Vol 1, No. 3, August 1999

*M. G. Deminov, A. T. Karpachev, and S. K. Annakuliev*

**Institute of Terrestrial Magnetism, Ionosphere, and Radio
Wave Propagation, Troitsk, Moscow Region, Russia**

*V. V. Afonin*

**Institute of Space Research, Moscow, Russia**

The midlatitude ionospheric trough is the region of decreased
electron density situated near the equatorial boundary of diffuse
precipitation of electrons with energies of 0.5-1 keV (see, e.g.,
* Rodger et al.* [1992]).
During the main phase of a magnetic storm,
one minimum in the latitudinal distribution of the ionospheric
plasma electron density is generally noted in this region
[*Deminov et al.,* 1995a].
During this period the position of the minimum of
the midlatitude ionospheric trough correlates with the magnitude of
the magnetic field of the ring current
*DR* better than it does with
the
*Kp* index
[*Deminov et al.,* 1995b].

During the magnetic storm recovery phase, the midlatitude
ionospheric trough (MIT) structure becomes more complex. A
qualitative analysis of sounding data from the Cosmos 900 satellite
at altitudes of 400-500 km for nighttime has shown that during the
recovery phase, the midlatitude ionospheric trough can be shown to
consist of two troughs rather than one
[*Deminov et al.,* 1995a].
One of these troughs
(MIT) tends to be situated near the diffuse precipitation
boundary (DPB), while the other (the ring ionospheric trough (RIT))
seems to be related to the magnetospheric ring current
[*Deminov et al.,* 1995a].
None of the known empirical models of the position of
the midlatitude ionospheric trough predicts the possibility of the
simultaneous existence of two troughs clearly spaced in latitude
(see, e.g.,
* Rodger et al.* [1992]).
Moreover, with two troughs
existing at subauroral latitudes, the very term "position of the
minimum of electron density of the midlatitude ionospheric trough"
becomes ambiguous.

To overcome this contradiction, it is expedient to seek
quantitative laws of variation of positions of the MIT and RIT as
independent structures during the recovery phase of a magnetic
storm. Knowledge of these laws is also essential for the
identification of these troughs from experimental data, since the
MIT is easily confused with the RIT, especially when only one of
these troughs is present
[*Deminov et al.,* 1995a].
It is the goal of
this paper to find out these laws on the basis of an analysis of
the Cosmos 900 sounding data at altitudes of
430 50 km for
nighttime in local winter and equinox at the recovery phase of 16
magnetic storms in 1978-1979.

Below we analyze the correlation of the invariant latitude
*F*_{T}(*T*) of the MIT minimum
and the invariant latitude
*F*_{R}(*T*) of the RIT minimum
as measured from the Cosmos 900
satellite at the universal time
*T* with
*DR*(*T*-*T*_{0} ) and
*Kp*(*T*), where
*T*_{0} is the characteristic time of delay of variation of
*F*_{T} or
*F*_{R} relative to
*DR*. Time
*T*_{0} is determined from the
condition of the highest correlation of the position of the MIT or
RIT with
*DR*. The employed dependence of the magnetic field of the
magnetospheric ring current
*DR* on the
*Dst* index and the solar wind
parameters is that reported by
* Deminov et al.* [1995b]:

(1) |

where
*DR* and
*Dst* are measured in nanoteslas;
*P* = 0.01*nV*^{2} is the
solar wind pressure, where
*V* is the solar wind velocity in
kilometers per second and
*n* is the density in cm
^{-3}. The
coefficient
*k* depends on the magnitude and sense of the
interplanetary magnetic field vertical component
*B*_{z} :
*k* = 0.2,
0.25, and 0.3 at
*B*_{z} > 1,
1 > *B*_{z} > -1, and
*B*_{z} < -1,
respectively. For analysis, we used the Cosmos 900 data on the
ionospheric trough position, obtained from the sounding
measurements of electron densities at altitudes of
430 50 km
during nighttime (1800-0600 MLT) in local winter and equinox
during 1977-1979. These data correspond to the recovery phases of
16 magnetic storms, for which data are available on the solar wind
parameters
[*Cousens and King*, 1986]
necessary to calculate
*DR*.

