Transient westward electric fields from the magnetosphere generate
equatorward plasma drifts of the order of kilometers per second in the
auroral ionosphere. This flow channel extends in north–south directions and
is produced in the initial pulse of Pi2 pulsations associated with the field
line dipolarization. Drifts in the ionosphere of the order of kilometers per
second that accumulated plasmas at the low-latitude end of the flow channel
are of such large degree that possible vertical transport effects (including
precipitation) along the field lines may be ignored. In this condition, we
suggest that plasma compression in the ionosphere initiated the dynamic
ionosphere. The dynamic ionosphere includes a nonlinear evolution of the
compressed ionospheric plasmas, generation of field-aligned currents to
satisfy the quasi-neutrality of the ionosphere, and parallel potentials
associated with the excitation of an ion acoustic wave. We will study how
the dynamic ionosphere created auroral expansion.
Introduction
“Auroras and solar corona observed at the solar eclipse are optical
phenomena unique in space physics. With enough knowledge about the
underlying physical processes, once auroras have been captured by a highly
sensitive imager, they provide an unexpected wealth of information about
plasma environment of the Earth” (Oguti, 2010). Plasma drifts in the
ionosphere observed by the balloon-measured electric fields (Kelley et al.,
1971), by the Ba releases (Haerendel, 1972), and by radar observations
(Nielsen and Greenwald, 1978) that did not match the expanding trajectories
of auroras were an example. They would have been observed in all-sky images
as violent motion of auroras propagating poleward (Akasofu et al., 1966) or
contact breakups initiated at the nearest approach to the hydrogen arc
(Oguti, 1973). To account for the differences in propagation directions, it
was suggested that the primary sources of auroral particles are in the
magnetospheric plasmas, and they developed poleward in terms of propagation
of rarefaction wave in the tail (Chao et al., 1977; Liu et al., 2012),
tailward regression/braking of the fast earthward flows referred to as BBFs
(Shiokawa et al., 1997; Haerendel, 2015), and onset instability of inner
plasma sheet pressure (Nishimura et al., 2010). The above explanations were
based on the observations that substorm expansion was initiated and
amplified at the substorm onset by the BBFs arriving at the inner boundary
of the plasma sheet from the tail (Kepko et al., 2004; Angelopoulos et al.,
2008; Machida et al., 2009).
We show that the electric fields in the dipolarization front (DF) that are
embedded in the leading edge of BBFs (Runov et al., 2011) triggered the
ballooning instability of the stretched flux tubes in the inner
magnetosphere. As a result, the stretched field lines returned to the
dipole-like configurations by producing the convection surge. Westward
electric fields associated with the convection surge were transmitted into
the auroral ionosphere and yield the compressibility in the auroral ionosphere.
The compressibility initiates the dynamic ionosphere and leads to an
alternative scenario of the poleward expansion of auroras that we discuss in
this paper. In this paper, field line reconfiguration and associated auroral
breakups at dipolarization onset will be summarized in Sect. 2. In Sect. 3, we will show that the auroral ionosphere becomes compressive transiently
during dipolarization. Section 4 will discuss generation of an ion acoustic
wave for creating parallel potentials in the topside ionosphere. This
contributes to the outflow. Poleward expansion of discrete auroras will be
discussed in Sect. 5 in terms of a nonlinear evolution of the accumulated
plasmas in the ionosphere. In the final section (Sect. 6), we summarize
our results and apply the dynamic ionosphere to the nonconjugate
auroras.
