Drift Compressional Mode Research Articles

Observing drift compressional waves in the nightside ionosphere using the Ekaterinburg radar

A review of researches related to ultra low frequency (ULF) waves studied using a midlatitude coherent decameter radar located near Ekaterinburg (EKB), Russia is presented. The radar was constructed similar to SuperDARN radars. During the experiment conducted in 2013–2015 three of its beams were surveyed successively with the integration time of 6 s providing time resolution of 18 s at each beam. In a few cases, data received in the nighttime ionosphere showed signatures of the drift compressional mode. In one of them, the wave exhibited clear dependence of frequency on azimuthal wave number m, which corresponds with the theory of drift compressional waves. In another case, merging of the drift compressional and Alfvén modes at some critical value of m was shown. A number of the observed waves’ frequencies were compared with the Alfvén ones inferred from the spacecraft data. The results showed that in a large part of cases waves had sub-Alfvénic frequencies. This finding complies with the assumption that at least a part of the waves observed with the radar should be identified with the drift compressional mode, whose frequency can be lower than frequency of field line resonance (FLR). Additionally, a case of simultaneous spacecraft and radar wave observation was presented. As the wave had poloidal structure, diamagnetic properties, and its frequency was considerably lower than the minimal frequency of the FLR, it was assumed that it was some kind of compressional mode, apparently the drift compressional wave.

Observing magnetospheric waves propagating in the direction of electron drift with Ekaterinburg Decameter Coherent Radar

This paper deals with Pc5 magnetospheric pulsations featuring positive azimuthal wave numbers registered with the mid-latitude coherent decameter radar located near Ekaterinburg (EKB). The azimuthal wave numbers are determined using adjacent high time resolution beams directed toward the magnetic pole. Approximately 13 % of all steady waves registered with the radar propagate eastward. We have examined ten cases of wave observations with both small and high positive wave numbers, which occurred between April 2014 and March 2015. We performed a wavelet analysis of the data sets, estimated wavelength in radial direction for four cases, and determined meridional phase propagation direction. In three cases, the results are consistent with field line resonance behavior. However, in the majority of the studied events wave frequencies are considerably lower than those of field line resonance, which were derived from satellite data on magnetic field and particle density. These waves may be classed with the drift-compressional mode.

Наблюдения магнитосферных волн, распространяющихся в направлении дрейфа электронов, с помощью Екатеринбургского когерентного радара

This paper deals with Pc5 magnetospheric pulsations featuring positive azimuthal wave numbers registered with the mid-latitude coherent decameter radar located near Ekaterinburg (EKB). The azimuthal wave numbers are determined using adjacent high time resolution beams directed toward the magnetic pole. Approximately 13 % of all steady waves registered with the radar propagate eastward. We have examined ten cases of wave observations with both small and high positive wave numbers, which occurred between April 2014 and March 2015. We performed a wavelet analysis of the data sets, estimated wavelength in radial direction for four cases, and determined meridional phase propagation direction. In three cases, the results are consistent with field line resonance behavior. However, in the majority of the studied events wave frequencies are considerably lower than those of field line resonance, which were derived from satellite data on magnetic field and particle density. These waves may be classed with the drift-compressional mode.

Drift Resonance of Compressional ULF Waves and Substorm‐Injected Protons From Multipoint THEMIS Measurements

AbstractA compressional Pc5 wave associated with localized hot proton injection was observed by the five THEMIS (Time History of Events and Macroscale Interactions during Substorms) spacecraft in the dusk sector of the Earth's magnetosphere at L ∼ 10RE on 21 May 2007. The wave magnetic field perturbation transverse to the background magnetic field was primarily poloidal, in agreement with the predominately azimuthal wave vector direction (with westward phase velocity). The observation followed two consecutive substorms, when the cloud of energetic particles comprised of the lower‐energy protons from the earlier substorm was mixed with higher‐energy protons from the subsequent one. The clear signatures of the wave‐particle drift resonance of protons modulated by the wave were observed. The wave period was found to be about 2 times longer than the corresponding Alfvén wave eigenmode period on the same L‐shells calculated with the THEMIS data. The increase of the particle energy with the distance from the Earth and the observed strong dependence of the wave frequency on the azimuthal wave number constitutes conditions for the gradient instability of the drift compressional mode (for the Alfvén mode one supposes the particle energy decrease with radial distance). Based on these results, we conclude that the observed wave was the drift compressional mode generated by the gradient instability.