Analysis of the dependence of the correlations of
*F*_{T}(*T*) and
*F*_{R}(*T*) with
*DR*(*T* - *T*_{0}) on
*T*_{0} for the entire
aforementioned array of data shows that these correlations are at
maximum at
*T*_{0} = 1. Here and hereinafter time is measured in
hours, and
*DR*(*T* - *T*_{0}) is in nanoteslas. For brevity, the times
*T* and
*T*_{0} are omitted; that is, expressions
*F*_{T}
*Kp* and
*F*_{R}
*DR* mean that
*F*_{T}(*T*) *Kp*(*T*) and
*F*_{R}(*T*) *DR*(*T* - *T*_{0}), where
*T*_{0} = 1.

The values of
*F*_{T} obtained from the Cosmos 900
data for the
recovery phases of 16 magnetic storms correspond to the following
ranges of variations of the magnetic activity indices:
-4 > *DR* > -62,
-19 > *DR* > -234, and
-13 > *DR* > -234 for the local magnetic
time intervals 1800-2200, 2200-0200, and 0200-0600 MLT,
respectively. Therefore for the premidnight hours (1800-2200 MLT),
the
*F*_{T} measurement data largely
relate to a relatively late
stage of the recovery phase of an intense magnetic storm. Because
of this, the statistical characteristics of models for premidnight
hours given below are approximate. In order to construct a model
from these initial data on the MIT position, we will require the
model being developed
*F*_{T}(*DR*, *t*, *L*) for the limiting cases
of very low ( *DR* = 0) and high (e.g.,
*DR* = -500 ) magnetic activities
not to contradict the model reported by
* Deminov et al.* [1995b]:

(2) |

(3) |

(4) |

Here and below, the invariant latitude
*F* and geographic
longitude
*L* are measured in degrees, the local magnetic
time
*t* is counted from midnight ( *t* = MLT - 24 before midnight and
*t* = MLT after midnight), the indices N and S correspond to
*F*(*L*) for the
northern and southern hemispheres,
*F*_{0} = 65.4, and
*F*_{L}(0) = 41.4.

It should be noted that the formula for
*F*_{T}(0, *t*, *L*)
was
obtained on the basis of the Cosmos 900 data for the periods of low
magnetic activity ( *Kp* 2) and the standard deviation of this
formula from the experimental data is
*s* = 2 [*Deminov
et al.,* 1992].
The formula for
*F*_{T}(-500, *t*, *L*)
is an
asymptotic approach to the empirical formula for
*F*_{T} during the
main phase of a magnetic storm
[*Deminov et al.,* 1995b],
which
demonstrates a tendency of MIT shifting equatorward with magnetic
activity increase. For example, for
*L* = 36 in the
near-midnight hours,
*F*_{T} = 55.6, 47.5, and 43.4 for
*DR* = -50,
-150, and
-250. Moreover, the
*F*_{T} dependence on
*L* is
weakened with an increase of magnetic activity and almost
completely disappears under
*DR* < -50.

The empirical model of the MIT position at the storm recovery phase
for the interval 1800-0600 MLT obtained on the basis of a
statistical analysis of the Cosmos 900 data, the model standard
deviation
*s* in degrees of latitude, and the coefficient
*R* of
correlation of the model with the initial Cosmos 900 data is

(5) |

Model (5) meets conditions (2): under none of the values of
*DR* can
the main ionospheric trough shift below the limiting latitude
*F*_{L}(*t*) or above the latitude
*F*_{T}(0, *t*, *L*).
It
follows from (5) that with decreasing magnetic activity during the
magnetic storm recovery phase, the MIT moves poleward up to the
high-latitude boundary
*F*_{T}(0, *t*, *L*).
In this motion of
the MIT toward high latitudes, the dependencies of
*F*_{T}(*DR*, *t*, *L*) on
*t* and
*L* become stronger.

