away from the ionosphere) and crossed (intothe ionosphere) circles represent the magnetic field lines. Electricfields are already shown in the figure.

3E region or E layer is one of the ionosphere layers composed of ionized gas lying between 90-150 km above the surface of the Earth.

Ionosphere-magnetosphere coupling and field-aligned currents 1305-3

It is interesting to analyze this equation in terms ofthe ratio νin/Ωi because the ion motion changes with it.At typical heights in the ionosphere, 100 km, the gyro-frency does not change in an appreciable way, as was al-ready discussed the magnetic field is considered practi-cally constant over ionospheric altitudes.4 What chan-ges drastically is the ion-neutral collision frequency, as aresult of the decreasing ion density with increasing alti-tude. At approximately 125 km of height above the sealevel, this ratio is taken as reference with νin/Ωi = 1.Above this height, collisions are so rare that ions movemostly under E×B drift. Below 125 km, collisions hap-pen with larger frequency and the movement of ions th-rough the electric field dominates. This response to theneutral density in the ionosphere suggests that thereare currents that obey a certain pattern, as we shalldiscuss in the sequence.

The movement of electrons in the ionosphere can bediscussed in the same way. It is straightforward to writean expression for the current density in the ionosphere.Since the electron velocity in terms of the current den-sity is represented by ve = −1/(ene) j, and the electrongyrofrequency has the opposite sign when compared tothe ion gyrofrequency, we may define the current den-sity perpendicular to the magnetic field solving Eq. (1)again

j⊥ =

ene

(νenΩe

)1 +

(νenΩe

)2

[E

B−(νenΩe

)E×B

B2

], (3)

where ne is the electron density. It is useful to redefineequation (3) in terms of the Pedersen (proportional toσP ) and Hall (proportional to σH) currents:

j⊥ = σPE+ σHE×B

B(4)

In order to describe in which regions these currentsexist, it is necessary to analyze Eq. (3). The Peder-sen current flows parallel to the electric field at altitu-des above 125 km. Although the ions have dominantmobility parallel to E, some of them drift in the direc-tion of E × B. The Hall current is located at lowerheights, where it flows in the direction opposite to theelectron E×B drift. When the ratio between the col-lision frequency and the electron gyrofrequency is closeto unity, both currents have approximately the samemagnitude. Fig. 3 shows Pedersen and Hall currentsplotted in terms of eneE/B against the ratio Ωe/νen.

Figura 3 - Pedersen (continuous line, red line in online version)and Hall (traced line, green line in online version) current densi-ties plotted in terms of the inverse of the collision frequency andgyrofrequency ratio, Ωe/νen, which increases with the height. Atan altitude close to 125 km, the ratio approaches one and bothcurrents have approximately the same magnitude. Below thisreference height, collisions are very likely to occur and the Hallcurrent density dominates. Finally, above this height, collisionsare so rare meaning that the ratio in Eq. (3) is almost null. The-refore, in those regions, the Pedersen current density dominates.

For future use, it is important to represent the cur-rent density in terms of the total height-integrated cur-rent perpendicular to the magnetic field

i⊥ = ΣPE+ΣHE×B

B, (5)

where ΣP,H =∫σP,Hdz are the height-integrated Pe-

dersen and Hall conductivity. On the dayside of theionosphere, these conductivities are of the order of10 mho, which is the unit that represents the inverseof the unit of electric resistance ohm commonly used inplasma physics.

The currents driven by the magnetosphere combinewith the magnetic field generating the force j×B. Theseelectromagnetic forces compensate the drag force of theneutral particles in the ionosphere, i.e., component ofj × B associated with the Pedersen current has direc-tion opposite to the atmospheric drift force of the neu-tral particles. Similarly, the component of the sameforce associated with the Hall current is directed op-positely to the electric field. Therefore, each Peder-sen/Hall component of j × B has direction pointingto the Hall/Pedersen direction, respectively. Assumingthat those currents have the same order of magnitude, itmay be inferred that they balance each other. Details ofhow the j×B force balances the neutral drag force andhow it connects with the magnetosphere may be foundin Refs. [11] and [12]. The height-integrated Joule hea-ting rate per unit area is represented by i⊥ ·E = ΣPE

2

Wm−2, which suggests that the Pedersen current beha-

4The Earth’s magnetic field in the radial direction has strength B(r) = B0

(REr

)3, where B0 is the magnitude of the magnetic field

on the Earth’s surface, RE is the Earth radius, and r the distance from the Earth’s center. Considering that the Earth’s radius isapproximately 6400 km, a distance variation inside the range of 100 km may be neglected.