Non-resonant instability of coupled Alfvén and drift compressional modes in magnetospheric plasma

A new mechanism of generation of the high-m compressional ULF waves in the magnetosphere is considered. It is suggested that the wave can be generated by the non-resonant instability of coupled Alfvén and drift compressional modes in the energetic component of the magnetospheric plasma. A stability analysis of the of the coupled modes in the inhomogeneous finite-β plasma in the dipole-like field in gyrokinetics is performed. A quadratic equation was obtained that determines mode frequency and the growth rate. The frequencies of both modes depend on the azimuthal wave number, m. The branches are merged at some critical m value, forming a mode with both real and imaginary parts of the wave frequency. This mode is amplified due to the instability called the drift coupling instability. The instability criterion was found. Its growth rate is determined by the mode coupling.

Наблюдения дрейфово-компрессионных волн с помощью среднеширотного декаметрового когерентного радара

Magnetospheric Pc5 pulsations observed on December 26, 2014 are analyzed. They were recorded in the nightside magnetosphere with a mid-latitude coherent decameter radar located near Ekaterinburg. It registers velocity variations in electric drift of ionospheric plasma caused by ULF waves in the magnetosphere. The westward direction of azimuthal propagation of wave coincides with the direction of magnetic drift of protons. A cross-wavelet analysis reveals that the frequency of oscillations depends on the wave number m, and the correlation between them is 0.90. The frequency increase from 2.5 to 5 mHz was followed by an increase in the absolute value m from 20 to 80. These features of the wave under study testify that it should be classified as a drift compressional mode which is typical for the ULF mode in kinetics. Existence conditions for it are the terminal pressure of plasma and its inhomogeneity across magnetic shells.

Multiradar observations of substorm‐driven ULF waves

AbstractA recent statistical study of ULF waves driven by substorm‐injected particles observed using Super Dual Auroral Radar Network (SuperDARN) found that the phase characteristics of these waves varied depending on where the wave was observed relative to the substorm. Typically, positive azimuthal wave numbers, m, were observed in waves generated to the east of the substorms and negative m to the west. The magnitude of m typically increased with the azimuthal separation between the wave observation and the substorm location. The energies estimated for the driving particles for these 83 wave events were found to be highest when the waves were observed closer to the substorm and lowest farther away. Each of the 83 events studied by James et al. (2013) involved just a single wave observation per substorm. Here a study of three individual substorm events are presented, with associated observations of multiple ULF waves using various different SuperDARN radars. We demonstrate that a single substorm is capable of driving a number of wave events characterized by different azimuthal scale lengths and wave periods, associated with different energies, W, in the driving particle population. We find that similar trends in m and W exist for multiple wave events with a single substorm as was seen in the single wave events of James et al. (2013). The variety of wave periods present on similar L shells in this study may also be evidence for the detection of both poloidal Alfvén and drift compressional mode waves driven by substorm‐injected particles.

Experimental evidence of drift compressional waves in the magnetosphere: An Ekaterinburg coherent decameter radar case study

AbstractA case study of shortwave radar observations of magnetospheric Pc5 ULF waves (wave periods of 150–600 s) that occurred on 26 December 2014 in the nightside magnetosphere during substorm activity is presented. The radar study of waves in the magnetosphere is based on analysis of scattering from field‐aligned irregularities of the ionospheric F layer. Variations of their drift velocity at F layer heights are associated with the wave electric field. Analysis of the observations from the Ekaterinburg (EKB) radar shows that the frequency f of the observed wave depends on the azimuthal wave number m (positive correlation of about 0.90): an increase in frequency from 2.5 to 5 mHz corresponds to increased m number from 20 to 80. Of the known types of waves in the magnetosphere corresponding to the Pc5 range, only drift compressional waves have such azimuthal dispersion: the frequency of the drift compressional mode is directly proportional to the azimuthal wave number and the gradient‐curvature drift velocity of energetic particles in the magnetic field. This wave has a kinetic nature and represents the most common kind of the compressional modes, demanding for its existence only finite pressure and plasma inhomogeneity across magnetic shells.

First results of the high-resolution multibeam ULF wave experiment at the Ekaterinburg SuperDARN radar: Ionospheric signatures of coupled poloidal Alfvén and drift-compressional modes

