Dmitri Klimushkin - Academia.edu (original) (raw)
Papers by Dmitri Klimushkin
Journal of Geophysical Research: Space Physics, 2016
Journal of Geophysical Research: Space Physics, 2013
Egs General Assembly Conference Abstracts, Apr 1, 2002
Theoretical study of Alfven waves in the magnetosphere has been addressed by a large number of pu... more Theoretical study of Alfven waves in the magnetosphere has been addressed by a large number of publications, the authors of which are guided by the desire to exploit increasingly more sophisticated models of the magnetosphere. This is because the Alfven waves are known to be very sensitive to changes in the magnetic field geome- try. Taking into account such factors as the field line curvature, and the plasma inho- mogeneity along field lines and across magnetic shells is of fundamental importance for understanding the properties of the waves in the magnetosphere, and for inter- preting phenomena observed. One such factor includes also the field-aligned currents. These currents give rise to magnetic field shear, i.e. a change in the field line slope to the ionosphere in the azimuthal direction at different magnetic shells. In this paper we have studied the Alfven wave structure in the box model of the magnetosphere: geospace plasma is assumed to be enclosed between two parallel, infinitely conduct- ing planes which simulate the Earth's ionospheres, and the field lines are straight but have a variable slope to the ionosphere in the azimuthal plane, the angle of which de- pends on the radial coordinate x. The model under investigation assumes that plasma density and, hence, the Alfven velocity depend on the radial component only. For this model we have established the Alfven resonance condition. It is shown that the res- onance can also occur in the case of a constant Alfven velocity if there is a change of the field line slope to the ionosphere. At resonance magnetic shells there is taking place a singularity of the wave field of the same form as in the absence of shear. It is found that the presence of shear leads to the noncoincidence of the poloidal and toroidal oscillation frequencies (it has been known previously that this phenomenon is caused by the field line curvature). Taking the magnetic field shear in the model under study gives rise to the Alfven wave dispersion across magnetic shells. The waves are traveling waves across magnetic shells, and the region where the wave is localized, is bounded in the radial coordinate by two turning points: the ordinary point, at which the mode is poloidally polarized, and the singular point where the wave is toroidally polarized. It is at this point where Alfven resonance occurs.
Annales Geophysicae, 2006
The paper employs the frame of a 1-D inhomogeneous model of space plasma,to examine the spatial s... more The paper employs the frame of a 1-D inhomogeneous model of space plasma,to examine the spatial structure and growth rate of drift mirror modes, often suggested for interpreting some oscillation types in space plasma. Owing to its coupling with the Alfvén mode, the drift mirror mode attains dispersion across magnetic shells (dependence of the frequency on the wave-vector's radial component, kr). The spatial structure of a mode confined across magnetic shells is studied. The scale of spatial localization of the wave is shown to be determined by the plasma inhomogeneity scale and by the azimuthal component of the wave vector. The wave propagates across magnetic shells, its amplitude modulated along the radial coordinate by the Gauss function. Coupling with the Alfvén mode strongly influences the growth rate of the drift mirror instability. The mirror mode can only exist in a narrow range of parameters. In the general case, the mode represents an Alfvén wave modified by plasma inhomogeneity.
Plasma Physics Reports, 2006
A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in th... more A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in the magnetosphere. The finite plasma pressure, the transverse equilibrium current, and the curvature of the magnetic field lines are taken into account. It is shown that these effects lead to a transverse dispersion of Alfvén waves and change the dispersion relation for slow magnetosonic waves. There are two transparency regions for MHD waves, one located near the Alfvén resonance and the other near the magnetosonic resonance. In the radial direction, each of these regions is bounded by a surface formed by conventional turning points (a poloidal surface) and a surface formed by singular turning points (a resonant surface). In each transparency region, the mode is a standing wave in the longitudinal direction and propagates in the transverse direction from the poloidal surface toward the resonant one, at which it is completely absorbed.