Auroras and field line reconfiguration associated with geomagnetic Pi2 pulsation
Poleward expansion of auroras arising out of the onset arc was observed in
the initial pulse of Pi2 pulsations (Saka et al., 2012). Statistical study
of field line inclinations at geosynchronous orbit for the intervals from
120 min prior to the Pi2 onset (T-120) to 60 min after the onset (T+60) is
presented in Fig. 1 (reproduced from Saka et al., 2010). The inclination
is measured positive northward from the D–V plane of the HVD coordinates. H
is positive northward parallel to dipole axis, V is radial outward, and D is
dipole east. It shows that field line inclination at geosynchronous orbit
(Goes5/6 at 285/252∘ in geographic coordinates)
decreased continuously in the growth phase and attained minimum inclination
angles, 33.6/49.4∘, 2 min before the initial peak of
Pi2 amplitudes. These inclination angles are smaller than 57.5/63.8∘ estimated by the IGRF (International Geomagnetic
Reference Field) model but rather fit the T89 model (Tsyganenko, 1989) for
Kp=4 (34.2/45.0∘). These field lines at the
geosynchronous altitudes can be mapped to the auroral ionosphere at
63.4/62.7∘ N in geomagnetic coordinates by T89 for
Kp=4. Following the Pi2 onset, field line inclination turned to increase
in a step-like manner at Goes5 while at Goes6, which is closer to the
equatorial plane than Goes5, transient dipolarization pulses were observed.
From these observations, we postulate that transient electric fields in DF
triggered the ballooning instability of the stretched flux tubes at the
arrival of BBFs. As a result, field lines turned back to dipole-like
configurations by producing the convection surge. The convection surge may
be observed by the geosynchronous satellites as the convection enhancement
of the plasma sheet electrons due to local breakdown of the last open
trajectories of plasma sheet electrons (Thomsen et al., 2002). The surge
occurred in all-sky images coincident with the onset of bead-like rippling
that leads to the breakups at the equatorward latitudes (Saka et al., 2014).
In the subsequent Pi2 pulses, an auroral surge was observed in all-sky
images between 66 and 74∘ N in geomagnetic latitudes,
referred to as a poleward boundary aurora surge (PBAS) (Saka et al., 2012).
They propagated eastward or westward at the poleward boundary of the auroral
zone and were interpreted as an auroral manifestation of flow bifurcation of
BBFs. In this onset scenario, the field line dipolarization finished in the
initial pulse of the Pi2 pulsations and increased field line inclination in
a step-like manner or generated dipolarization pulses. The convection surge
occurred once in the initial pulse of BBFs (DF) but was not repeated in the
following pulses in the BBF train. This correlation suggests that auroral
breakup may not repeat in the Pi2 wave packet but occurs at its initial
pulse.
Inclination angles in degrees measured positive northward from the
V–D plane from 120 min prior to the Pi2 onset (T-120) and to 60 min after
the Pi2 onset (T+60) reproduced from Saka et al. (2010). Magnetometer data
of Goes 5/6 were represented in HVD coordinates: H is positive northward
parallel to dipole axis, V is radial outward, and D is dipole east. Epoch
superposition of 30 Pi2 events and mean angles calculated from them are
plotted in top and in lower panels, respectively. Mean inclination angle at
2 min before the initial peak of Pi2 amplitudes (T=0) was 33.6∘
for G5 and 49.4∘ for G6 in dipole coordinate. Dipolarization was
step-like at Goes5, while at Goes6 it was composed of dipolarization pulses.
The average satellite latitudes estimated by T89 model were 10.3
and 7.9∘ N for Goes5 and Goes6, respectively.
Horizontal plasma flows in the ionosphere
We assume that westward electric fields associated with the convection surge
were transmitted along the field lines to the auroral ionosphere by the
guided poloidal mode (Radoski, 1967). The electric fields would be amplified
during the projection into the ionosphere over 100 mV m-1 and created an
equatorward flow through E×B drift of the order of kilometers per
second in the auroral ionosphere. The flows would be confined in a flow
channel expanding north–south in the midnight sector. The low-latitude end
of the flow channel was at the latitudes of the onset arc. The high-latitude
end may not expand beyond the poleward boundary of auroral zone.
Longitudinal width of the flow channel may form a streamer (e.g., Nishimura
et al., 2010) and develops after the breakups in about 1 to 2 h of local
time (∼1000 km along 65∘ N) corresponding to
the horizontal-scale size of plasma flow vortices associated with Pi2 (Saka et
al., 2014).
