High-altitude signatures of ionospheric density depletions caused by
  field-aligned currents
Microsoft Word - Karlsson et al 2007.doc
High-altitude signatures of ionospheric density depletions caused by 
field-aligned currents 
T. Karlsson1, N. Brenning1, O. Marghitu2,3, G. Marklund1, S. Buchert4
1 Space and Plasma Physics, Royal Institute of Technology (KTH), Stockholm, Sweden. 
2 Institute for Space Sciences, Bucharest, Romania. 
3 Also at Max-Planck-Institut für extraterrestrische Physik, Garching, Germany. 
4 Swedish Institute of Space Physics, Uppsala, Sweden. 
Abstract. We present Cluster measurements of large electric fields correlated with intense downward 
field-aligned currents, and show that the data can be reproduced by a simple model of ionospheric 
plasma depletion caused by the currents. This type of magnetosphere-ionosphere interaction may be 
important when considering the mapping between these two regions of space. 
1. Introduction 
A system of magnetic field-aligned current sheets closing via Pedersen currents in the 
ionosphere will set up an ionospheric electric field. For constant conductivity, and for 
sheets extending to infinity along the field-line and one of the perpendicular 
directions, we get: 
1 1 1P
P P P P
E j d d Bτν τν νμ ν μ
= = = =
Σ Σ Σ ∂ Σ∫ ∫        (1) 
where ν is the direction perpendicular to the sheet, τ  the tangential direction, Eν is the 
normal electric field, JP and ΣP, the height integrated Pedersen current and 
conductivity, Bτ the tangential magnetic field, j// the field-aligned current (positive for 
downward currents) and μ0 the magnetic permeability of vacuum. This kind of 
correlation between Eν and Bτ can be seen rather often in the dayside auroral oval (e.g. 
Ishii et al., 1992). When the conductivity is not constant, the above correlation breaks 
down; in this paper we will present data from the Cluster spacecrafts, where this 
correlation is replaced with a correlation between Eν and  j//, i.e. the derivative of Bτ . 
2. Cluster data 
We present electric and magnetic field data from the EFW (Gustafsson et al., 1997) 
and FGM (Balogh et al., 2001) instruments on the Cluster satellites, which have an 
apogee of 19.8 RE and a perigee of 4.0 RE, in radial  distance. We first present data 
from a northern hemisphere auroral oval crossing, on Feb 18, 2004, from 08:58:20 to 
09:10:00 UT. The Cluster radial distance during this time period was about 4.2 RE, 
and the satellite separations between approximately 350 and 1100 km. In Figure 1 we 
show the residual magnetic field vectors along the satellite tracks projected onto a 
plane perpendicular to the geomagnetic field. The two perpendicular directions in the 
figure roughly correspond to geomagnetic North, and East. The diamonds at the 
bottom end of the tracks indicate the satellite positions at 08:58:20 UT. (The data is 
color coded: black – S/C 1, red – S/C 2, green – S/C 3, blue – S/C 4.) The satellites 
move relatively close to a pearls-on-a-string configuration. The main feature of the 
data is the crossing of three sheets of field-aligned current, from bottom to top a 
relatively smooth sheet of upward current approximately 800 km wide, a thinner sheet 
of downward current (≈250 km), and finally a wider sheet of predominantly upward 
currents (~1000 km wide). (The meridional mapping factor to ionospheric altitude is 
11.6.) This current system remains essentially stationary in space for the whole  200 s 
period between the crossings of the central current sheet by S/C 1 and S/C 4, which is 
the reason we have chosen to present this event. We have applied minimum variance 
analysis on the magnetic field data from all four S/C, and have used the average 
resulting angle of 5.8° to establish the sheet-aligned coordinate system. We have then 
used the infinite current sheet approximation to calculate the field-aligned current j// 
from the tangential component of the residual magnetic field Bτ . In Figure 2 we 
present j// and the normal electric field Eν measured by Cluster. All values are mapped 
to ionospheric altitude. Also presented is the result of a model calculation described in 
Section 3. The correlation between Eν and j// is clear for all S/C in the downward 
current region. This type of correlation is rather uncommon, but a manual inspection 
of around 300 auroral zone crossings resulted in identification of 23 similar events, 
i.e. in about 8% of the crossings, all for downward currents. 17 of the 23 events where 
encountered during winter conditions and 15 on the night side. 
3. Comparison data – model 
The close relation between the electric field and the local downward field-aligned 
current (DFAC) suggests that there is a relation between the DFAC and the 
conductivity, since an infinitesimally thin current sheet gives a negligible contribution 
to the ionospheric closure current across the sheet, Jν. However, with a coupling to a 
local decrease in the conductivity it can produce a local increase in Eν (Figure 3). 