Annales Geophysicae, 2005
Spatial localization and azimuthal wave numbers m of poloidal Alfvén waves generated by energetic... more Spatial localization and azimuthal wave numbers m of poloidal Alfvén waves generated by energetic particles in the magnetosphere are studied in the paper. There are two factors that cause the wave localization across magnetic shells. First, the instability growth rate is proportional to the distribution function of the energetic particles, hence waves must be predominantly generated on magnetic shells where the particles are located. Second, the frequency of the generated poloidal wave must coincide with the poloidal eigenfrequency, which is a function of the radial coordinate. The combined impact of these two factors also determines the azimuthal wave number of the generated oscillations. The beams with energies about 10 keV and 150 keV are considered. As a result, the waves are shown to be strongly localized across magnetic shells; for the most often observed second longitudinal harmonic of poloidal Alfvén wave (N=2), the localization region is about one Earth radius across the magnetic shells. It is shown that the drift-bounce resonance condition does not select the m value for this harmonic. For 10 keV particles (most often involved in the explanation of poloidal pulsations), the azimuthal wave number was shown to be determined with a rather low accuracy, -100<m<0. The 150 keV particles provide a little better but still a poor determination of this value, -90<m<-70. For the fundamental harmonic (N=1), the azimuthal wave number is determined with a better accuracy, but both of these numbers are too small (if the waves are generated by 150 keV particles), or the waves are generated on magnetic shells (in 10 keV case) which are too far away. The calculated values of γ/ω are not large enough to overcome the damping on the ionosphere. All these have cast some suspicion on the possibility of the drift-bounce instability to generate poloidal pulsations in the magnetosphere.
P. Mager, Institute of Solar-Terrestrial Physics, p.mager@iszf.irk.ru
Annales Geophysicae, 2008
The generation of a high-m Alfvén wave by substorm injected energetic particles in the magnetosph... more The generation of a high-m Alfvén wave by substorm injected energetic particles in the magnetosphere is studied. The wave is supposed to be emitted by an alternating current created by the drifting particle cloud or ring current inhomogeneity. It is shown that the wave appears in some azimuthal location simultaneously with the particle cloud arrival at the same spot. The value of the azimuthal wave number is determined as m∼ω/ω d , where ω is the eigenfrequency of the standing Alfvén wave and ω d is the particle drift frequency. The wave propagates westward, in the direction of the proton drift. Under the reasonable assumption about the density of the energetic particles, the amplitude of the generated wave is close to the observed amplitudes of poloidal ULF pulsations.
ABSTRACT The compressional and Alfven modes in non-uniform space plasmas are described by a syste... more ABSTRACT The compressional and Alfven modes in non-uniform space plasmas are described by a system of two integro-differential kinetic equations taking into account drift-bounce wave-particle interaction, finite plasma pressure, plasma and magnetic field inhomogeneity along field lines and transverse to magnetic shells, and mode coupling due to field line curvature. If the wave frequency is sufficiently lower than the bounce frequency, then the system describes a drift compressional mode with the eigenfrequency of order of diamagnetic drift frequency. If the wave is propagating in the same azimuth direction as protons, it interacts with particles and can be unstable when the plasma temperature grows with L-shell or has non-Maxwellian (bump-on-tail) distribution. In a parallel direction, the mode is strongly localized near the equator. In a transverse direction, it is enclosed between two magnetic shells, the resonance shell and the cut-off shell, where the wave vector radial component turns into infinity and zero, accordingly. The coupling between the drift compressional and Alfven modes strongly effects the ballooning instability.
Annales Geophysicae, 2006
Through the combined action of the field line curvature and finite plasma pressure in some region... more Through the combined action of the field line curvature and finite plasma pressure in some regions of the magnetosphere (plasmapause, ring current) there can exist global poloidal Alfvén modes standing both along field lines and across magnetic shells and propagating along azimuth. In this paper we investigate the spatio-temporal structure of such waves generated by an impulsive source. In general, the mode is the sum of radial harmonics whose structure is described by Hermitian polynomials. For the usually observed second harmonic structure along the background field, frequencies of these radial harmonics are very close to each other; therefore, the generated wave is almost a monochromatic oscillation. But mixing of the harmonics with different radial structure causes the evolution of the initially poloidal wave into the toroidal one. This casts some doubts upon the interpretation of observed high-m poloidal waves as global poloidal modes.