In the flow channel, drift across the magnetic fields for the jth species
(Uj⊥) can be written in the F region as (Kelley, 1989)
Uj⊥=1BE-kBTjqj∇nn×B^.
Here, E denotes westward electric fields in the flow channel and
B^ denotes a unit vector of the magnetic fields B, downward
in the auroral ionosphere. Symbols kB, Tj, qj, and n are the
Boltzmann constant, temperature of the jth species, charge of the jth species, and
density of electrons (ions), respectively. The electric field of the order
of 100 mV m-1 exceeded the diffusion (second term) by 3 orders of
magnitude in the low-temperature ionosphere. The E×B drift predominated
in the F region and the diffusion term may be ignored. In the E region, drift
trajectories may be written (Kelley, 1989) for electrons by
Ue⊥=1B[E×B^]
and for ions by
Ui⊥=bi[E+κiE×B^].
Here, bi is the mobility of ions defined as Ωi/(Bνin), and κi is defined as
Ωi/νin. Symbols Ωi and
νin are ion gyrofrequency and ion-neutral collision frequency,
respectively. B^ denotes a unit vector of the magnetic fields
B. To derive Eqs. (2) and (3), pressure gradient term (diffusion) was
again ignored. In the E region (κi=0.1), plasma accumulation in
equatorward latitudes by the imposed westward electric fields was produced
by Eq. (2) for electrons and the second term in Eq. (3) for ions. Electrons
smoothly moved equatorward while ions stopped in the original place because
of low mobilities caused by high ion-neutral collisions. However, electron
accumulation in lower latitudes increased southward electric fields and
simultaneously ion drifts in the first term of Eq. (3) start. If the southward
electric fields grew to exceed the westward electric fields by an order of
magnitude, ion drifts in the first term of Eq. (3) and electron drifts in Eq. (2)
balanced to satisfy the quasi-neutrality. This is equivalent to the
generation of the Pedersen currents in the ionosphere. Thus, quasi-neutral
electrostatic potential is generated in the E region, positive in poleward
and negative in equatorward. The Pedersen currents would have closed to the
field-aligned current (FAC), upward from the negative potential region and
downward into the positive potential region to sustain the steady-state
electrostatic potential in the ionosphere. Plasma drifts in the ionosphere,
both in E and F regions, create a cavity in the high-latitude end of the
flow channel and density pileup at the low-latitude end of the flow channel.
We will focus on the density accumulation in the flow channel and discuss
vertical transport of these accumulated materials. The development of the
cavity in the flow channel may be the subject of another paper.
Vertical plasma flows in the ionosphere
A transient compression of the ionospheric plasmas at the low-latitude edge
of the flow channel would excite the ion acoustic wave in the ionosphere
traveling along the field lines in the upward and downward directions from the
density peak of the F region. Figure 2 shows altitude distribution of the
pre-onset density profile of electrons (black) and doubled density profile
caused by the accumulation in red. The electron density profile in black was
plotted using the sunspot maximum condition in the nightside given in Prince Jr. and
Bostick Jr. (1964). The traveling ion acoustic waves, upward and downward, are
denoted by vertical arrows. Ion acoustic wave propagating downward may be
eventually absorbed in the neutrals, while the upward wave may propagate
along the field lines further upward. We will focus only on the upward-traveling ion acoustic wave. Electron motions produced the parallel
electric fields in accordance with the Boltzmann relation (Chen, 1974),
E//=-kBTeq∇//nene.
Here, kB is the Boltzmann constant, q is electron charge, Te is
electron temperature, and ne is electron density (ne=ni).
Equation (4) gives electric field strengths of the order of 0.4 and
2.0 µV m-1 for Te=1000 K and Te=5000 K, respectively, when the
e-folding distance of density dropout along the filed lines was 200 km. For
ions, steady-state motions exist in the ionosphere in the altitudes where
ion-neutral collision frequencies exceed ion acoustic wave frequencies. In
that case, parallel motions can be written as (Kelley, 1989)
Vi//=biE//-Di∇//nn-gνin.