Such decreases in the conductivity coupled to DFACs have been modeled by Doe at 
al. (1995), Blixt and Brekke (1996), Karlsson and Marklund (1998, 2005), and 
Streltsov and Marklund (2006). A few radar observations of ionospheric density 
cavities which may be related to this mechanism have been reported by Doe et al. 
(1993), Aikio et al. (2002), and Nilsson et al. (2005). The reason that a cavity is 
formed in DFAC regions is that the parallel current is mainly carried by electrons, 
whereas the Pedersen current is carried by ions. In regions where the downward 
parallel and perpendicular currents couple there will then be a net outflow of current 
carriers.   
Here we model this interaction in a heuristic way by prescribing the conductances by 
, // //
, for downward
0, for ward
down s
P P 0
k j j
Σ = Σ − ⎨
Σ = Σ
  (2) 
where ΣP,0 and kdown,s (>0) are constants, with s = 1-4, for the four spacecraft 
crossings. We ignore any effects on the conductance from the upward currents, since 
we will concentrate on the electric field behavior in the downward current region. We 
also set a minimum value for  the Pedersen conductivity of 0.2 S, which represents the 
background conductivity due to galactic cosmic rays, which are always present. 
Current continuity and the assumption of an infinite current sheet yields 
( ) ( ) ( ) ( ) ( ) ( )
0 0 0 0P HJ j d E E
ν ν τν
ν ν ν ν ν ν ν′ ′= + Σ − Σ∫           (3) 
where Jν is the height-integrated ionospheric current normal to the sheet. Eτ is 
constant if we use the electrostatic approximation ( 0∇× ≡E ). (2) and (3) then give 
( ) ( ) ( )
( ) ( )
1P H H
P P P
E E E j d
ν ν τ ν
ν ν ν ν
ν ν ν
Σ Σ − Σ
′ ′= + +
Σ Σ Σ ∫  (4) 
Using the observed values for j// along each of the satellite tracks, we can calculate Eν, 
as a function of ΣP,0 = ΣP(ν0), Eν (ν0), Eτ, and kdown,s. Before t ≈ 320 s the electric field 
is small and rather constant and we can assume that it can be mapped to the 
ionosphere and be taken as the background field of our model. However, there is an 
offset in the electric field component aligned with the direction towards the sun, due 
to a photo electron sheet. Using data from the electron drift instrument (EDI) on S/C 1 
we correct for this and then take the average electric field for 60 s prior to the crossing 
of the large DFAC, which we use as our background ionospheric electric field: Eν (ν0) 
= 0, Eτ = -6 mV/m (values mapped to the ionosphere).  
In principle the conductance could be calculated from the electron data, but this is a 
very uncertain procedure in the absence of energetic precipitating electrons, and 
outside the scope of this paper. Instead we assume a reasonable background 
conductance. The results are rather robust with respect to the chosen value of  ΣP,0, but 
the numerical value of kdown will of course vary within a factor of 2-3 depending on 
the choice of conductance. By trial and errorr we then find that the following 
parameters reproduce the electric field behavior in the DFAC region well:, ΣP,0 = 5 S 
and kdown,1 = 0.33 Sm2/μA, kdown,2 = 0.43 Sm2/μA, kdown,3 = 0.44 Sm2/μA, kdown,4 = 0.68 
Sm2/μA, where the subscript on the k’s indicate S/C number. Eν thus calculated is 
plotted in green in Figure 2. Thus the same set of parameters, except for kdown, 
reproduces the DFAC electric field quite well. It is interesting that kdown has an 
increasing trend with time; in Figure 4 we plot the values of kdown as a function of time 
from the first crossing of the current sheet. The crossing time is defined as the time 
when the current maximum is encountered, and the error bars in the t-direction 
indicate when the current is half the maximum value. A linear fit is reasonable which 
means that we can write 0( )downk t tκ= − , with κ = 1.4·10
-3 Sm2/μAs, and t0 ≈ -200 s, 
consistent with a gradual deepening of the density cavity, beginning about 200 s 
before the first satellite crossing.  
Revisiting the data from the simulations by Karlsson et al. [1998] we can calculate 
κ. In the simulations, the development of kdown settles down to a reasonably linear 
dependence on time after the first tens of seconds, from which we can estimate κ. The 
value of κ depends on various initial conditions of the simulations but for some 
realistic situations varied from around 1·10-5 to 2·10-3 Sm2/μAs, which is in agreement 
with the above measurement.  
For this event the horizontal ionospheric current Jν ,//, resulting from the feeding 
field-aligned currents was comparable to the current associated with the background 
electric field: | Jν ,//| ≈ 20 mA/m,  |Eτ ΣH(ν0)| ≈ 30 mA/m. Below we show two cases 
where one of these current contributions dominates over the other one.  