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ves like a load and the Hall current does not dissipateenergy in the ionosphere.

These currents, well known as large-scale currents,are depicted in Fig. 2 and Fig. 4. Also represented inFig. 4 are other important currents, called field-alignedcurrents (FACs). Their importance and dynamic re-lations with both Pedersen and Hall currents will bediscussed in the following section.

Figura 4 - Schematic representation of the large-scale currents inthe region near the polar cap. Perdersen and Hall currents, aswell as the Region 1 and Region 2 currents, are shown. Imagedownloaded from http://commons.wikimedia.org.

3. Current circuits in the magnetosphere-ionosphere system

The system of currents shown in Fig. 2 is based onDungey’s idea of open field lines in the magnetosphere.In that diagram the arrowed lines represent the plasmaflux in the ionosphere, the dashed lines represent theboundary between open and closed field lines, and theshort arrows represent the electric field. The dotted andcrossed circles indicate the flow direction of the FACs,where the former indicate currents upward and the lat-ter currents downward in relation to the ionosphere.

As we have derived previously, the Pedersen currentalways flows in the direction parallel to the electric fieldand, therefore, cannot close in the ionosphere. In orderto satisfy the divergence of the current density, somelarge-scale currents must exist. These currents are cal-led Region 1 and Region 2 currents, and are also classi-fied as FACs. Region 1 currents are located in regionsof higher latitudes, while Region 2 currents are foundin regions of lower latitudes. Region 1 currents are di-rected toward the ionosphere on the dawn side, andthe Region 2 currents flow away from the ionosphere inthe same region. On the other hand, on the dusk sidethe situation is the opposite: Region 1 currents flowupward and Region 2 currents downward. For a detai-

led discussion on how these currents close in the mag-netosphere, see [12]. These field-aligned currents werefirst observed in 1966 by Zmuda et al. [15], based on aseries of measurements of magnetic disturbances. Tenyears later, Iijima and Potemra [16], and in other futureworks, based on a series of measurements of magneticdisturbances, found that the Regions 1 and 2 currentsobey an almost permanent pattern in the ionosphere-magnetosphere system.

As we have seen in the discussion of currents andconductivities in the ionosphere, the Pedersen conduc-tivity may be thought as working like a“load”in anelectric circuit. This circuit is coupled to the mag-netosphere through the FACs, and the solar wind isthen known as an MHD generator, which is the voltagesource for such circuit. In order to understand how themagnetosphere is linked to the MHD generator, the sca-lar product j · E < 0 indicates the source (generator),while in the low ionosphere the Pedersen currents arethe load with j · E > 0. The flow of energy and mo-mentum takes place due to the existence of a perturbedmagnetic field which points in the direction of the sun.This perturbation is located in the direction midnight-noon in Fig. 2. As a result, a Poynting flux pointingdownward arises due to the interaction of this pertur-bed magnetic and the electric fields, which is orientedfrom dawn to dusk.

4. Conclusion

The discussion of the coupling between the magne-tosphere and the ionosphere was based on Dungey’smodel of open magnetic field lines. This conditionthen implies that there is a flux of both momentumand energy driven by the solar wind MHD generatorin the magnetosphere into the ionosphere, that beha-ves like a load in a coupled electric circuit. This dis-cussion was motivated by the model based on interac-tion among several currents located in the ionospherein low altitude, and how they are closed with the mag-netosphere through field-aligned currents (FACs). Dueto the fact that electricity flows easily through the fi-eld lines in a plasma, the argument that the transferof energy and momentum takes place because of theexistence of such currents was supported. The reasonfor the existence of these currents is that the resistivebehavior of the ionosphere requires FACs to close thedivergence of the current density. Then, if the conduc-tivity in the ionosphere were constant, FACs would notexist and the coupling between the magnetosphere andthe ionosphere would not take place.

Acknowledgments

The author is pleased to thank Dr. Charlie Farrugia forsuggesting this subject and for his valuable discussions.

Ionosphere-magnetosphere coupling and field-aligned currents 1305-5

The author is also grateful to Dr. Eberhard Mobiusand Ian Cohen for reading the manuscript and givingimportant suggestions.

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