A continuous experiment was carried out at the Ekaterinburg (EKB) stereoradar of the Russian segment of SuperDARN in order to examine the spatio-temporal characteristics of radar-detected magnetospheric ULF waves. The study of magnetospheric oscillations is based on analysis of scattering from field-aligned F-layer irregularities. Their E×B drift Doppler velocity at F-layer heights is associated with the background electric field in the ionosphere. During the experiment one of the radar channels operates in 0–2 beam scanning, with an integration time of 6s, which corresponds to the total 18-s time resolution at each beam. This allows detecting magnetospheric ULF waves with periods of 40s and up. Beam 0 is along the 132 magnetic meridian, so the registered velocity oscillations correspond to the wave electric field azimuthal component. Operation of the radar in this mode was started in December 2013.The first ULF wave events observed in the experiment and presented here occurred on 14 December 2013 and 2 January 2014 in the nightside magnetosphere during two geomagnetic disturbances classified as small magnetic storms and associated with high speed streams from coronal holes. Both the ULF events occurred after substorm-like auroral disturbances. The ULF waves observed during these events are classified as Pc5 geomagnetic pulsations. Two oscillation branches were observed, the higher and the lower frequency ones. As the azimuthal wave numbers m increase, the branches converge and merge into a single oscillation branch at some critical azimuthal wave number value m⋆. This ω(m) dependence is characteristic of the coupled Alfvén and drift-compressional waves which according to theory merge if the azimuthal wave number exceeds some critical value. This merged single oscillation branch represents an unstable drift ballooning coupling mode. Thus, the following interpretation of the observed events can be suggested; at m<m⋆ the higher and lower frequency branches can be identified with the Alfvén and drift-compressional modes, respectively, and at m>m⋆ the single branch can be identified with the drift ballooning coupling mode.

Drift‐compressional modes generated by inverted plasma distributions in the magnetosphere

The polarization and field‐aligned structure of drift‐compressional modes and the corresponding plasma instability are studied in a gyrokinetic framework in the axisymmetric model of the magnetosphere with isotropic plasma. The plasma is assumed to be composed of core cold particles and an admixture of hot protons, with an inverted distribution of hot protons. Such plasma experiences a compressional resonance when the wave frequency is equal to an eigenfrequency of the drift‐compressional mode. In this resonance, the wave is dominated by the field‐aligned and azimuthal magnetic field components and is narrowly localized along the field line at the equator, the same as the plasma to magnetic pressure ratio β. The plasma instability occurs when the temperature diamagnetic drift velocity is less than the magnetic drift velocity or opposite in direction. Furthermore, the narrower the inverted distribution, the higher the instability growth rate and the smaller the value of β required for the instability to occur. The growth rate reaches its highest values when a positive radial temperature gradient and a negative radial density gradient occur simultaneously.

On the ballooning instability of the coupled Alfvén and drift compressional modes

The paper examines the ballooning instability in gyrokinetic approximation taking into account the effects of finite-β, magnetic field line curvature, and diamagnetic drift. We used a simple model with a constant curvature of magnetic field lines which enabled us to obtain analytical results. The possible plasma oscillatory modes comprise the poloidal Alfvén and drift compressional modes, coupled due to the magnetic field line curvature and plasma inhomogeneity. The frequencies of these modes depend on the westward current value. As this value grows, the frequencies of these two branches approach to each other, and the branches are merged at some critical value of the current. Then an instability develops which is called the drift ballooning coupling instability. There are three major differences of the drift ballooning coupling instability from the ordinary MHD ballooning instability: (1) the drift ballooning coupling instability is not aperiodic, there is a real part of the oscillation frequency of the order of the drift frequency, (2) only the mode with the same direction of the azimuthal phase speed as the velocity of the ion diamagnetic drift can be unstable, (3) the instability threshold depends on the diamagnetic drift frequency.

Spatial structure and stability of coupled Alfvén and drift compressional modes in non-uniform magnetosphere: Gyrokinetic treatment

The spatial structure and stability properties of the coupled Alfvén and drift compressional modes in a space plasma are studied in a gyrokinetic framework in a model taking into account field-line curvature and plasma and magnetic field inhomogeneity across the magnetic shells. The perturbation is found to be localized in two transparent regions, the Alfvén and drift compressional transparent regions, where the wave vector radial component squared is positive. Both regions are bounded by the resonance and cut-off surfaces, where the wave vector radial component turns into infinity and zero, respectively. An existence of the drift compressional resonance is one of the most important results of this work. It is argued that on the surface of this resonance the longitudinal and azimuthal components of the wave's magnetic field have a pole and logarithmic singularities, respectively. The instability conditions and expressions for the growth rate of the coupled modes have been obtained. In the Alfvénic transparent region, an instability occurs in the presence of the negative plasma temperature gradient. This instability does not lead to a non-stationary wave behavior: all the energy gained from the resonance particles was finally absorbed owing to any dissipation process. In a drift compressional transparent region, a necessary condition for the instability is the growth of the temperature with the radial coordinate. The growth rate is almost independent of the radial coordinate, which means that the wave energy gained from the particles cannot disappear. It will lead to an ever increasing wave amplitude, and no stationary picture for the unstable drift compressional mode is possible.

