A Three-Dimensional Ray-Tracing Study of R-X Mode Waves during High Geomagnetic Activity

We further present a three-dimensional (3D) ray-tracing study on the propagation characteristic of the superluminous R-X mode waves during high geomagnetic activity following our recent two-dimensional results [J. Geophys. Res. 112(2007)A10214]. We perform numerical calculations for this mode which originates at specific altitude r=2.0R_E in the source cavity along a 70° night geomagnetic field line. We demonstrate that the ray path of the R-X mode is essentially governed by the azimuthal angle of the wave vector k. Ray paths starting with azimuthal angle 180° (or in the meridian plane) can reach the lowest latitude, but stay at relatively higher latitudes with the azimuthal angles other than 180° (or off the meridian plane). The results further supports the previous finding that the R-X mode may be physicallypresent in the radiation belts under appropriate conditions.     

Simulation of Resonant Interaction between Energetic Electrons and Whistler-Mode Chorus in the Outer Radiation Belt

We construct a realistic model to evaluate the chorus wave-particle interaction in the outer radiation belt L = 4.5. This model incorporates a plasmatrough number density model, a field-aligned density model and a realistic wave power and frequency model. We solve the 2D bounce-averaged momentum-pitch-angle Fokker-Planck equation and show that the Whistler-mode chorus can be effective in the acceleration of electrons, and enhance the phase space density for energies of -1 MeV by a factor from 10 to 10^3 in about two days, consistent with the observation. We also demonstrate that ignorance of the electron number density variation along field line and magnetic local time in the previous work yields an overestimate of energetic electron phase space density by a factor 5-10 at large pitch-angle after two days, suggesting that a realistic plasma density model is very important to evaluate the evolution of energetic electrons in the outer radiation belt.     

Storm-Time Strong Field-Aligned Ion Upflow in Region of the SED Plume

We report the observations from the GPS TEC and DMSP F-13 satellites showing that very strong upward field-aligned （FA） ion velocity and flux in the outer region of the storm-enhanced density （SED） occurred in the event of the geomagnetic storm on 29-31 May 2003. By a method of coordinate transformation, upward FA ion velocities in excess of 25Orals are obtained from the observations of the DMSP F-13 satellite. Further, an FA ion flux is estimated to be about 4.5 x 1013 ions/m2 s in the dusk sector. The estimated FA ion velocity and flux provide a powerful direct proof to support the scenario that there is a strong coupling of particles between the ionosphere and plasmasphere in the region of the SED plume. In the process, FA ion flux transports from the ionosphere to the plasmasphere in the region of the SED plume. Therefore, the plume of SED in the ionosphere provides an important source to the enhanced density of O^＋ in the storm-time plasmasphere.     

Dynamic Evolution of Outer Radiation Belt Electrons due to Whistler-Mode Chorus

Following our preceding work, we perform a further study on dynamic evolution of energetic electrons in the outer radiation belt L=4.5 due to a band of whistler-mode chorus frequency distributed over a standard Gaussian spectrum. We solve the 2D bounce-averaged Fokker-Planek equation by allowing incorporation of cross diffusion rates. Numerical results show that whistler-mode chorus can be effective in acceleration of electrons at large pitch angles, and enhance the phase space density for energies of about 1 MeV by a factor of 10^2 or above in about one day, consistent with observation of significant enhancement in flux of energetic electrons during the recovery phase of a geomagnetic storm. Moreover, neglecting cross diffusion often leads to overestimates of the phase space density evolution at large pitch angle by a factor of 5-10 after one day, with larger errors at smaller pitch angle, suggesting that cross diffusion also plays an important role in wave-particle interaction.     

Effects of Charge in Heavy Ions on Solitary Kinetic Alfvén Waves in Double-Ion Plasmas

After the charge of heavy ions is considered, a Sagdeev equation is obtained for the solitary kinetic lfvén waves (SKAWs) in a low-β (m_e/m_p « β « or m_p/m_e » α » 1), three-component (electrons, protons, and highly charged heavy ions) plasma. Numerical results show that the charge number q of heavy ions can cause the width of the solitary structure to decrease, but increase for the maximum of electron density n_em≤ 1.2 and the initial abundance of heavy ions C_b0 ≤ 0.1. The parallel phase speed of the waves increases with larger q.     

Bounce-Averaged Acceleration of Energetic Electrons by Whistler Mode Chorus in the Magnetosphere

We construct the bounce-averaged diffusion coefficients and study the bounce-averaged acceleration for energetic electrons in gyroresonance with whistler mode chorus. Numerical calculations have been performed for a band of chorus frequency distributed over a standard Gaussian spectrum specifically in the region near L = 4.5, where peaks of the electron phase space density occur. It is found that whistler mode chorus can efficiently accelerate electrons and can increase the phase space density at energies of about 1 MeV by more than one order of magnitude about one day, in agreement with the satellite observations during the recovery phase of magnetic storms.     