Annales Geophysicae, 2010
A case study of SuperDARN observations of Pc5 Alfvén ULF wave activity generated in the immediate... more A case study of SuperDARN observations of Pc5 Alfvén ULF wave activity generated in the immediate aftermath of a modest-intensity substorm expansion phase onset is presented. Observations from the Hankasalmi radar reveal that the wave had a period of 580 s and was characterized by an intermediate azimuthal wave number (m=13), with an eastwards phase propagation. It had a significant poloidal component and a rapid equatorward phase propagation (~62° per degree of latitude). The total equatorward phase variation over the wave signatures visible in the radar field-of-view exceeded the 180° associated with field line resonances. The wave activity is interpreted as being stimulated by recently-injected energetic particles. Specifically the wave is thought to arise from an eastward drifting cloud of energetic electrons in a similar fashion to recent theoretical suggestions (Mager and Klimushkin, 2008; Zolotukhina et al., 2008; Mager et al., 2009). The azimuthal wave number m is determined by the wave eigenfrequency and the drift velocity of the source particle population. To create such an intermediate-m wave, the injected particles must have rather high energies for a given L-shell, in comparison to previous observations of wave events with equatorward polarization. The wave period is somewhat longer than previous observations of equatorward-propagating events. This may well be a consequence of the wave occurring very shortly after the substorm expansion, on stretched near-midnight field lines characterised by longer eigenfrequencies than those involved in previous observations.
Journal of Geophysical Research: Space Physics, 2015
Plasma Physics Reports, 2006
A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in th... more A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in the magnetosphere. The finite plasma pressure, the transverse equilibrium current, and the curvature of the magnetic field lines are taken into account. It is shown that these effects lead to a transverse dispersion of Alfvén waves and change the dispersion relation for slow magnetosonic waves. There are two transparency regions for MHD waves, one located near the Alfvén resonance and the other near the magnetosonic resonance. In the radial direction, each of these regions is bounded by a surface formed by conventional turning points (a poloidal surface) and a surface formed by singular turning points (a resonant surface). In each transparency region, the mode is a standing wave in the longitudinal direction and propagates in the transverse direction from the poloidal surface toward the resonant one, at which it is completely absorbed.
Earth, Planets and Space, 2007
In this paper the spatial structure of azimuthally small-scale Alfvén waves in magnetosphere exci... more In this paper the spatial structure of azimuthally small-scale Alfvén waves in magnetosphere excited by the impulse source is studied. The source is suddenly switched on at a definite moment and works as e −iω 0 t during the finite time interval. The influence of factors which lead to the difference of toroidal and poloidal eigenfrequencies (like curvature of field lines and finite plasma pressure) is taken into account. Due to these factors, a radial component of the group velocity of Alfvén wave appears. An important value is the time moment, t 0 , when a wave front moving with radial component of wave group velocity from the poloidal surface (a magnetic surface where the source frequency ω 0 coincides with the poloidal frequency) passes the given magnetic shell with the radial coordinate x. The temporal evolution at all the points, where the front has not come yet, is determined by the phase mixing of the initial disturbance. At the points through which the wave front has already passed, the wave field structure almost coincides with the structure of monochromatic wave. The region where the front propagates is bounded by the interval between the poloidal surface and the toroidal one (that is, the Alfvén resonance surface). For this reason, outside this region the evolution is always determined by the phase mixing, which leads to much smaller amplitudes than between poloidal and toroidal surfaces. After the source turned off, a back wave front is formed, which comes through the given point in direction from the poloidal surface to the toroidal one. After the back front has come, the monochromatic wave structure disappears and there is only a weak disturbance, which steadily disappears because of the phase mixing and the final conductivity of ionosphere.
Kinematics and Physics of Celestial Bodies, 2014
The problem of propagation of azimuthally small scale ULF modes in plasma with 1D inhomogeneity a... more The problem of propagation of azimuthally small scale ULF modes in plasma with 1D inhomogeneity and variable curvature of magnetic lines of force is analyzed. The propagation regions and the transverse structure of stable Alfven and cusp modes, as well as unstable ballooning modes, are determined. It is shown that long living ballooning and cusp modes can exist. Our results qualitatively describe the behavior of ULF modes with continuous spectrum in the geomagnetosphere and can be used for interpretation of spacecraft and SuperDARN radar measurement data.
