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# A new scenario applying traffic flow analogy to poleward expansion of auroras

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.

“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.

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.

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**×

**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**

*B*^{∘}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 *j*th species
(*U*_{j⊥}) can be written in the F region as (Kelley, 1989)

Here, ** E** denotes westward electric fields in the flow channel and
$\widehat{\mathit{B}}$ denotes a unit vector of the magnetic fields

*B*, downward in the auroral ionosphere. Symbols

*k*

_{B},

*T*

_{j},

*q*

_{j}, and

*n*are the Boltzmann constant, temperature of the

*j*th species, charge of the

*j*th 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***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**

*B*and for ions by

Here, *b*_{i} is the mobility of ions defined as Ω_{i}∕(*B**ν*_{in}), and *κ*_{i} is defined as
Ω_{i}∕*ν*_{in}. Symbols Ω_{i} and
*ν*_{in} are ion gyrofrequency and ion-neutral collision frequency,
respectively. $\widehat{\mathit{B}}$ 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 (*κ*_{i}=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.

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),

Here, *k*_{B} is the Boltzmann constant, *q* is electron charge, *T*_{e} is
electron temperature, and *n*_{e} is electron density (*n*_{e}=*n*_{i}).
Equation (4) gives electric field strengths of the order of 0.4 and
2.0 µV m^{−1} for *T*_{e}=1000 K and *T*_{e}=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)

Here, *b*_{i} and *D*_{i} denote the mobility and diffusion coefficient of ions
defined by $\frac{{q}_{\mathrm{i}}}{{M}_{\mathrm{i}}{\mathit{\nu}}_{\mathrm{in}}}$ and $\frac{{k}_{\mathrm{B}}{T}_{\mathrm{i}}}{{M}_{\mathrm{i}}{\mathit{\nu}}_{\mathrm{in}}}$, respectively. The symbols *M*_{i}, *q*_{i}, *ν*_{in}, 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 $\mathrm{1.6}\times {\mathrm{10}}^{-\mathrm{3}}$ s^{−1} for the wavelength of 1000 km and $\mathrm{4.0}\times {\mathrm{10}}^{-\mathrm{4}}$ 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.

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.

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:

Here *n* is plasma density, and *U* denotes drift velocity in the flow channel in *x*.
Substituting Δ*U*=10^{3}m s^{−1} and Δ*x*=10^{4} m, we have
$\frac{\mathrm{\Delta}n}{\mathrm{\Delta}t}={\mathrm{10}}^{\mathrm{10}}$ m^{−3} s^{−1} for the background
density*n*_{0}=10^{11} m^{−3}. This gives a density pileup of the order of
$\frac{\mathrm{\Delta}n}{{n}_{\mathrm{0}}}=\mathrm{100}$ % in 10 s. If the equatorward drift in
the flow channel is an order of 10^{3} 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.

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 (*E*_{i}) and reflected westward electric fields may be
written as $E=\left(\mathrm{2}{\mathrm{\Sigma}}_{\mathrm{A}}\left({\mathrm{\Sigma}}_{\mathrm{A}}+{\mathrm{\Sigma}}_{\mathrm{P}}\right)\right){E}_{\mathrm{i}}$, where Σ_{A} and Σ_{P} are the Alfven
conductance defined by 1∕*μ*_{0}*V*_{A} and height-integrated
Pedersen conductance in the ionosphere, respectively (Kan et al., 1982).
Symbols *μ*_{0} and *V*_{A} 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; $E/{E}_{\mathrm{i}}=\mathrm{2}$ for a low conductivity of the
ionosphere satisfying ${\mathrm{\Sigma}}_{\mathrm{P}}/{\mathrm{\Sigma}}_{\mathrm{A}}\ll \mathrm{1}$, and $E/{E}_{\mathrm{i}}=\mathrm{0}$ for a high conductivity of the
ionosphere satisfying ${\mathrm{\Sigma}}_{\mathrm{P}}/{\mathrm{\Sigma}}_{\mathrm{A}}\gg \mathrm{1}$. Noting that Σ_{P} 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**⋅∇)

**in the equation of motion. From the ionospheric screening process discussed above, we tentatively assume that flow velocity**

*U**U*is a function of the density

*n*. Then the conservation Eq. (7) may be written as

Here, *Q*(*n*) is a mass flux defined by *Q*(*n*)=*n**U*(*n*). This relation can be reduced to
the nonlinear wave equation,

Here *c*(*n*) is a wave propagation velocity defined by $c\left(n\right)=U\left(n\right)+n{U}^{\prime}\left(n\right)$, *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 *U*_{m} and *n*_{m}. Here, *U*_{m} and *n*_{m} 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 $U\left(n\right)=\mathrm{1}-n$. Noting that
${Q}^{\prime}\left(n\right)=c\left(n\right)$, this relation is reduced to the equation $Q\left(n\right)=n(\mathrm{1}-n)$, 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*=*T*_{1}), red (*T*=*T*_{2}), green (*T*=*T*_{3}), blue
(*T*=*T*_{4}), and to purple (*T*=*T*_{5}). After *T*=*T*_{5}, the waves propagate
upstream (poleward) as a shock. The shock velocity, *V*, is given as (Whitham, 1999)

Here, subscript 1 is for the values ahead of shock and subscript 2 is for the
values behind. Noting that *Q*(*n*_{2})=0 and substituting
$Q\left({n}_{\mathrm{1}}\right)={n}_{\mathrm{1}}({n}_{\mathrm{2}}-{n}_{\mathrm{1}})$, the Eq. (10) can be reduced to $V=-{n}_{\mathrm{1}}$ 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 −0.3*U*_{m}. Here, *U*_{m} denotes maximum drift velocity
in the ionosphere where ionospheric screening effects vanished by the
condition ${\mathrm{\Sigma}}_{\mathrm{P}}/{\mathrm{\Sigma}}_{\mathrm{A}}\ll \mathrm{1}$. 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.

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.

No data sets were used in this article.

The author declares that there is no conflict of interest.

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).

This paper was edited by Matina Gkioulidou and reviewed by two anonymous referees.

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- Abstract
- Introduction
- Auroras and field line reconfiguration associated with geomagnetic Pi2 pulsation
- Horizontal plasma flows in the ionosphere
- Vertical plasma flows in the ionosphere
- Nonlinear evolution of the horizontal flows
- Summary and discussion
- Data availability
- Competing interests
- Acknowledgements
- Review statement
- References

- Abstract
- Introduction
- Auroras and field line reconfiguration associated with geomagnetic Pi2 pulsation
- Horizontal plasma flows in the ionosphere
- Vertical plasma flows in the ionosphere
- Nonlinear evolution of the horizontal flows
- Summary and discussion
- Data availability
- Competing interests
- Acknowledgements
- Review statement
- References