Characteristics of Wave--Particle Interaction in a Hydrogen Plasma

We study the characteristics of cyclotron way,particle interaction in a typical hydrogen plasma. The numerical calculations of minimum resonant energy Emin, resonant wave frequency ω, and pitch angle diffusion coefficient Dαα for interactions between R-mode/L-mode and electrons/protons are presented. It is found that Emin decreases with ω for R-mode/electron, L-mode/proton and L-mode/electron interactions, but increase with ω for R-mode/proton interaction. It is shown that both R-mode and L-mode waves can efficiently scatter energetic （10 keV-100 keV） electrons and protons and cause precipitation loss at L = 4, indicating that perhaps waveparticle interaction is a serious candidate for the ring current decay.     

Pitch Angle Distribution Evolution of Energetic Electrons by Whistler-Mode Chorus

We develop a two-dimensional momentum and pitch angle code to solve the typical Fokker-Planck equation which governs wave-particle interaction in space plasmas. We carry out detailed calculations of momentum and pitch angle diffusion coefficients, and temporal evolution of pitch angle distribution for a band of chorus frequency distributed over a standard Gaussian spectrum particularly in the heart of the Earth＇s radiation belt L = 4.5, where peaks of the electron phase space density are observed. We find that the Whistler-mode chorus can produce significant acceleration of electrons at large pitch angles, and can enhance the phase space density for energies of 0.5 - 1 MeV by a factor of 10 or above after about 24h. This result can account for observation of significant enhancement in flux of energetic electrons during the recovery phase of a geomagnetic storm.     

Second-Order Resonant Interaction of Ring Current Protons with Whistler-Mode Waves

We present a study on the second-order resonant interaction between the ring current protons with Whistler-mode waves propagating near the quasi electrostatic limit following the previous second-order resonant theory. The diffusion coefficients are proportional to the electric field amplitude E, much greater than those for the regular first-order resonance, which are proportional to the electric field amplitudes square E^2. Numerical calculations for the pitch angle scattering are performed for typical energies of protons Ek = 50 keV and 100 keV at locations L = 2 and L = 3.5. The timescale for the loss process of protons by the Whistler waves is found to approach one hour, comparable to that by the EMIC waves, suggesting that Whistler waves may also contribute significantly to the ring current decay under appropriate conditions.     

Bounce-averaged Pitch-angle Diffusion by Electromagnetic Ion Cyclotron Waves in Multi-ion Plasmas

We present a study on the gyroresonant interaction particles in multi-ion （H^＋, He^＋, and O^＋） plasmas between electromagnetic ion cyclotron waves and ring current We provide a first evaluation of the bounce-averaged pitch angle diffusion coefficient 〈Dαα〉 for three typical energies of 50, 100 and 150keV at L ≈ 3.5, the heart of the symmetrical ring current. We show that in the H^＋-band and He^＋-band, 〈Dαα〉 can approach - 10^-4 s^-1 for ion H^＋, and - 5 × 10^-5 s^-1 /or ion He^＋; meanwhile, in the O^＋-band, 〈Dαα〉 can reach - 10^-5 s^-1 for ions He^＋ and O^＋. The results above show that the EMIC wave can efficiently produce precipitation loss of energetic （- 100 keV） ions （H^＋, He^＋ and even O^＋）, and such a wave tends to be a serious candidate responsible for the ring current decay.     

Nonlinear Evolution of Lower-Hybrid Drift Instability in Harris Current Sheet

We perform 2.5-dimensional particle-in-cell simulations to investigate the nonlinear evolution of the lower hybrid drift instability (LHDI) in Harris current sheet. Due to the drift motion of electrons in the electric field of the excited low hybrid drift (LHD) waves, the electrons accumulate at the outer layer, and therefore there is net positive charge at the inner edge of the current sheet. This redistribution of charge can create an electrostatic field along the z direction, which then modifies the motions of the electrons along the y direction by E×B drift. This effect strongly changes the structure of the current sheet.     

Short Wavelength Ion Temperature Gradient Driven Instability in Noncircular Flux Surface Plasmas with Finite Aspect Ratio

By employing the local equilibrium of shaped tokamak plasmas, a gyrokinetic model with integral eigenmode equations is developed to investigate effects of the finite aspect ratio and noncircular flux surface on short wavelength ion temperature gradient （SWITG） driven modes. It is found that when nonadiabatic electron and trapped particle effects are not considered, the SWITG mode can be stabilized by finite aspect ratio A, elongation and triangularity δ, and can be destabilized by the Shafranov shift gradient θRo/θr.     