Journal of Geophysical Research-Space Physics, 2013
1] A previous case study observed a ULF wave with an eastward and equatorward phase propagation (... more 1] A previous case study observed a ULF wave with an eastward and equatorward phase propagation (an azimuthal wave number m, of ∼13) generated during the expansion phase of a substorm. The eastward phase propagation of the wave suggested that eastward drifting energetic electrons injected during the substorm were responsible for driving that particular wave. In this study, a population of 83 similar ULF wave events also associated with substorm-injected particles have been identified using multiple Super Dual Auroral Radar Network radars in Europe and North America between June 2000 and September 2005. The wave events identified in this study exhibit azimuthal wave numbers ranging in magnitude from 2 to 92, where the direction of propagation depends on the relative positions of the substorm onsets and the wave observations. We suggest that azimuthally drifting energetic particles associated with the substorms are responsible for driving the waves. Both westward drifting ions and eastward drifting electrons are implicated with energies ranging from ∼1 to 70 keV. A clear dependence of the particle energy on the azimuthal separation of the wave observations and the substorm onset is seen, with higher energy particles (leading to lower m-number waves) being involved at smaller azimuthal separations.
Plasma Physics Reports, 2002
The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is s... more The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is solved using a simplified model: a cold plasma is inhomogeneous in one direction, and the magnetic field lines are straight. The waves are assumed to travel in the plane perpendicular to the radial coordinate (i.e., the coordinate along which the plasma and magnetic field are inhomogeneous). It is shown that the character of the singularity at the resonance surface is the same as that in a homogeneous magnetic field. It is found that the shear gives rise to the transverse dispersion of Alfvén waves, i.e., the dependence of the radial component of the wave vector on the wave frequency. In the presence of shear, Alfvén waves are found to propagate across magnetic surfaces. In this case, the transparent region is bounded by two turning points, at one of which, the radial component of the wave vector approaches infinity and, at the other one, it vanishes. At the turning point for magnetosonic waves, the electric and magnetic fields are finite; however, the radial component of the wave vector approaches infinity, rather than vanishes as in the case with a homogeneous field. © 2002 MAIK "Nauka/Interperiodica".
Journal of Geophysical Research: Space Physics, 2016
Journal of Geophysical Research: Space Physics, 2013
Egs General Assembly Conference Abstracts, Apr 1, 2002
Theoretical study of Alfven waves in the magnetosphere has been addressed by a large number of pu... more Theoretical study of Alfven waves in the magnetosphere has been addressed by a large number of publications, the authors of which are guided by the desire to exploit increasingly more sophisticated models of the magnetosphere. This is because the Alfven waves are known to be very sensitive to changes in the magnetic field geome- try. Taking into account such factors as the field line curvature, and the plasma inho- mogeneity along field lines and across magnetic shells is of fundamental importance for understanding the properties of the waves in the magnetosphere, and for inter- preting phenomena observed. One such factor includes also the field-aligned currents. These currents give rise to magnetic field shear, i.e. a change in the field line slope to the ionosphere in the azimuthal direction at different magnetic shells. In this paper we have studied the Alfven wave structure in the box model of the magnetosphere: geospace plasma is assumed to be enclosed between two parallel, infinitely conduct- ing planes which simulate the Earth's ionospheres, and the field lines are straight but have a variable slope to the ionosphere in the azimuthal plane, the angle of which de- pends on the radial coordinate x. The model under investigation assumes that plasma density and, hence, the Alfven velocity depend on the radial component only. For this model we have established the Alfven resonance condition. It is shown that the res- onance can also occur in the case of a constant Alfven velocity if there is a change of the field line slope to the ionosphere. At resonance magnetic shells there is taking place a singularity of the wave field of the same form as in the absence of shear. It is found that the presence of shear leads to the noncoincidence of the poloidal and toroidal oscillation frequencies (it has been known previously that this phenomenon is caused by the field line curvature). Taking the magnetic field shear in the model under study gives rise to the Alfven wave dispersion across magnetic shells. The waves are traveling waves across magnetic shells, and the region where the wave is localized, is bounded in the radial coordinate by two turning points: the ordinary point, at which the mode is poloidally polarized, and the singular point where the wave is toroidally polarized. It is at this point where Alfven resonance occurs.