One can obtain from formula (5) that
*F*_{T} = 56.3, 47.5, and 43.9
for
*DR* = -50,
-150, and
-250, respectively, under
*L* = 36 in
the near-midnight hours. These values almost completely coincide
with the values for the storm main phase presented above.
Therefore formula (5) presented by
* Deminov et al.* [1995b]
for
*F*_{T} provides a
*F*_{T} variation continuously under
a transition
to the storm main phase.

A qualitative analysis has shown
[*Deminov et al.,* 1995a]
that at
the initial stage of the recovery phase of an intense storm, the
MIT and RIT coincide; that is, they are looked upon as one trough
moving toward higher latitudes. At a later stage, the velocities of
motion of the MIT and RIT toward higher latitudes differ, and the
high-latitude boundary of this motion proves to be far more
equatorward for the RIT than it is for the MIT. During this period,
positions of the MIT and RIT become different, and this difference
is maximum at a later stage of the recovery phase of an intense
storm. The empirical model of the RIT position at the storm
recovery phase obtained on the basis of a statistical analysis of
the Cosmos 900 data reflects these patterns:

(6) |

where
*F*_{R}(0) = 56,
*DR*_{0} = -100,
*F*_{T}(*DR*, *t*, *L*),
and
*F*_{T}(*DR*_{0}, *t*,
*L*) are determined by equation (5).
Statistical characteristics of model (6) are
*s* = 0.9 and
*R* = 0.96.

Formula (6) is correct if
*DR*_{min} < -60, where
*DR*_{min} is the
lowest for the given storm value of
*DR*, which is usually observed
at the end of the storm main phase. For RIT to form, it is
necessary to have the trough at the end of a magnetic storm
equatorward from the
*F*_{R}(0). If this condition is not
fulfilled,
the RIT is not observed as a separate structure.

It follows from model (6) that at none of the values of
*DR* can the
ring ionospheric trough shift equatorward of
*F*_{L}(*t*) and
poleward of
*F*_{R}(0). The high-latitude boundary
*F*_{R}(0) of
the RIT poleward motion does not depend on local time and
longitude. The MIT and RIT coincide at
*DR* *DR*_{0}. For the range
*DR*_{0} < DR < -60, the difference between
*F*_{T}(*DR*, *t*, *L*) and
*F*_{R}(*DR*, *t*, *L*) normally does not exceed the value of
deviation of the initial data from these models. That is why at the
storm recovery phase, at
*DR* < -60, the main and ring ionospheric
troughs are normally looked upon as one trough moving toward higher
latitudes. With magnetic activity further decreasing, the MIT and
RIT clearly differ in both the region of localization and the
character of dependence of this localization on magnetic activity:
the MIT still moves toward higher latitudes, while the RIT stops
near
*F*_{R}(0). During this period,
*F*_{R}(*DR*, *t*, *L*) does
not practically depend on
*DR*, *t*, and
*L*, and the dependence of
*F*_{T}(*DR*, *t*, *L*) on
*t* and
*L* becomes stronger. In the
limiting case
*DR* = 0, the difference between positions of the MIT
and RIT is determined by the boundaries
*F*_{T}(0, *t*, *L*)
and
*F*_{R}(0) and averages to ~10^{o}.

Figures 1, 2, and 3 illustrate visually typical dependencies of the trough position on the parameters, which were used in models (5) and (6). In Figures 1, 2, and 3, solid lines, dashed lines, solid cirkles, and open circles correspond to model (5), model (6), experimental data for MIT, and experimental data for RIT, respectively.

Figure 1
shows the dependency of the MIT and RIT positions on
*DR* at
fixed
*t* = 0 and
*L* = 36 according to models (5) and (6)
together with the Cosmos 900 data reduced to these values of
*t* and
*L*. The procedure of reduction, for example, of
measured values
of the trough latitude
*F*_{T}(*t*, *L*)
under fixed
*t*, *L* and
*DR* to
*t* = 0 and
*L* = 36 is

where
*F*_{T}(*DR*, *t*, *L*) and
*F*_{T}(*DR*, 0, 36) are determined
by model (5). It is worth noting that the
*F*^{N}(*L*)
and
*F*^{S}(*L*)
functions coincide under
*L* = 36.
The values
of correlation coefficients
*R* and standard deviations
*s* presented above for equations (5) and (6) correspond
to the data in
Figure 1.