Here, bi and Di denote the mobility and diffusion coefficient of ions
defined by qiMiνin and kBTiMiνin, respectively. The symbols Mi, qi, νin, and
g are ion mass, electric charge of ions, ion-neutral collision frequency,
and gravity, respectively. Ion-neutral collision frequencies from 400 to
1000 km in altitudes were plotted in Fig. 3 using the nighttime sunspot
maximum condition in Prince Jr. and Bostick Jr. (1964). Frequencies of ion acoustic
wave were calculated by substituting the wavelength of ion acoustic wave into
the dispersion relation. The wavelength was assumed to be identical to
initial accumulation distance along the field lines. We chose two cases of
1000 and 4000 km. Phase velocity of the ion acoustic wave of the order of
1600 m s-1 for the electron temperatures of 5000 K yields the wave frequencies
of 1.6×10-3 s-1 for the wavelength of 1000 km and 4.0×10-4 s-1 for 4000 km. These frequencies were overlaid in Fig. 3.
Steady-state ion motions can be adopted up to 800 km for a wavelength over
1000 km.
Vertical profiles from 90 to 1000 km in altitudes of electron
number density in two conditions: pre-onset in black and after accumulation
in red. The nighttime sunspot maximum condition given in Prince Jr. and Bostick Jr. (1964) was used to plot the pre-onset condition. Vertical arrows directing
upward and downward denote traveling ion acoustic waves propagating along
the field lines from the density peak of the F layer.
Ion-neutral collision frequency (νin) in altitudes from 400 to 1000 km calculated using the nighttime sunspot maximum condition in Prince Jr.
and Bostick Jr. (1964). Wave frequencies of ion acoustic wave are overlaid for two wavelengths: 1000 and 4000 km along field lines (see text).
Altitude profiles of steady-state ion flows were evaluated substituting 1000 K
for ion temperatures and the same e-folding distance in Eq. (4). The ions
are oxygen and parallel electric fields are given by the Eq. (4). A
snapshot of the velocity profile in altitudes from 400 to 800 km is shown
in Fig. 4 for the two cases of electron temperatures: 5000 K for black dots
and 1000 K for red dots. For the low-temperature case (1000 K),
no ion upflow occurred because the parallel electric fields could not overcome
gravity. We suggest that electron temperatures over 2700 K would be needed to
excite ion upflow. When electron temperature was set to 5000 K, the ion velocity of 15 m s-1 at 400 km in altitudes increased rapidly to 1369 m s-1 at 800 km. The
altitude profile of the flow velocity in Fig. 4 matched type-2 ion outflow
observed by the EISCAT radar (Wahlund et al., 1992). We conclude that the ion
upflow in topside ionosphere was caused primarily by the parallel electric
fields excited by the upward-traveling ion acoustic wave. Below 600 km in
altitudes, upflow velocity was 1 to 2 orders of magnitude smaller than
the equatorward drift in the flow channel. Upflow velocity became comparable
to the horizontal drift over 800 km in altitudes and exceeded the phase
velocity of ion acoustic wave. Ion outflow velocity exceeding the phase velocity of ion acoustic wave along the field lines may excite a shock at the topside ionosphere. A part
of them developed to ion acoustic double layers (Sato and Okuda, 1980;
Hasegawa and Sato, 1982; Hudson et al., 1983; Ergun et al., 2002) which were
observed at the altitudes of 6000–8000 km (Mozer et al., 1977; Temerin et
al., 1982). Those ion acoustic double layers would have produced parallel
potential structures referred to as inverted-V-type electric fields.
Steady-state parallel velocity in altitudes for ions (oxygen)
produced by parallel electric fields: 0.4 µV m-1 (Te=1000 K) in red
dots and 2.0 µV m-1 (Te=5000 K) in black dots. Vertical flows in
altitudes from 400 to 800 km are shown. Flow velocity is positive upward
and negative downward.
