Plasma pressure generated auroral current system: A case study



[1] An anti-sunward directed azimuthal pressure gradient drives meridional currents perpendicular to the magnetic field in the dusk and dawn closed field line regions. These currents are closed through the auroral ionosphere consisting of a pair of upward and downward sheet field aligned currents cross connected in the ionosphere. Using a conjunction of FAST and Polar the intensity of the up-down sheet FAC pair was measured in the dusk sector in typical auroral conditions. The T96 field model was used to define the geometry and it predicted that field lines at the satellites were stretched to 15 RE. The steady state pressure gradient current was calculated through a surface in the magnetosphere separating the upward and downward going FAC. With the field stretching predicted by the model a typical quiet time azimuthal pressure gradient of 0.01 nPa/Re generated sufficient current to be the source of the observed auroral current loops.

1. Introduction

[2] Auroral arcs are frequently observed in the evening pre-midnight hours stretching east west across the night sky for several hours in the polar regions. It is relatively well established, primarily from the presence of trapped protons, that these arcs occur on closed field lines and these regions are not directly connected to interplanetary space. Therefore the current generator has to be also in the closed field line region.

[3] The importance of pressure gradients as current generators in the magnetosphere [Cole, 1963] and that they are a possible source of auroral field aligned currents (FACs) has been recognized for some time [Vasyliunas, 1970]. The continuity of currents demands that any divergence of the current density perpendicular to the magnetic field must effect a change in the FAC density. The importance of pressure gradients in generating the auroral currents is fully recognized by auroral arc models [e.g., Haerendel, 2007]. Shiokawa et al. [1998]showed statistically from single satellite data that an azimuthal pressure gradient is present on the night-side in the neutral sheet when the magnetic field has a dipolar configuration near the time of passage of high speed ion flows during magnetically active times. Under these circumstances substantial FACs (4.1 × 105 A per 3 hour local time sector equivalent to 190 A/km at 65 degree latitude) were seen and it was discussed that it could be the source of the substorm current system. Shiokawa et al. [1998] was a statistical study representing substorm associated effects. During magnetically active times in the presence of high speed ion flows the magnetic field models are inaccurate and it is not possible to evaluate the position of the generator and the auroral circuit on a one to one basis. In another statistical study Wing and Newell [2000]used orbiting low altitude satellites like DMSP to generate a plasma pressure map at low altitudes and by assuming pressure isotropy mapped the plasma properties to the equatorial plane along the magnetic field using “a modified Tsyganenko 1989 magnetic field model”. This study showed strong, mostly radial pressure gradients in the night side magnetosphere and their modeled FAC-s derived from the pressure gradients agreed well with the direction and magnitude of the region 1 and region 2 current systems. This was a remarkably successful statistical study considering the averaging over different geophysical conditions and the use of the magnetic field model to map low altitude satellite data to model magnetospheric particle densities and temperatures. With the advent of multi satellite missions such as CLUSTER and THEMIS, it is now possible to make direct measurements of the plasma pressure and hence its gradient [Xing et al., 2011]. These measurements show that during quiescent times the night side azimuthal pressure gradients are of the order of 0.01 nPa/Re and it can increase by a large factor before and during substorm onset.

[4] Auroral arcs often occur in quiescent steady state situations in which magnetospheric field configuration should be well represented by empirical field models such as the T96 [Tsyganenko, 1996] model. In such steady state situations, unlike in the case of dynamic auroral substorms, it should be possible to map the auroral magnetic field lines relatively accurately to the current source region. We also know that arcs are mostly the result of electron precipitation driven by FACs flowing in and out of the auroral ionospheres. These currents can be measured accurately by magnetometers on low altitude polar orbiting satellites and by mapping these currents to the magnetospheric source regions and imposing the conditions of current continuity we can establish on a case-by-case basis whether the current requirement can be satisfied by a steady state magnetospheric generator. In a closed field line region and in isotropic plasma theB generator currents are largely due to the plasma pressure gradients and it is difficult to postulate other current sources.

