WDS'11 Proceedings of Contributed Papers, Part II, 51–55, 2011.
ISBN 978-80-7378-185-9 © MATFYZPRESS
Quasi-Periodic Oscillation of the Terrestrial Day-Side Magnetosphere
A. Voshchepynets and O. Agapitov
Taras Shevchenko Nation University of Kiev, Faculty of Physics, Kiev, Ukraine.
Abstract. We study the dynamics of the magnetosphere response to the solar wind
parameters changes using the Alfven velocity distribution in the Earth’s magnetosphere
obtained on the base of the IGRF and T89 Earth magnetic field models and plasma
density diffusive equilibrium model. We use the solution of the eigenvalue problem for
the trapped waves in the day-side magnetosphere cavity as the initial condition for the
simulation. Numerical simulation of the magnetosonic wave packages propagation in
3D magnetosphere cavity shows the occurrence of two global quasi-periodic modes of
the dayside magnetosphere: cavity modes at the sub-solar region and wave guide modes
at the magnetosphere flanks. The periods obtained in the numerical simulation are
consistent with the theoretical predictions and the THEMIS measurements.
Introduction
Periodic disturbances of the geomagnetic field have been observed since 1886. Dungey [Dungey,
1967] first suggested that pulsations were standing Alfven waves on dipolar field lines (toroidal
modes). He also identified poloidal compressional waves, which should propagate across the
background magnetic field, and subsequently completed the first decoupled studies of the modes.
Southwood [Southwood, 1974] and Chen and Hasegava [Chen and Hasegava, 1974] presented the first
attempts of a full theoretical analysis of the coupled pulsation problems. They proposed that the solar
wind, incident upon the magnetospheric cavity and driving the magnetosheath flow, could excite a
travelling Kelvin-Helmholtz surface wave upon the magnetopause. Having an evanescent structure
within the magnetosphere, this wave mode could tunnel to excite resonant field line oscillations deep
within the magnetosphere. These models however, often require excessive magnetosheath velocity to
explain the observed pulsation [Hughes, 1994].
Later treatments suggest that global fast modes could be exited throughout the entire
magnetospheric cavity in response to sudden impulse in the solar wind [Kivelson et al., 1984;
Kivelson and Southwood, 1985]. In this model, standing waves would be set up between the large
Alfven velocity gradient at an outer boundary (often assumed to be magnetopause) and turning point
within the magnetosphere. The evanescent tail of the modes, beyond the turning point, then drives the
Alfven resonance. Numerical and theoretical investigations of these phenomena [Kivelson and
Southwood, 1986; Inhester, 1987; Allan et al., 1986; Zhu and Kivelson, 1988; Lee and Lysak, 1991]
has been used to predict the frequencies of the cavity mode harmonic, and hence the frequencies of the
observed driven nightside/ early morning Pc5 Field Line Resonance [Samson et al.1992].
Papers by Wright [Wright et al., 1994] have considered the propagation of the compressional
modes down a waveguide. The waveguide models an open magnetospheric cavity where energy can
propagate downtail.
Further studies considered that the both the Kelvin-Helmholtz and the cavity/waveguide
mechanisms may be responsible for coupling solar wind energy into ULF pulsation, the dominant one
at any time probably depending upon the solar wind and magnetosheath conditions.
Observations
The analysis of the THEMIS data captured during multiple crossing of the MP in 2007 makes it
possible to conclude, that the observed quasi-periodic displacement of the MP surface are the
manifestation of the same event in different regions of the magnetosphere [Agapitov et al, 2009]. The
displacement of MP surface is associated with natural oscillations of the dayside magnetosphere –
cavity modes. Period of the oscillations are estimated to be in a range of 6 minutes, which is close to
the periods of the observed MP displacement. Cavity modes lead to the appearance of disturbances on
the MP surface, which are subsequently carried away in the region of the tail of magnetosphere.
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VOSCHEPYNETS AND AGAPITOV: OSCILLATION OF DAY-SIDE MAGNETOSPHERE
Figure 1. Configuration of the THEMIS satellites during August 17, 2007. Captured magnetic field
showed on the left panel.
Two different types of the equatorial magnetopause surface displacement are distinguished: the
one-dimensional motion as a holistic structure (flapping) and the movement of the running surface
perturbation on the magnetosphere flanks (waving).
The dynamics of the magnetic field captured aboard the five THEMIS spacecraft (THA, THB,
THC, THD, and THE) at 7:00–9:00 UT, August 17, 2007 is shown in Fig.1. THB, THC and THD
were near the magnetopause. They registered several crossing of the MP surface. Simultaneously THA
and THE registered the low-frequency oscillations of the geomagnetic field with the main component
along the background magnetic field inside the magnetosphere. Oscillations captured aboard THA and
THE are identified as the trapped fast MHD waves. The displacements of the MP surface and the perturbation inside the magnetosphere have the same temporal characteristics. The polarization properties
of the observed waves correspond to the theoretical prediction for the properties of the cavity modes.
Numerical Simulation
In this paper, we present a global perturbation of the magnetic field of the Earth as a set of wave
packets. Theory suggests that these waves are fast magnetosonic waves, which are responsible for
transferring energy from the solar wind to the ionosphere. Temporal evolution of the global
perturbation is directly related to spread of these wave packets in the region bounded by two surfaces
(magnetopause–plasmapause) and with nonuniform distribution of the velocity of the wave in the
medium. We used ray-tracing method to simplify equation that describes propagation of the fast
magnetosonic waves in such complicated case. These allow us to obtain system of the first order
differential equations from the dispersion equation .Dispersion equation of the Alfven wave has been
taken as a source equation for further simplification. However it should not affect the simulation
result, because in the frequency range close to the electron cyclotron frequency dispersion branches of
these types of waves coincide. After using ray tracing method source equations can be expressed in the
following way:
,
,
where is wave vector, —radius vector and ω—frequency of the wave.
is local Alfven velocity.