Figure 2
shows the dependencies of the MIT and RIT positions on
*t* for the fixed
*L* = 36 and
*DR* = -20 or
-100 according to models
(5) and (6) together with the Cosmos 900 data reduced to these
values of
*L* and
*DR*. It can be seen that RIT actually does not
depend on LT ( *R* = 0.1 and
*s* = 0.9 ).
The MIT dependency on
LT is the most significant under low magnetic activity:
*R* = 0.80 and
*s* = 1.5 under
*DR* = -20 and
*R* = 0.68 and
*s* = 1.5 under
*DR* = -150.

Figure 3 shows the dependencies of the MIT and RIT positions
on
geographic longitude
*L* under the fixed values of
*t* = 0 and
*DR* = -20 for the northern and southern hemispheres together with the
Cosmos 900 data reduced to these values of
*t* and
*DR*. It can be seen
that RIT actually does not depend on
*L* ( *R* = 0.1 and
*s* = 0.9 for
the northern hemisphere and
*R* = 0.07 and
*s* = 1 for the
southern hemisphere). The MIT dependency on
*L* is well
manifested for the southern hemisphere
(*R* = 0.74 and
*s* = 1.2) and
is much less pronounced for the northern hemisphere
(*R* = 0.27,
*s* = 1.7). Thus
the
*F*_{T} dependence on
*L* could not have been taken into account. However,
this dependency
provides a reasonable agreement with the experimental data under
transition from the recovery phase of a magnetic storm to quiet
conditions; so the dependency is left in the model.

Figures 1, 2, and 3 illustrate one more characteristic feature: the higher
the
magnetic activity level, the more accurate is model (5). Under high
magnetic activity the
*F*_{T} dependency on
*DR* dominates, because
the
*F*_{T} dependencies on
*t* and
*L* are significantly
weakened. As a result, model (5) for the recovery phase of a storm
is more accurate than the MIT position model for quiet conditions:
*s* = 2.0 for
*F*_{T} = *F*_{T}(0,
*t*, *L*) under
*Kp* < 2 and
*s* = 1.5 for
*F*_{T} = *F*_{T}(0,
*t*, *L*).
Figure 1
also demonstrates that it is impossible to provide the
above indicated accuracy under
*DR* > -60 without dividing the
troughs into MIT and RIT.

Models (5) and (6) make it possible to predict localization of the
MIT and RIT at the storm recovery phase and
from experimental data
to distinguish
the MIT from the RIT. However, because of the
initial data set's not being large enough, these models are not
capable of quantitatively predicting the probability of occurrence
of the MIT and RIT at
*DR* < -60. Therefore we will resort to
qualitative characteristics of these probabilities. Analysis shows
that at the recovery phase of an intense storm at
*DR* > -60, it is
rare that the MIT and RIT are observed simultaneously as
two troughs clearly spaced in latitude. During the premidnight
hours the MIT is normally more clearly pronounced than the RIT, and
frequently the RIT fails to be present in the experimental data at
all. For the postmidnight hours, the opposite tendency prevails: at
-30 > *DR* > -60 the RIT alone is often noted, but the MIT appears as
an additional trough at lower magnetic activity. During the
premidnight hours, at
-30 > *DR* > -60, the probabilities of
occurrence of the MIT or RIT do not differ significantly, and two
troughs clearly spaced in latitude can be noted simultaneously.
Additional analysis shows that for a weak magnetic storm, the
probability of occurrence of the RIT decreases. Occurrence of the
RIT at the recovery phase seems to require the trough to shift
equatorward of
*F*_{R}(0) by the end of the storm
main phase. It
should be noted that the RIT sometimes occurred 1-2 days after the
storm ended, including during the evening hours.