[5] In this paper we will verify that an azimuthal pressure gradient current generator in the closed field line regions of the magnetosphere can produce the required current in steady state conditions by considering a well documented set of measurements of the aurora and the associated auroral current system [Schriver et al., 2003, hereinafter S-2003) when FAST and Polar were on the same field line. We used the T96 field model to describe the field configuration and calculated the current generated by an azimuthal pressure gradient consistent with steady state non-substorm conditions.

2. Basic Equations

[6] To derive the pressure gradient current, one can start by considering the most significant components of the ion (or electron) average drift velocity, vdin a non-uniform magnetic field confined in a small region:

display math

where ρ = the gyro radius, v = the perpendicular velocity, n = plasma density, q = electronic charge, E = electric field, B = the vector magnetic field, B = the magnitude of B, the curly brackets signify averages, m = particle mass, vp = B parallel velocity, κ = the field curvature vector and M is the magnetization per unit volume or –pB /B2. The four terms are (1) the gradient B drift, (2) the curvature B drift, (3) E × B drift and (4) the magnetization drift [e.g., Siscoe, 1983]. The last term, the magnetization drift, has three components in a non-uniform magnetic field. The first one of these is a function of the pressure gradient ∇p, and the other two are functions of the total (B) pressure and the magnetic field gradients. Siscoe [1983] showed that these last two components oppose the gradient B drift and the total B current flow due to the ions becomes:

display math

where ∇p = pressure gradient, pp = B parallel plasma pressure and p = B plasma pressure.

[7] We have neglected the inertial and gravitational terms. For an isotropic pressure distribution and with the inclusion of the electron E × B drift cancelling the ion E × B component, the current carried by the ions reduces to:

display math

This is the same formula that applies to the case of uniform B field. It is interesting to note therefore that in steady state conditions in an isotropic plasma the gradient and curvature B and the residual magnetization currents cancel. Thus the magnetosphere, when it contains non-uniform plasma, acts as a current generator but only when the plasma pressure is non-uniform.

[8] An alternate starting point is to consider the force balance in a quasi-static system between the Lorentz force acting on the ions and electrons and the pressure gradient force. In a steady state situation the equation for each species is:

display math

Taking the cross product with B will yield (equation 3).

[9] It is conventional to eliminate the current variable (J = qn v) by replacing it by ∇ × B from Maxwell's equations. The resulting (∇ × B) × Byields two terms containing the magnetic field, the magnetic pressure and the magnetic tension terms. This approach is useful in making self-consistent models because only a single variableBneeds to be considered and many magnetospheric MHD models currently in use are based on this formulation. These models are intrinsically non-linear, providing relatively little intuitive insight into what the dominant processes are and how the energy conversion proceeds from plasma dynamics to auroral currents. The concepts of magnetic pressure and tension forces are mathematical tools and their introduction may result in systems that are hard to visualize.

[10] Figure 1 shows the model described by Shiokawa et al. [1998]based on the Bostrom case 2 type FAC system. Plasma enters the magnetosphere from the night side plasma sheet region and forms a pressure bulge with a gradient in the anti-sunward (-x direction) near tail plasma sheet region. The existence of such a pressure bulge in the midnight region was shown for example byGkioulidou et al. [2009]. In Figure 1 the pressure gradient current (red arrows) flows earthward. This current closes through a return loop consisting of a pair of FACs and a poleward (south to north) ionospheric current on the dusk side. Although not shown the opposite current is produced on the dawn side. We will proceed here by simply considering the continuity of the current instead of dealing with the magnetic pressure and tension forces.

Figure 1.

A pressure bulge in the antisunward plasma sheet creating an anti-sunward pressure gradient (dashed arrow), B pressure gradient current (red), apparent electric field driving the return current (green), field aligned and ionospheric return loop (narrow black) and potential plasma drift opposite to the pressure gradient (black thick arrow). The dawn side current system was not shown for simplicity.