Annales Geophysicae, 2006
The paper employs the frame of a 1-D inhomogeneous model of space plasma,to examine the spatial s... more The paper employs the frame of a 1-D inhomogeneous model of space plasma,to examine the spatial structure and growth rate of drift mirror modes, often suggested for interpreting some oscillation types in space plasma. Owing to its coupling with the Alfvén mode, the drift mirror mode attains dispersion across magnetic shells (dependence of the frequency on the wave-vector's radial component, kr). The spatial structure of a mode confined across magnetic shells is studied. The scale of spatial localization of the wave is shown to be determined by the plasma inhomogeneity scale and by the azimuthal component of the wave vector. The wave propagates across magnetic shells, its amplitude modulated along the radial coordinate by the Gauss function. Coupling with the Alfvén mode strongly influences the growth rate of the drift mirror instability. The mirror mode can only exist in a narrow range of parameters. In the general case, the mode represents an Alfvén wave modified by plasma inhomogeneity.
Plasma Physics Reports, 2006
A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in th... more A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in the magnetosphere. The finite plasma pressure, the transverse equilibrium current, and the curvature of the magnetic field lines are taken into account. It is shown that these effects lead to a transverse dispersion of Alfvén waves and change the dispersion relation for slow magnetosonic waves. There are two transparency regions for MHD waves, one located near the Alfvén resonance and the other near the magnetosonic resonance. In the radial direction, each of these regions is bounded by a surface formed by conventional turning points (a poloidal surface) and a surface formed by singular turning points (a resonant surface). In each transparency region, the mode is a standing wave in the longitudinal direction and propagates in the transverse direction from the poloidal surface toward the resonant one, at which it is completely absorbed.
Annales Geophysicae, 2005
Spatial localization and azimuthal wave numbers m of poloidal Alfvén waves generated by energetic... more Spatial localization and azimuthal wave numbers m of poloidal Alfvén waves generated by energetic particles in the magnetosphere are studied in the paper. There are two factors that cause the wave localization across magnetic shells. First, the instability growth rate is proportional to the distribution function of the energetic particles, hence waves must be predominantly generated on magnetic shells where the particles are located. Second, the frequency of the generated poloidal wave must coincide with the poloidal eigenfrequency, which is a function of the radial coordinate. The combined impact of these two factors also determines the azimuthal wave number of the generated oscillations. The beams with energies about 10 keV and 150 keV are considered. As a result, the waves are shown to be strongly localized across magnetic shells; for the most often observed second longitudinal harmonic of poloidal Alfvén wave (N=2), the localization region is about one Earth radius across the magnetic shells. It is shown that the drift-bounce resonance condition does not select the m value for this harmonic. For 10 keV particles (most often involved in the explanation of poloidal pulsations), the azimuthal wave number was shown to be determined with a rather low accuracy, -100<m<0. The 150 keV particles provide a little better but still a poor determination of this value, -90<m<-70. For the fundamental harmonic (N=1), the azimuthal wave number is determined with a better accuracy, but both of these numbers are too small (if the waves are generated by 150 keV particles), or the waves are generated on magnetic shells (in 10 keV case) which are too far away. The calculated values of γ/ω are not large enough to overcome the damping on the ionosphere. All these have cast some suspicion on the possibility of the drift-bounce instability to generate poloidal pulsations in the magnetosphere.
P. Mager, Institute of Solar-Terrestrial Physics, p.mager@iszf.irk.ru
Annales Geophysicae, 2008
The generation of a high-m Alfvén wave by substorm injected energetic particles in the magnetosph... more The generation of a high-m Alfvén wave by substorm injected energetic particles in the magnetosphere is studied. The wave is supposed to be emitted by an alternating current created by the drifting particle cloud or ring current inhomogeneity. It is shown that the wave appears in some azimuthal location simultaneously with the particle cloud arrival at the same spot. The value of the azimuthal wave number is determined as m∼ω/ω d , where ω is the eigenfrequency of the standing Alfvén wave and ω d is the particle drift frequency. The wave propagates westward, in the direction of the proton drift. Under the reasonable assumption about the density of the energetic particles, the amplitude of the generated wave is close to the observed amplitudes of poloidal ULF pulsations.