The
*Kp* index is more often used as an indicator of magnetic
activity for the position of the ionospheric trough at subauroral
latitudes (see, e.g.,
* Rodger et al.* [1992]).
To estimate the
effectiveness of using the
*Kp* index in determining the dependence
of the MIT position on magnetic activity, we will use the same
Cosmos 900 data array as that used in constructing model (5).

The empirical model of the MIT position at the storm recovery phase for the interval 1800-0600 MLT, obtained from statistical analysis of these data, has the following form:

(7) |

where
*F*(*t*) and
*F*(*L*) are determined
by relationships (3)
and (4). This model is seen to be less accurate than model (5).
Statistical characteristics of models (5) and (7) depend on local
time (see Table 1).
The Cosmos 900 data for 1800-2200 MLT largely
refer to a relatively later stage of the recovery phase of an
intense magnetic storm. As is seen from Table 1, models (5) and (7)
feature the same accuracy for these conditions. For premidnight and
postmidnight hours, model (5) is far more accurate than model (7).

Practically all of the previously constructed empirical models of
position of the electron density minimum at subauroral latitudes
are based on data arrays, each of which includes both quiet
conditions and all the storm phases. Analysis shows that, for such
data sets, the relative number of cases when the RIT is noted
instead of the MIT is generally small. Therefore it can be assumed
that the empirical models thus constructed correspond to the MIT. A
nearly complete set of such models has been constructed using,
basically, the Cosmos 900 data for nighttime conditions in local
winter 1978-1979
[*Deminov et al.,* 1992].
For an altitude of 430 km,
the model of
* Deminov et al.* [1992]
can be presented in the form

(8) |

The accuracy of this model is typical of the accuracy of known
models of this type. For example, at
*F*(*L*) = 0, equation
(8)
practically does not differ from the most frequently used model of
* Kohnlein and Raitt* [1977].
Table 1
lists the statistical
characteristics of model (8) for the same Cosmos 900 data set on
the MIT position that was used in determining relationships (5) and (7).
The standard deviation related accuracy of model (5) for
premidnight and postmidnight hours is seen to be about 3 times that
of model (8). For premidnight hours, the difference in accuracy of
models (5), (7), and (8) is slight. Allowing for corrections to the
model of
* Kohnlein and Raitt* [1977]
associated with the
interplanetary magnetic field
[*Ben'kova et al.,* 1989]
does not
alter the situation. Statistical characteristics of the model of
* Ben'kova et al.* [1989]
from the same Cosmos 900 data on the MIT
position are
*s* = 3.6 and
*R* = 0.88 for the entire interval
1800-0600 MLT,
*s* = 3.6 and
*R* = 0.85 for 2200-0200 MLT,
and
*s* = 4.2 and
*R* = 0.86 for 0200-0600 MLT.

Thus for premidnight and postmidnight hours, the
*DR* index is a
better indicator, compared with the
*Kp* index, of magnetic activity
for the MIT position at the recovery phase of an intense magnetic
storm. For these conditions, the accuracy of model (5) is about 2
and 3 times that of model (7) and that of known models, model (8)
included, respectively. For premidnight hours (1800-2200 MLT), at a
relatively later stage of the recovery phase of an intense magnetic
storm, the difference in accuracy of (5) and (7) is insignificant.

Analysis shows that the use of the
*Kp* index in constructing an
empirical model of the RIT position at the storm recovery phase
leads to relatively great errors. The coefficient of correlation of
such a model with the Cosmos 900 data does not exceed 0.82, and it
would be impractical to introduce
*Kp* as an indicator of
magnetic activity for the RIT position. Model (6) seems to be the
first empirical model of the RIT position.

It should be noted that model (5) is based on satellite data for local winter and equinox. Use of the model for local summer conditions requires special analysis because dependencies of the MIT position on magnetic activity level may evidently be different for local winter and summer.

We now consider the possible causes of dynamics of the midlatitude ionospheric trough at the recovery phase of a magnetic storm, which follow from models (5) and (6).