[11] The pressure gradient is a current source or current generator and depending on the effective “resistance” of the FAC and the ionospheric segment of the closure loop a potential difference is produced. The generator will appear to create an “external” electric field indicated with green arrows and the equivalent “battery terminals” (shown as + and −). The sense of the FAC current is such that on the dusk side the poleward current is upward carried by downward accelerated auroral electrons. It is the reverse on the dawn side, consistent with the direction of the region 1 and region 2 current system [Iijima and Potemra, 1976]. Large electric fields and corresponding increased convection speeds are often seen in the dawn and dusk magnetosphere that are in excess of the quiescent convection speed derived from the applicable cross polar cap potential [e.g., Hanson et al., 1993]. In this treatment we neglected a uniformly superposed convection electric field because it causes no additional currents on the scale of the aurora.

3. Observation of the Auroral Current Loop

[12] On June 9, 1997 FAST and Polar were magnetically conjugate on the dusk side and FAST passed through the auroral oval, providing a snapshot of the integrated auroral FACs and the corresponding particle precipitation. This event was analyzed and published by S-2003. During this overpass Polar and FAST were at 24,843 km and 2500 km altitude respectively on the dusk side and the field line mapped to the aurora at 20 MLT. We have illustrated this schematically in Figure 2. FAST and Polar were crossing a pair of FACs, which were the continuation of pressure gradient currents generated mainly at the low latitude portion of the flux tube. We are considering the pressure gradient current flowing through the surface separating the up and the down going FAC that occurred at 69.3° latitude. The FAST data are illustrated in Figure 3. Besides drawing the assumed generator current loop we also added a note highlighting that the most poleward aurora is Alfvenic showing a strong contribution from electrons that are accelerated from the ionosphere by Alfven waves. These type of auroras at the polar cap boundary often carry large FACs [e.g., Chaston et al., 2003] and in our case a substantial upward current was also seen. In this work we assumed that these FACs at the poleward boundary of the aurora are located at the open and closed field line boundary and that they are probably associated with convection reversal at the boundary. Here we are considering only the two symmetrical portions of the FAC as measured by FAST, the upward flowing current region between 70.2 and 69.3 degrees and the downward one between 69.3 and 68.4. The upward current region is consistent with the particle spectrogram which shows inverted V type precipitation with energies up to ∼6 keV. The downward current region shows minimal electron and some significant ion precipitation (the ion spectrograms are not shown on Figure 3). The lack of up-going electron signature in the downward current region is most likely because of the low altitude of the FAST observation.

Figure 2.

Schematic illustration of FAST and Polar crossing a pair of FAC, which are the continuation of currents generated in the –y direction near the low latitude portion of the flux tube by pressure gradients. The two field lines selected at different longitudes and at the same magnetic latitude as FAST and Polar are also shown. We considered a small region (illustrated in blue) bounded by B parallel length dl and the B distance, dw. between two field lines. In reality the field lines were highly stretched and bent back towards the tail.

Figure 3.

(a–c) The FAST data as shown by Schriver et al. [2003]. We added the illustration of the presumed FAC currents and the B pressure gradient generator current.

[13] The magnetic field component perpendicular to the orbit trajectory shows a downward deflection of about 250 nT when the satellite passed through the upward current region and about the same positive deflection due to the downward current region. We consider this FAC pair as the return current generated by the pressure gradient. Although the magnetic field data shows a smooth transition registering the integrated effects of the currents, it can be seen from the particle spectrograms that the auroral electron flows were highly structured. Nevertheless the amplitude of the field change measured by the satellite magnetometer as the satellite over-crossed the current provided a very accurate measure of the total equivalent sheet current as long as the current sheet extends over a large distance in the longitudinal dimension. The current density in A/m is taken in the longitudinal (dw) dimension. Using the assumption that the FAC-s are infinite sheet currents the change in field going through each of them is B = 4πI/10, where B is in nT and I is the sheet current density in A/km. The 250 nT magnetic field variation measured by FAST yields an average sheet current density of 200 A/km for the up and the down going legs of the FAC sheet pair.