ABSTRACT The compressional and Alfven modes in non-uniform space plasmas are described by a syste... more ABSTRACT The compressional and Alfven modes in non-uniform space plasmas are described by a system of two integro-differential kinetic equations taking into account drift-bounce wave-particle interaction, finite plasma pressure, plasma and magnetic field inhomogeneity along field lines and transverse to magnetic shells, and mode coupling due to field line curvature. If the wave frequency is sufficiently lower than the bounce frequency, then the system describes a drift compressional mode with the eigenfrequency of order of diamagnetic drift frequency. If the wave is propagating in the same azimuth direction as protons, it interacts with particles and can be unstable when the plasma temperature grows with L-shell or has non-Maxwellian (bump-on-tail) distribution. In a parallel direction, the mode is strongly localized near the equator. In a transverse direction, it is enclosed between two magnetic shells, the resonance shell and the cut-off shell, where the wave vector radial component turns into infinity and zero, accordingly. The coupling between the drift compressional and Alfven modes strongly effects the ballooning instability.
Annales Geophysicae, 2006
Through the combined action of the field line curvature and finite plasma pressure in some region... more Through the combined action of the field line curvature and finite plasma pressure in some regions of the magnetosphere (plasmapause, ring current) there can exist global poloidal Alfvén modes standing both along field lines and across magnetic shells and propagating along azimuth. In this paper we investigate the spatio-temporal structure of such waves generated by an impulsive source. In general, the mode is the sum of radial harmonics whose structure is described by Hermitian polynomials. For the usually observed second harmonic structure along the background field, frequencies of these radial harmonics are very close to each other; therefore, the generated wave is almost a monochromatic oscillation. But mixing of the harmonics with different radial structure causes the evolution of the initially poloidal wave into the toroidal one. This casts some doubts upon the interpretation of observed high-m poloidal waves as global poloidal modes.
Annales Geophysicae, 2010
A case study of SuperDARN observations of Pc5 Alfvén ULF wave activity generated in the immediate... more A case study of SuperDARN observations of Pc5 Alfvén ULF wave activity generated in the immediate aftermath of a modest-intensity substorm expansion phase onset is presented. Observations from the Hankasalmi radar reveal that the wave had a period of 580 s and was characterized by an intermediate azimuthal wave number (m=13), with an eastwards phase propagation. It had a significant poloidal component and a rapid equatorward phase propagation (~62° per degree of latitude). The total equatorward phase variation over the wave signatures visible in the radar field-of-view exceeded the 180° associated with field line resonances. The wave activity is interpreted as being stimulated by recently-injected energetic particles. Specifically the wave is thought to arise from an eastward drifting cloud of energetic electrons in a similar fashion to recent theoretical suggestions (Mager and Klimushkin, 2008; Zolotukhina et al., 2008; Mager et al., 2009). The azimuthal wave number m is determined by the wave eigenfrequency and the drift velocity of the source particle population. To create such an intermediate-m wave, the injected particles must have rather high energies for a given L-shell, in comparison to previous observations of wave events with equatorward polarization. The wave period is somewhat longer than previous observations of equatorward-propagating events. This may well be a consequence of the wave occurring very shortly after the substorm expansion, on stretched near-midnight field lines characterised by longer eigenfrequencies than those involved in previous observations.
Journal of Geophysical Research: Space Physics, 2015
Plasma Physics Reports, 2006
A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in th... more A study is made of the spatial structure of small-scale azimuthal magnetohydrodynamic waves in the magnetosphere. The finite plasma pressure, the transverse equilibrium current, and the curvature of the magnetic field lines are taken into account. It is shown that these effects lead to a transverse dispersion of Alfvén waves and change the dispersion relation for slow magnetosonic waves. There are two transparency regions for MHD waves, one located near the Alfvén resonance and the other near the magnetosonic resonance. In the radial direction, each of these regions is bounded by a surface formed by conventional turning points (a poloidal surface) and a surface formed by singular turning points (a resonant surface). In each transparency region, the mode is a standing wave in the longitudinal direction and propagates in the transverse direction from the poloidal surface toward the resonant one, at which it is completely absorbed.