By the end of the main phase of an intense magnetic storm, the
midlatitude trough, the boundary of diffuse electron
precipitations, the plasmapause at the equatorial plane of the
magnetosphere, and the maximum of the ring current ion energy
density are all found at the lowest latitudes ( *L* shells) but, it
seems, never cross the equatorial boundary
*F*_{L}(*t*). In this
context, a significant contribution to the ring current energy
density is made by the O
^{+} ions, especially for
*E* < 30 keV
[*Hamilton et al.,* 1988].
At the recovery phase of a magnetic storm,
all these structures shift toward higher latitudes, to their values
specific to quiet conditions.

For intense storms, two stages of the recovery phase can be
isolated. The first, fast stage with a characteristic time of
5-9 hours seems to be determined by the
energetic O
^{+} ion losses
of the ring current, while the second, far slower stage is
determined by the energetic H
^{+} ions
[*Hamilton et al.,* 1988].
By
the end of the first stage, all the aforementioned structures seem
to be found near
*L* = 3, which corresponds to
*F* = 55. By that
time, the vertical distribution of the electron density in the
equatorial plane of the magnetosphere appears like two steps: in
addition to the internal plasmapause near
*L* = 3, an external
plasmapause forms at higher
*L* shells (see a review by
* Singh and Horwitz* [1992]).
The value
*L* = 3 corresponds to the median position
of the internal plasmapause
[*Singh and Horwitz,* 1992],
the maximum
density of the residual ring current ion energy
[*Hamilton et al.,* 1988;
* Lui et al.,* 1987],
and practically coincides with the
boundary latitude
*F*_{R}(0) for the RIT. This means
that with a
subsequent decrease in magnetic activity, the internal plasmapause,
the magnetospheric ring current, and the RIT remain near
*L* = 3.
Because of this, at the second stage of the storm recovery phase,
the MIT and RIT clearly distinguish themselves. At this stage, out
of all the aforementioned structures, only the MIT, the DPB, and
possibly the external plasmapause continue their motion toward
higher values of
*L*.

Comparison of the aforementioned structures suggests that the
latitude of the RIT minimum is found near the internal plasmapause,
but at somewhat smaller
*L* shells. Formation of this minimum at
altitudes of 350-450 km seems to relate to the following chain of
processes: Coulomb interactions of the ring current ions with the
surrounding electrons within the plasmasphere, where a major role
is played by the O
^{+} ions with energies below 20 keV
[*Kozyra et al.,* 1987];
heating of the surrounding electrons in the region of
this interaction; formation of a peak of the electron temperature
and the subauroral red arcs at ionospheric altitudes through
heat transfer along the
*L* shells from the region of heating
[*Kozyra et al.,* 1987];
and an increase in the coefficient of recombination
of ionospheric electrons at
*F* region
altitudes
through
vibrationally excited species, such as N
_{2}^{*} and O
_{2}^{*} in the
region of the electron temperature peak (see, e.g.,
* Rodger et al.* [1992])
and, as a result, formation of the RIT. An additional cause
of the decrease in density of the ionospheric ions of the
*F*2 layer
can be the sequence of the processes: precipitation of energetic
O
^{+} ions from the ring current, heating of the thermosphere,
increase of the molecular components in the thermosphere
composition at
*F*2 layer
altitudes,
and increase in the
recombination rate of the ionospheric electrons
[*Fuller-Rowell et al.,* 1990].
These processes seem to be the main causes of formation
of the RIT. The close relationship of the RIT with the
magnetospheric ring current justifies the name of this trough. It
also follows from this relationship that, at the storm recovery
phase, the invariant latitude of the maximum of the rate of heating
of the ionospheric plasma in the ring current region is described
by equation (6).