Nonlinear evolution of the horizontal flows
Accumulation of electrons and ions occurred at the equatorward end of the
flow channel. We can estimate a rate of accumulation by the following
relation:
ΔnΔt=-n0ΔUΔx.
Here n is plasma density, and U denotes drift velocity in the flow channel in x.
Substituting ΔU=103m s-1 and Δx=104 m, we have
ΔnΔt=1010 m-3 s-1 for the background
densityn0=1011 m-3. This gives a density pileup of the order of
Δnn0=100 % in 10 s. If the equatorward drift in
the flow channel is an order of 103 m s-1 (E=100 mV m-1 in the auroral
ionosphere) and electron production by the precipitation does not exceed the
accumulation rate, which was 100 % of the background density in 10 s, both outflows and precipitation may not bring significant changes
to the flux carried by E×B drift in the flow channel. We then
approximate one-dimensional (along the drift path in x) conservation equation
in the flow channel.
∂n∂t+∂∂x(nU)=0
A question arises regarding maximum accumulation of plasmas at the
equatorward end of the flow channel. One possible mechanism to suppress
accumulation may be associated with the ionospheric screening that decreased
the amplitudes of penetrated (total) westward electric fields by the
increasing ionospheric conductivities. In a two-dimensional ionosphere with
uniform height-integrated conductivity, total electric fields E given by a
sum of the incident (Ei) and reflected westward electric fields may be
written as E=2ΣAΣA+ΣPEi, where ΣA and ΣP are the Alfven
conductance defined by 1/μ0VA and height-integrated
Pedersen conductance in the ionosphere, respectively (Kan et al., 1982).
Symbols μ0 and VA denote magnetic permeability in vacuum and Alfven velocity, respectively. The amplitude ratio of total electric fields to incident electric fields is a function of the conductance ratio of Pedersen and
Alfven; E/Ei=2 for a low conductivity of the
ionosphere satisfying ΣP/ΣA≪1, and E/Ei=0 for a high conductivity of the
ionosphere satisfying ΣP/ΣA≫1. Noting that ΣP is proportional to the plasma density in
the ionosphere, the total electric fields monotonically decreased with
increasing plasma densities caused by accumulation itself and by the
precipitations associated with the auroral activity. Another explanation may
be suggested in the polarization electric fields (eastward) produced by the
accumulation itself. These electric fields grew quickly with density
accumulation and decreased the incident electric fields (westward) by the
superposition. In addition to the above scenarios, we surmise that excess
accumulation of the ionospheric plasmas may be suppressed through the term
(U⋅∇)U in the equation of motion. From the
ionospheric screening process discussed above, we tentatively assume that
flow velocity U is a function of the density n. Then the conservation Eq. (7) may be written as
∂n∂t+∂∂xQ(n)=0.
Here, Q(n) is a mass flux defined by Q(n)=nU(n). This relation can be reduced to
the nonlinear wave equation,
∂n∂t+c(n)∂n∂x=0.
Here c(n) is a wave propagation velocity defined by c(n)=U(n)+nU′(n), U(n) is a
drift velocity in the flow channel, and U′(n) denotes braking/acceleration of the
drift velocity by increasing and decreasing density. The Eq. (9) is
often referred to as propagation of kinematic waves to describe traffic
flow (Lighthill and Whitham, 1955). In the following, we use dimensionless
units normalized by Um and nm. Here, Um and nm denote
maximum drift velocity at n=0 and maximum density for complete stops of the
drift, respectively. Assuming a constant braking in the flow channel, we
define U by a linear function of density n as U(n)=1-n. Noting that
Q′(n)=c(n), this relation is reduced to the equation Q(n)=n(1-n), which is identical to the case
for the traffic flow (Whitham, 1999). Both the U and Q are plotted in Fig. 5a
as a function of n. A nonlinear evolution of the density waves is presented
in Fig. 5b by the characteristic curves. In the case of vehicles in
traffic, the initial flows started from n=0 and stopped at n=1.0 by the
tailback of cars. For the case of the ionosphere, the ionospheric density
started from a finite density, n=0.3 in Fig. 5b, and increased to
n=1.0 to terminate the flow by the full screening. The nonlinear
evolution of the density profile in time is shown in Fig. 5b in colors
from black (T=T1), red (T=T2), green (T=T3), blue
(T=T4), and to purple (T=T5). After T=T5, the waves propagate
upstream (poleward) as a shock. The shock velocity, V, is given as (Whitham, 1999)
V=Q(n2)-Q(n1)n2-n1.