[14] The symmetrical portion magnetic signature at Polar is of the order of 30 nT. Using the same sheet current approximation we find the sheet current density measured by Polar is 24 A/km or 8.3 times less than at FAST. We expect that the same FAC would be flowing between two adjacent field lines at Polar and at FAST except the distance between the field lines at Polar is greater. As a quick consistency check we scaled the sheet current by the distance between the two field lines at the altitude of each satellite and found that the sheet current density ratio should have been 7.3. In summary, the two satellites measured a pair of up and down going FACs that were approximately the same when allowing for the mapping of the background B field.

4. Calculation of the Pressure Gradient Currents

[15] We assumed a steady state isotropic plasma with a pressure gradient of 0.01, nP/Re in the −x direction. This was a typical pressure gradient measured during quiescent times prior to substorm onsets [Xing et al., 2011]. We calculated the pressure gradient current flowing through the surface separating the up and the down going FAC. We considered two field lines adjacent in longitude at this (69.3° magnetic latitude) separated by an arbitrarily chosen 1.55° magnetic longitude (azimuth). To calculate the pressure gradient current we numerically integrated the current density through the surface by considering small surface increments bounded by dl and dw where dl (meters) was taken parallel to the field and dw (also meters) was the perpendicular distance between the two adjacent mapped field lines (see Figure 2). The greatest contribution comes from the equator because the pressure gradient current has a 1/B dependence, which is combined with the large distance between adjacent field lines.

[16] To define the field lines we used the T96 field model [Tsyganenko, 1996]. Both field lines were taken at the approximate latitude of the FAC reversal (Magnetic Latitude 69.3°). One of these field lines was at the longitude of FAST (302.45°) while the other field line was taken at the same latitude but slightly larger longitude (304.0°). The two adjacent field lines are illustrated in Figure 4.

Figure 4.

Tsyganenko 96 field line trace of the two field lines (one of them conjugate to FAST and Polar) at mag. Lat. of 93.2°, which is at the boundary between the up down FAC. (a) View projected on the equatorial plane. (b) Side view from dusk side.

[17] We calculated the pressure gradient current density parallel to y

display math

where kTi and kTe are the ion and electron thermal energy respectively in eV, inline image is the ion density gradient, e is the electronic charge (Coulombs) and B is the magnetic field (Tesla). kTi was taken to be 5000 eV from Hydra data between 0429 and 0435 UT (S2003, Figure 7c) and kTe was conservatively estimated to be about 1000 eV although the field aligned spectral width of the precipitating electrons was more. To find the total B current going through the area bounded by the two field lines we numerically integrated the current through the region bounded by the two field lines. The integrated current was 26 kA for the ions and 5 kAmp for the electrons for an assumed pressure gradient of 0.01 nP/RE.

[18] At FAST altitude 2500 km the two field lines were 90.77 km apart in the azimuth, or longitude direction and the 200 A/per km sheet current density represented a total FAC of 18 kAmp between the two field lines. These results compare favorably with the generated current. Note that the bulk of the current should flow in the northern hemisphere where the satellites were observing because the atmosphere was sunlit.

5. Energy Conservation

[19] The pressure gradient current generator can be regarded as having high internal impedance and the magnitude of the generated current is relatively independent of the resistance R of the return (load) circuit. The electrical potential across the circuit will be Φ = I R. The electric field E = inline image where L is the length of the current generating region in the y direction. The electric field causes an E × B/B2 (v = E/B) drift in the sunward (+x) direction against the Lorentz force = I B L. The power extracted is the velocity times the opposing force or v (I B L). But the velocity v is inline image or = inline image. The power is inline image or I R2, which is exactly the same as the power dissipated in the auroral current circuit.