Gyrokinetic particle simulation of drift-compressional modes in dipole geometry

Gyrokinetic particle simulation of low frequency compressional modes has been developed using flux coordinates in the global magnetic dipole geometry. The compressional component is formulated in a scalar form of the parallel magnetic perturbation, and the gyro-averaging is performed explicitly in the configuration space. A reduced gyrokinetic model, in which the compressional perturbations are decoupled from the shear Alfvén and electrostatic perturbations, has been implemented. Linear simulation results have been verified using a numerical Nyquist analysis of the dispersion relation in the slab limit. Global simulations of unstable drift-compressional modes in the dipole geometry with kinetic ions find that finite Larmor radius (FLR) effects reduce the linear growth rate significantly but change little the real frequency. Global eigenmode structures show that the modes are even along the equilibrium magnetic field and broadened by the FLR effects in the radial direction. Radial propagation away from the region of excitation is observed.

Finite gyroradius theory of drift compressional modes

A dispersion relation for ultralow frequency drift compressional modes in high pressure plasmas with finite gyroradius is derived from the linearized gyrokinetic‐Maxwell equations with cold electrons and narrow eigenmode localization width along the field line. The dispersion relation demonstrates instability under two different conditions: 1) when the density gradient and proton temperature gradient are in opposite directions, or 2) when the magnetic guiding center drift is reversed with respect to the proton diamagnetic drift, i.e., drift reversal, which could occur during periods of strong magnetospheric disturbance. Furthermore, it is found that the most unstable modes have short azimuthal wavelengths comparable to the proton gyroradius.

Theory of hot particle stability

The investigation of stabilization of hot particle drift reversed systems to low frequency modes has been extended to arbitrary hot beta βH, for systems that have unfavorable field-line curvature. Steep profile equilibria are considered where the thickness of the pressure drop Δ, is less than plasma radius rp. The analysis describes layer modes which have mΔ/rp &amp;lt;1, where m is the mode number, and radial structure larger than Δ. Stabilization is classified as either being ‘‘robust,’’ where all excitations are positive energy, or ‘‘fragile,’’ where stability criteria exist to magnetohydrodynamic (MHD)-like and drift-compressional instabilities, but positive and negative energy waves are present (with the possibility that negative energy waves are destabilized by dissipative mechanisms). It is shown that in making a continuous transition from the fragile stability regime to the robust stability regime one must go through an unstable region. To bridge the unstable band in a physical manner one must either produce robust stability conditions very rapidly, or use transient stability techniques such as ponderomotive forces or transient minimum-B coils. The positive energy stabilization terms of the layer mode from wall stabilization terms and finite Larmor radius terms are explicitly exhibited. It is shown the robust stability can even be achieved with only wall stabilization for all possible m values of the layer modes if βH &amp;gt; (2)/(3) . When robust stability conditions are fulfilled, the hot particles will have their bounce frequency less than their grad-B drift frequency. This allows for a low bounce frequency expansion to describe the axial dependence of the magnetic compressional response. Such as expansion provides for another negative energy source in the theory, with the system then being susceptible to the drift compressional instability if dβH/dr &amp;gt;dβw/dr, where βw is the beta of the background plasma. If robust stabilization conditions are not fulfilled, the regions of fragile stability are extremely small if the MHD-like modes, the diamagnetic compressional and drift-compressional modes are to be simultaneously avoided.

Eigenmode analysis of compressional waves in the magnetosphere

Recent multiple satellite observations of compressional Pc 5 waves indicate for the first time that the field‐aligned mode structure of the compressional magnetic field was antisymmetric with respect to the earth's magnetic equator. To understand the mode structures of low frequency compressional waves, a comprehensive eigenmode analysis of compressional Alfven instabilities was performed for a two component anisotropic plasma in a dipole magnetic field. The eigenmode equations derived from the gyrokinetic equations are solved analytically and numerically for both the drift mirror and the drift compressional instabilities. The solutions indicate that the drift mirror mode has an antisymmetric compressional component with respect to the magnetic equator, whereas the drift compressional mode has a symmetric one. For typical storm time plasma parameters near geosynchronous orbit, it is suggested that the recently observed compressional Pc 5 wave was in a nonlinearly saturated state of the drift mirror instability.

Alfven waves and drift compressional modes in multispecies plasmas

The stability of a multispecies plasma under magnetospheric storm conditions is investigated. The dynamics of the impurity ions are incorporated in the hot plasma component response, since the response (to perturbations) of the cold component is totally dominated by the electrons. The coupling between drift compressional and shear Alfven modes is studied in weak and strong coupling limits, the coupling being weakened when a finite fraction of the hot ions belongs to the heavy species. The characteristic growth rates of the mirror instability, modified by the presence of heavy impurity ions, are determined. For the case of strong coupling, the dominant unstable mode is a compressional Alfven oscillation, driven by the finite density gradient of the plasma. The main effect of the impurity ions, in this case, is to stabilize the mode through their inertia. The instability is found to be self‐limiting with increasing plasma pressure, and the asymptotic normalized growth rate is determined.