We used the 4-thorder Runge–Kutta method for numerical solution of differential equation.100000
such wave packets was used in present modulation.
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VOSCHEPYNETS AND AGAPITOV: OSCILLATION OF DAY-SIDE MAGNETOSPHERE
Local Alfven speed is the parameter of the medium which is included in the system of equation. It
is necessary to have knowledge about the value of magnetic field and plasma density all over in the
magnetosphere to obtain the spatial profile of the velocity distribution. We obtain the magnetosphere
magnetic
field
from
the
IGRF
(International
Geomagnetic
Reference
Field)
[http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html] model and T89 [Tsyganenko, 1989] model.
Following the [Muto and Hayakawa, 1987] we represented ion and electron density by isothermal
diffusive equilibrium model [Angerami and Thomas, 1964] with few additional factors such as the
plasmapause effect and effects of lower ionosphere. As is known, location of the plasmapause varies
with time, but average plasmapause location is 4 RE. In this paper plasmapause located at the 5 RE.
The resulting spatial distribution of the Alfven velocity is shown in Fig. 2.
We use eigenmodes of system, in which speed of fast MHD waves is distributed similary to
distribution of the Alfven velocity obtained in these state. The first 3 modes of one-dimensional case
and the corresponding profiles of the perturbations in the magnetosphere are shown in Fig. 3.
Figure 2. Spatial distribution of the Alfven velocity in the XY plane in GSM system.
Figure 3. The initial perturbations of the magnetosphere magnetic field. Top panel shows dependence
of the global disturbance from the geocentrically distance (cut along the X axis of the GSM system).
Displayed in arbitrary units. Bottom panel represent appropriate disturbance from the top panel in 2D
case. The distribution of global disturbances presented in the equatorial plane of GSM. Color indicates
the amplitude of the wave in relative terms: red color correspond to1, black color to –1.
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VOSCHEPYNETS AND AGAPITOV: OSCILLATION OF DAY-SIDE MAGNETOSPHERE
Results
The results of the modeling of the behavior of global disturbances in the dayside magnetosphere
are shown in Fig. 4 and Fig.5. In the first case, we simulated the evolution of the first harmonic
(Fig. 3, left panel). Periodic appearance of the initial structure is clearly seen, especially near the
subsolar point. Period of oscillation is about 300 s. Such configuration of the perturbation of the
magnetic field leads to the imbalance between the solar wind dynamic pressure and magnetic pressure
of the magnetosphere and hence the displacement of the magnetopause. This movement corresponds
to the phenomenon observed by satellites—flapping, which is the one-dimensional motion of the
magnetopause as a monolithic structure. Amplitude of displacement at the subsolar region can reach
one Earth’s radius (RE).
The dynamics of the global disturbances after the generation of the higher harmonics (Fig 3, the
right panel) in the initial moment was considered in the second case (Fig.5). A group of waves moving
toward the tail was observed on the flanks of the magnetosphere. As previously, changes of magnetic
pressure would change position of the surface of the magnetopause, in this time having a wavelike
shape. Thus we are dealing with the second type of motion of the magnetopause—waving, associated
with waveguide modes, which are realized on the flanks of the magnetosphere. The wave amplitude
varies with time and reaches a maximum of 1 RE. Velocity of the magnetopause surface waves
coincide with the rate of fast MHD waves in the nearby region of the magnetosphere.
Figure 4. Changes of the global perturbation of the magnetic field in the magnetosphere with time in
the plane of the geomagnetic equator. Color indicates amplitude (in arbitrary units). The time delay
between neighboring pictures 150 s.
Figure 5. Changes of the global perturbation of the magnetic field in the magnetosphere with time in
the plane of the geomagnetic equator. Color indicate amplitude (in arbitrary units) The time delay
between images – 10 s.
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VOSCHEPYNETS AND AGAPITOV: OSCILLATION OF DAY-SIDE MAGNETOSPHERE
Model doesn’t takes into account motion of the magnetopause caused by perturbation of the
magnetic field in the magnetosphere. Presence of the wave like structures on the MP surface will lead
to additional scattering of the wave packets on magnetopause. This will reduce quality of the resonator
and decreasing of the observed effects.
Conclusion
Numerical simulation of the fast MHD wave propagation processes in the dayside magnetosphere
represents two characteristic types of the magnetospheric eigenmodes –the cavity modes in the
subsolar region and the waveguide modes on the magnetosphere flanks. The cavity modes manifest
themselves as quasi-periodic oscillations of magnetic field that are often observed in the dayside
magnetosphere. The openness of the magnetospheric cavity leads to decreasing of intensity of the
oscillations. The obtained periods for the cavity modes are consistent with results of the spacecraft
observation and the theoretical prediction. Arbitrary configuration of the surfaces in the system
magnetopause–plasmapause defines region where cavity modes can be trapped. More natural
configuration of the magnetopause should be used for better modeling of these phenomena. The
generation of the wavelike structures on the magnetosphere flanks is possible only in case of
generation of the higher harmonic of global disturbance. Similar effect was obtained in earlier work,
where the initial condition of global perturbation was set by harmonic function with high azimuthal
number. Modulation shows that the existence of such processes on the flanks of magnetosphere can
lead to formation of the wavelike structures on the magnetopause.
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