6. Discussion

[20] In our case study an azimuthal pressure gradient of 0.01 nPascal/Rewas sufficient to generate the auroral current observed. The June 9, 1997 period was fairly disturbed. The pressure gradient current has a 1/B dependence and highly inflated field lines that pass through large regions of low magnetic field are much more effective in generating pressure gradient currents than shorter dipole like field lines. This highlights the requirement for strong field inflation or field line stretching to create a strong auroral current system with moderate pressure gradients. Auroras occur only at high latitudes where the field lines are stretched. The presence of proton precipitation collocated or mostly equatorward of the pre-midnight arcs suggests that these field lines containing the arcs are highly distorted with steep curvatures at the equator that enhance proton precipitation.

[21] It would seem that the pressure gradient current generator would have high internal impedance with relatively little feedback from the ionospheric loads. The return (load) currents should however divide into the two hemispheric branches depending on the load impedance of the hemispheres and thus influencing auroral conjugacy. Higher currents would be expected to flow in the more conductive ionospheres.

[22] What is the source of the auroral acceleration potential? Both the upward (70.2° to 69.3°) and downward (69.3° to 68.4°) current carrying flux tubes cover great distances at the equator. Even in an un-inflated dipole the radial separation of these field lines at the equator is about 6000 km. Thus thein situ measurements of the electric field from Polar (S-2003) of a few mV/m accounts for an apparent potential of more than 6000 Volts over the width of the up or down flowing FAC structure and this potential may be seen as the auroral acceleration potential in the upward FAC region.

[23] In this work we are discussing a possible source of the large-scale current generator of the auroral current loop. We have little to say about what causes the filamentation of the upward currents to cause narrow auroral arcs structures. It appears that there is a mechanism that makes the auroral upward FAC generation highly nonlinear and it is probably self-enhancing. It is much more non-linear than can be predicted by Knight's relationship.Haerendel [2007] suggests the presence of a “ledge” in the ion pressure distribution, which maps down to the ionosphere to produce the auroral arc. It should be possible to see large changes in the plasma pressure distribution by high altitude satellites when they cross regions above auroral arcs.

7. Conclusions

[24] In a closed field line region pressure gradients can be the most significant current sources during quiescent conditions. During these conditions it is also possible to reliably model the magnetic field and the integrated pressure gradient current can be calculated reliably. We considered the auroral current system as consisting of pressure gradient generator feeding a dissipative return loop, through a FAC pair and the current connecting them in the ionosphere. The FAC currents are azimuthal current sheets and their magnitude can be measured accurately by the magnetic field data on polar orbiting satellite passing through them. In this case study good agreement was found between the magnitude of the FAC sheet current pair as obtained by FAST and Polar in a simultaneous coordinated measurement. The azimuthal plasma pressure gradient of 0.01 nPa/RE used in our calculations is characteristic of quiet times [Xing et al., 2011] and it was sufficient to power the auroral current system as seen by the two satellites. As the pressure gradient current generation is proportional to 1/B it is highly dependent on the configuration of the magnetic field. In our case study the field lines, as modeled by the T96 field model, were extended and therefore favored the current generation. The pressure gradient current generates an apparent electric field and the electric field measured on Polar (S-2003) is integrated over the latitude extent of the upward or downward FAC portions several kV potential could be realized, which was sufficient to account for the auroral acceleration potential seen. It can be shown that the power extracted by the sunward drift of the plasma carrying the pressure gradient current acting against the Lorentz force is equal to the IR2 dissipation of the auroral current loop.


[25] Helpful discussions with Richard Wolf of Rice University, Chris Chaston and Forrest Mozer of UC Berkeley and some comments by Gerhard Haerendel are gratefully acknowledged. Parts of this work were supported by the NASA THEMIS program under contract number NAS5-02099 and by NSF under grant numbers 0636899 and 0840398.