Here, subscript 1 is for the values ahead of shock and subscript 2 is for the
values behind. Noting that Q(n2)=0 and substituting
Q(n1)=n1(n2-n1), the Eq. (10) can be reduced to V=-n1 in dimensionless unit. The propagation velocity of the shock is related to
the densities ahead. For the case of n=0.3 in Fig. 5b, shock velocity can
be estimated to be -0.3Um. Here, Um denotes maximum drift velocity
in the ionosphere where ionospheric screening effects vanished by the
condition ΣP/ΣA≪1. The shock
velocity may be of the order of kilometers per second, which is comparable but
opposite to the equatorward drift in the flow channel.
(a) Normalized flux (Q)–density (n) curve (thin curve) and
velocity (U)–density (n) line (thick line) in flow channel. Vertical scale of the
U–n line is shown to the right; the scale of the Q–n curve is to the left. Dotted line at
n=0.5 indicates the critical density where c(n) vanishes; waves are stationary
relative to the ground. Waves propagate forward/backward at a density
below/above the critical density. (b) Nonlinear evolution of the density
accumulation. Density increased in a step-like manner from T1 to
T5.
Summary and discussion
We proposed that the localized electric field drift introduced
compressibility in the auroral ionosphere, which in turn generated
field-aligned currents in the ionosphere for the quasi-neutrality, ion
acoustic wave for parallel acceleration, and auroral expansions by nonlinear
evolution of the ionospheric compression. We called the compressive
ionosphere a dynamic ionosphere.
We apply this dynamic ionosphere to describe the asymmetry of discrete
auroras in sunlit and dark hemispheres in the nightside sector (nonconjugate
auroras). We suggest that the imbalance of the Pedersen conductance leads to the
nonconjugate auroras: Pedersen conductance in the sunlit ionosphere is larger than that in the dark hemisphere. Larger Pedersen conductance or weaker electric fields in
the sunlit ionosphere would have caused a weaker compressibility from which
ion acoustic wave may not be excited or excited with only weak parallel
potentials. This condition may reduce the occurrence probability of the
discrete auroras and average energy of precipitating electrons in the sunlit
hemisphere as exemplified in Newell et al. (1996) and Liou et al. (2001).
Weaker electric fields in the sunlit ionosphere may also require a longer
interval to accumulate enough plasmas to excite ion acoustic wave. Such an
instance is described in Sato et al. (1998) where onset of auroral breakups in the sunlit ionosphere delayed that in the dark ionosphere.
Finally, we note that poleward expansion as described here is an auroral
event occurring in the initial pulse of Pi2 pulsations. In the succeeding
pulses in the Pi2 wave trains, auroras are composed of poleward surge
propagating at the poleward boundary of auroral zone (PBAS) (Saka et al.,
2012). We suppose that PBASs may be directly correlated to the reconnection
processes inherent in the plasma sheet. This topic may be the subject of
another paper.
Data availability
No data sets were used in this article.
Competing interests
The author declares that there is no conflict of interest.
Acknowledgements
The author would like to express his sincere thanks to all the members of
the Global Aurora Dynamics Campaign (GADC) (Oguti et al., 1988). We also
gratefully acknowledge the STEP Polar Network (http://center.stelab.nagoya-u.ac.jp/cawses/datact/datact8.html, last access: May 2019). Geomagnetic coordinates
and footprints of the satellites are available at the Data Center for Aurora
in NIPR (http://polaris.nipr.ac.jp/~aurora, last access: November 2018).
Review statement
This paper was edited by Matina Gkioulidou and reviewed by two anonymous referees.
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