As was noted above, the RIT stops moving at the second, relatively
slow stage of the storm recovery phase, whereas the MIT and the
DPB continue to move toward higher latitudes to their values
characteristic of quiet conditions. The variation in the flux of
precipitating electrons (with energies of about 1 keV) with
latitude is one of the main causes of formation of the polar wall
of the MIT
[*Gal'perin et al.,* 1990].
For a pronounced MIT to form
at this period seems to require that the DPB be pronounced as well;
that is, an abrupt change in the precipitating electron flux with
latitude should take place. Normally, the DPB is far more
pronounced in premidnight hours than in postmidnight hours
[*Gal'perin et al.,* 1990].
Because of this, the MIT may not be noted
in postmidnight hours. The relationship between the MIT and DPB is
also tracked in the character of the dependence of the position of
these structures on magnetic activity. In particular, it follows
from the DPB model of
* Gussenhoven et al.* [1983]
and model (8) for
the MIT that correlation of these structures with
*Kp* is maximum for
the interval 1800-2100 MLT. For premidnight and postmidnight
hours, the
*DR* index is a better indicator, compared with
*Kp*, of
magnetic activity for the MIT position at the recovery phase of an
intense magnetic storm (see Table 1). The close relationship
between the MIT and DPB suggests that the same law is specific to
the DPB as well.

At the second, relatively slower stage of the magnetic storm
recovery phase, relaxation of
*DR* is far delayed in relation to the
decrease of
*Kp*. As is seen from Table 1, in transition from dusk to
premidnight hours, the accuracy of model (5) increases, whereas the
accuracy of models (7) and (8) decreases. This means that
relaxation of the MIT position to a value characteristic of quiet
conditions proceeds faster in dusk than in premidnight hours. Such
a relationship seems to hold for the DPB as well. This effect
appears to be associated with the fact that the electron
precipitation that forms the DPB occurs virtually locally in the
coordinate system
*L* shell-longitude because of the low electric
field of the magnetospheric convection at subauroral latitudes at
the storm recovery phase. As a result, the DPB position at a fixed
MLT is determined not only by the characteristic lifetime of these
electrons, but also by the DPB position in the previous sector of
MLT because of the Earth's rotation. The MIT and RIT are found more
poleward in dusk hours than in premidnight hours. As a result,
relaxation of the DPB and MIT positions to values characteristic of
quiet conditions will proceed faster in premidnight than
near-midnight hours. Formally, this leads to a relatively higher
correlation of the MIT and DPB positions with
*Kp* in premidnight
hours compared with postmidnight hours.

1. An empirical model of the dynamics of the position of the MIT
minimum at altitudes of
430 50 km at the recovery phase of an
intense magnetic storm is constructed for the nighttime during
local winter and equinox. The accuracy of this model with respect
to standard deviations for premidnight and postmidnight hours is 3
times that of the known models. This increased accuracy
is attained by isolation of
the magnetic storm recovery phase, separation of the MIT from the
RIT, and introduction of a magnetic activity indicator for the MIT
position: the ring current magnetic field
*DR*, which is a better
index than
*Kp*. In dusk hours at a later stage of the recovery
phase, the
*DR* index is not much more effective to use in comparison
with
*Kp* because of the relatively fast relaxation of the MIT
position to the undisturbed value during these hours. Much the same
dependence of the model accuracy on local time seems to be
characteristic of the DPB as well. The relatively fast relaxation
of the MIT and DPB positions to the undisturbed value in
premidnight hours may be associated with the effect of the Earth's
rotation, that is, with the dependence of the position of these
structures at a fixed MLT on their position in the previous MLT
sector.

2. For the same geophysical conditions, an empirical model of the
RIT minimum position is constructed, wherein the
*DR* index is the
magnetic activity indicator. This model seems to be the first
empirical model of the RIT minimum position. A qualitative analysis
shows that the RIT is closely associated with the magnetospheric
ring current. It follows from this relationship that the model of
the RIT position can be used for determining the invariant latitude
of the maximum of the rate of heating of the ionospheric plasma in
the magnetospheric ring current region. The
*Kp* index is impractical
to use for the description of variation of the RIT position.

3. The empirical models constructed make it possible to predict localization of the MIT and RIT at the storm recovery phase. They are also essential for identification of these troughs from experimental data, since the MIT is easy to confuse with the RIT, especially when only one of these troughs is noted.

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^{+} in the formation of stable auroral red arcs,
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