Earth, Planets and Space, 2007
In this paper the spatial structure of azimuthally small-scale Alfvén waves in magnetosphere exci... more In this paper the spatial structure of azimuthally small-scale Alfvén waves in magnetosphere excited by the impulse source is studied. The source is suddenly switched on at a definite moment and works as e −iω 0 t during the finite time interval. The influence of factors which lead to the difference of toroidal and poloidal eigenfrequencies (like curvature of field lines and finite plasma pressure) is taken into account. Due to these factors, a radial component of the group velocity of Alfvén wave appears. An important value is the time moment, t 0 , when a wave front moving with radial component of wave group velocity from the poloidal surface (a magnetic surface where the source frequency ω 0 coincides with the poloidal frequency) passes the given magnetic shell with the radial coordinate x. The temporal evolution at all the points, where the front has not come yet, is determined by the phase mixing of the initial disturbance. At the points through which the wave front has already passed, the wave field structure almost coincides with the structure of monochromatic wave. The region where the front propagates is bounded by the interval between the poloidal surface and the toroidal one (that is, the Alfvén resonance surface). For this reason, outside this region the evolution is always determined by the phase mixing, which leads to much smaller amplitudes than between poloidal and toroidal surfaces. After the source turned off, a back wave front is formed, which comes through the given point in direction from the poloidal surface to the toroidal one. After the back front has come, the monochromatic wave structure disappears and there is only a weak disturbance, which steadily disappears because of the phase mixing and the final conductivity of ionosphere.
Kinematics and Physics of Celestial Bodies, 2014
The problem of propagation of azimuthally small scale ULF modes in plasma with 1D inhomogeneity a... more The problem of propagation of azimuthally small scale ULF modes in plasma with 1D inhomogeneity and variable curvature of magnetic lines of force is analyzed. The propagation regions and the transverse structure of stable Alfven and cusp modes, as well as unstable ballooning modes, are determined. It is shown that long living ballooning and cusp modes can exist. Our results qualitatively describe the behavior of ULF modes with continuous spectrum in the geomagnetosphere and can be used for interpretation of spacecraft and SuperDARN radar measurement data.
Journal of Geophysical Research-Space Physics, 2013
1] A previous case study observed a ULF wave with an eastward and equatorward phase propagation (... more 1] A previous case study observed a ULF wave with an eastward and equatorward phase propagation (an azimuthal wave number m, of ∼13) generated during the expansion phase of a substorm. The eastward phase propagation of the wave suggested that eastward drifting energetic electrons injected during the substorm were responsible for driving that particular wave. In this study, a population of 83 similar ULF wave events also associated with substorm-injected particles have been identified using multiple Super Dual Auroral Radar Network radars in Europe and North America between June 2000 and September 2005. The wave events identified in this study exhibit azimuthal wave numbers ranging in magnitude from 2 to 92, where the direction of propagation depends on the relative positions of the substorm onsets and the wave observations. We suggest that azimuthally drifting energetic particles associated with the substorms are responsible for driving the waves. Both westward drifting ions and eastward drifting electrons are implicated with energies ranging from ∼1 to 70 keV. A clear dependence of the particle energy on the azimuthal separation of the wave observations and the substorm onset is seen, with higher energy particles (leading to lower m-number waves) being involved at smaller azimuthal separations.
Plasma Physics Reports, 2002
The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is s... more The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is solved using a simplified model: a cold plasma is inhomogeneous in one direction, and the magnetic field lines are straight. The waves are assumed to travel in the plane perpendicular to the radial coordinate (i.e., the coordinate along which the plasma and magnetic field are inhomogeneous). It is shown that the character of the singularity at the resonance surface is the same as that in a homogeneous magnetic field. It is found that the shear gives rise to the transverse dispersion of Alfvén waves, i.e., the dependence of the radial component of the wave vector on the wave frequency. In the presence of shear, Alfvén waves are found to propagate across magnetic surfaces. In this case, the transparent region is bounded by two turning points, at one of which, the radial component of the wave vector approaches infinity and, at the other one, it vanishes. At the turning point for magnetosonic waves, the electric and magnetic fields are finite; however, the radial component of the wave vector approaches infinity, rather than vanishes as in the case with a homogeneous field. © 2002 MAIK "Nauka/Interperiodica".