The morphology of electrostatic tripolar regions

Electrostatic tripolar regions in plasmas develop a skewness of their own electric potential waveform as a peculiar morphological property, which distinguishes them from symmetric electrostatic solitary waves. Within the collision-less, kinetic treatment developed here, this property holds if the velocity distributions of electrons and ions are singular in value, irrespective of their smoothness at the region’s boundary and of the smoothness of the potential waveform and of the electron and ion density distributions. These singularities are integrable, and are of the logarithmic and jump type: the former occur at isolated points in phase space; the latter occur on the left branch of the electron separatrix and on the left branch of the ion sub-separatrix. The distributions are non-negative if, at its local extrema, the potential waveform is skewed to the left, in agreement with observations, and if the skewness is smaller than a given bound: a sufficient condition for such skewness to be small about the minimum of the potential waveform is that a sufficiently fast electron beam exists on the high-potential boundary of the tripolar region. In those special cases in which the particle distributions are continuous in value, the above mentioned singularities affect their space and velocity derivatives. These results could be extracted from very general considerations on the degree of smoothness of the spatial distribution of the electric potential and on the non-negativity of the electron and ion distributions, without the assistance of any specific models.     

Interhemispheric Comparison of Dipole Tilt Angle Effects on Latitude of Mid-Altitude Cusp

A statistical study of interhemispheric comparison of dipole tilt angle effect on the latitude of the mid-altitude cusp is preformed by a data set of the Cluster cusp crossings over a 5-year period. The result shows that the dipole tilt angle has a clear control of the cusp latitudinal location. When the dipole tilts sunwards, the cusp is shifted poleward. The northern cusp moves 1° ILAT for every 15.4° increase in the dipole tilt angle, while the southern cusp moves 1° ILAT for every 20.8° increase in the dipole tilt angle. This suggests that an interhemispheric difference appears in the dependence of cusp latitudinal location on the dipole tilt angle.     

Kinetic theory of instabilities responsible for magnetic turbulence in laboratory rotating plasma

The problem of instabilities responsible for magnetic turbulence in collisionless laboratory rotating plasma is investigated. It is shown that the standard mechanism of driving the magnetorotational instability (MRI), due to negative rotation frequency gradient, disappears in such a plasma. Instead of it, a new driving mechanism due to plasma pressure gradient is predicted.     

Effects of positron density and temperature on ion acoustic dressed solitons in an electron–positron–ion plasma

Ion acoustic dressed solitons in a three component plasma consisting of cold ions, hot electrons and positrons are studied. Using reductive perturbation method, Korteweg–de Vries (KdV) equation and a linear inhomogeneous equation, governing respectively the evolution of first and second order potentials are derived for the system. Renormalization procedure of Kodama and Taniuti is used to obtain nonsecular solutions of these coupled equations. It is found that electron–positron–ion plasma system supports only compressive solitons. For a given amplitude of soliton on increasing the positron concentration, velocity of the KdV as well as dressed soliton increases. For any arbitrary values of soliton's amplitude and positron concentration, velocity of the dressed soliton is found to be larger than that of the KdV soliton. For small amplitude of solitons, the width of KdV as well as dressed soliton decreases as positron concentration increases and width of dressed soliton is found to be larger than that of the KdV soliton. However, for a large value of soliton's amplitude as concentration of positrons increases, instead of decreasing width of dressed soliton starts to increase.     

Dust Lattice Waves of Dusty Plasma Chain with an External Magnetic Field

Dust lattice waves of a one-dimensional plasma crystal chain with an external magnetic field are investigated. When the magnetic field is in the vertical direction （θ- 0）, perpendicular to the chain, the vertical transverse mode is not affected, while the horizontal transverse mode is coupled with the longitudinal mode. In the high frequency range, we obtain an ‘upper-hybrid＇ dust lattice mode and in the low frequency range, we obtain a ＇lower-hybrid＇ dust lattice mode. Between the two modes, a ＇gap＇ is formed. When the magnetic field is oriented to the chain （0 = π/2）, the longitudinal mode is not affected while both the horizontal and vertical transverse modes are shifted due to the effect of the magnetic field.     

Weak Nonlinearity of Ablative Rayleigh--Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh-Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh-Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.     

Oscillations of Magnetized Dust Grains in Plasma Sheath with Negative Ions

The oscillations of a single magnetized dust grain in electronegative plasma sheath are investigated taking into account the existence of an external magnetic field. The influence of the content of negative ions and the magnetic field intensity on the properties of the dust vibration is analysed. The result shows that the existence of the negative ions in plasma reduces the dust oscillation frequency and drops the equilibrium position of dust, whereas the magnetic field raises the equilibrium position and also reduces the dust oscillation frequency on the condition considered.