First (Figure 5a) we show data from a northern hemisphere auroral oval pass on  Apr 
27, 2002, with MLT ≈ 22, ILat ≈ 66º, and the geocentric distance 4.9  RE. We show 
data only from S/C 4, but similar signatures can be seen on S/C 2 and 3.  Using the 
same method as above we calculate j//, ΣP, and Eν. In the figure the modeled Eν and ΣP 
is plotted in red. j// is not shown, but has a maximum (downward) value of 34 μA/m2. 
For this event upward accelerated electrons are observed from t ≈ 70950 s, which 
complicates the mapping of the background ionospheric electric field. We instead 
here consider it as a free parameter. The fact that the constant background current 
(driven by the background electric field) dominates over Jν ,// (440 mA/m vs. 90 
mA/m) means that the electric field traces out the form of the conductivity, which in 
turn traces out the DFAC. We thus get a very detailed correlation between the electric 
field and the DFAC, and a unipolar Eν field signature at the density cavity.  
In Figure 5b we present data from an auroral crossing on Jan 11, 2005. MLT ≈ 22, 
ILat  ≈ 66º, geocentric distance 4.3 RE, max(j//,down) = 32  μA/m2. Here the background 
ionospheric current is dominated by Jν ,//. This means that the ionospheric current is 
not constant across the low-conductivity region, and we should not expect such a 
detailed correlation between Eν and j// as in the above case. In fact, what we see is that 
the electric field is large inside the low-conductivity region of the DFAC, but since 
the ionospheric current changes sign inside this region, the electric field also does, and 
produces a bipolar electric field signature. A small westward background electric field 
shifts the zero crossing of the total current Jν slightly from that of Jν ,//. 
4. Discussion and conclusions 
The correlation between large electric fields and DFACs presented here is consistent 
with them being associated with ionospheric low-conductivity regions. A correlation 
between the electric field and the derivative of the magnetic field could also be the 
result of a partially reflected Alfvén wave, but this would not explain why we only 
observe this correlation for downward currents, or the preference for night-
/wintertime conditions. The correlation is also not consistent with the signatures of a 
U-shaped potential structure. There, the largest current is associated with the centre of 
the structure, where the perpendicular electric field has its minimum. In fact, in order 
for the electric field correlation with the DFAC to map all the way out to Cluster 
altitudes, we must assume that there is no field-aligned potential drop along the 
magnetic field line. In that case the correlation represents the naked high-altitude 
signature of the ionospheric density depletion. In many cases we would expect large 
DFACs to be associated with such a parallel potential drop [e.g. Elphic et al, 1998]; 
this may be one of the reasons why events of the type we have presented here are 
relatively rare; we will only see them before such a potential drop has developed. 
Another reason could be that generally rather low background conductivities will be 
required.  
Reversing the argument, observations of large perpendicular electric fields at 
magnetospheric altitudes is generally taken as proof that there is a parallel potential 
drop above the ionosphere. Our results show that this is not necessarily true, but that 
at least part of this potential drop may be situated deep in the ionosphere, in the E and 
lower F regions, where the currents partially close through the developing density 
cavity [Karlsson and Marklund, 1998]. This should be taken into account when 
interpreting high-altitude electric field data.   
For the first event, the current system is stable for around 200 s. The close to linear 
evolution of kdown, can be seen as a first observational comparison with modeling of 
the temporal evolution of ionospheric density cavities.  The 200 s time scale is, 
according to the modeling work quoted above, a typical time scale for creating a deep 
ionospheric plasma depletion. We would expect to see this type of events for 
conditions of some moderate geomagnetic activity (to create large DFACs), but not 
during e.g. the substorm expansion phase, where the current systems would probably 
move around too much on time scales faster than the depletion time. We have checked 
this by inspecting the Auroral Electrojet index for the 23 events. Only four of the 
events where encountered during the expansion phase, whereas the rest were observed 
during periods that had a medium level of activity; growth or recovery phase or steady 
magnetospheric convection events. This is further support for the model presented 
above. 
Acknowledgements 
The authors are grateful to G. Haerendel for some suggestions and comments. 
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Figure 1. Magnetic field perpendicular to the geomagnetic field for the time period 
2004-02-18 08:58:20-09:10:00 UT.
Figure 2. Measured (blue) and modeled (green) normal electric field, and measured 
field-aligned current (red) for the same time period as Figure 1. Note that in this 
figure downward current is plotted as negative current. 
Figure 3. Schematic of the connection between DFAC, current closure and iono-
spheric cavity formation.  
Figure 4. Temporal evolution of kdown. 
Figure 5.  Measured (black) and modeled (red) quantities. Time is in seconds from 
00:00:00 UT.
