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.     

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.     

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.     

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.     

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.     

Reflection of Electromagnetic Waves by a Nonuniform Plasma Layer Covering a Metal Surface

Reflection coefficients of electromagnetic waves in a nonuniform plasma layer with electrons, positive ions and negative ions, covering a metal surface are investigated by using the finite-difference-time-domMn method. It is shown that the reflection coemcients are influenced greatly by the density gradient on the layer edge, layer thickness and electron proportion, i.e., the effect of the negative ions. It is also found that low reflection or high attenuation can be reached by properly choosing high electron proportion, thick plasma layer, and smooth density gradient in the low frequency regime, but sharp density gradient in the high frequency regime.     

Speed and shape of solitary waves in relativistic warm plasma

Large-amplitude solitary waves are investigated in a relativistic plasma with finite ion-temperature. The mass of electron is also considered. The Sagdeev’s pseudopotential is determined in terms ofu, the ion speed. It is found that there exists a critical value ofu ₀, the value ofu at which (u′)²=0, beyond which the solitary waves cease to exist. The critical value also depends on the parameters likeν, the soliton velocity;μ, the electronion mass ratio orσ, the temperature ratio of ion to electron. This result reproduces our previous result [Czech. J. Phys., Vol. 54 (2004), No. 4, 489–496] when the ion temperature is neglected.     

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.     

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.     

Ion acoustic shock waves in a relativistic electron-positron-ion plasmas

The Korteweg-de Vries-Burger (KdVB) equation is derived for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma. Electrons, positrons are considered isothermal and ions are relativistic. The travelling wave solution has been acquired by employing the tangent hyperbolic method. The vivid display of the graphical results is presented and analyzed. It is observed that amplitude and steepness of the shock wave decrease with increase of the relativistic streaming factor, the positron concentration and they increase with the increase of the coefficient of kinematic viscosity and vice versa. It is determined that at low temperature the shock wave propagates, whereas at very high temperature the solitary wave propagates in the system. The results may have relevance in astrophysical plasmas as well as in inertial confinement fusion plasmas.     

Self-guiding electromagnetic beams in relativistic electron–positron plasmas

Nonlinear interaction of an intense electromagnetic (EM) beam with relativistically hot electron–positron plasma is investigated by invoking the variational principle and numerical simulation, resting on the model of generalized nonlinear Schrödinger equation with saturating nonlinearity. The present analysis shows the dynamical properties including the possibilities of trapping and wave-breaking of EM beams. These properties of EM beams may give a significant clue for the gamma-ray burst.     

Propagation and Interaction of Ion-Acoustic Solitary Waves in a Two-Dimensional Plasma Consisting of Isothermal Electrons and Hot Ions

We study the propagation and interaction of ion-acoustic solitary waves in a simple two-dimensional plasma by using the extended Poincare Lighthill-Kuo perturbation method. We consider the interaction between two ion-acoustic solitary waves with different propagation directions in such a system, and obtain two Korteweg-de Vries equations for small but finite amplitude solitary waves along both ξ and η trajectories. The effects of the ratio of ion temperature σ the ratio of heat capacity γ and the colliding angle a on the amplitude, the width of the new nonlinear wave created by the collision between two solitary waves are studied. The effects of these parameters on both the colliding solitary waves are examined as well. It is found that all the above-mentioned parameters have significant effects on the properties of these nonlinear waves.     

Modelling Energetic Electrons by a Kappa-Loss-Cone Distribution at Geostationary Orbit

We adopt a recently developed relativistic kappa-loss-cone （KLC） distribution to model energetic electrons energy spectra observed at the geostatlonary orbit in the storm of 3-4 November 1993. The KLU distribution is found to fit well with the observed data from four satellites during different universal times. This suggests that the electron flux obeys the power-law not only at the lower energies but also at the relativistic energies, and the KLU distribution may provide a better understanding of environments in those space plasmas where relativistic electrons are present.     

Fast magnetization in counterstreaming plasmas with temperature anisotropies

Counterstreaming plasmas exhibits an electromagnetic unstable mode of filamentation type, which is responsible for the magnetization of plasma system. It is shown that filamentation instability becomes significantly faster when plasma is hotter in the streaming direction. This is relevant for astrophysical sources, where strong magnetic fields are expected to exist and explain the nothermal emission observed.     

Long-Range Surface Plasmon Polaritons Guided by a Thin Metal Stripe

A long-range surface plasmon polariton （LRSPP） waveguide consisting of a 15nm thick gold stripe embedded in a homogeneous polymer BCB is reported. LRSPPs are excited by TM-mode input light successfully using an end-fire method. By scanning the output coupling fibre, the near field of the LRSPP is measured. The propagation loss of as low as 2.34 dB/mm is demonstrated.     

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.     

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.     

Modulation instability of intense laser beam in an electron-positron plasma

Modulation instability of an intense right-hand elliptically polarized laser beam propagating through an electron-positron plasma is investigated by a new method. The nonlinear dispersion relation, in which the relativistic and ponderomotive nonlinearities are taken into account, is obtained for the laser radiation in electron-positron plasma by the Lorentz transformation. The Karpman equation is generalized to the case of three dimensions with three field components. When the nonlinear frequency shift of the electromagnetic field in plasma is involved, the nonlinear evolution equation for the slowly varying envelope of the laser field is obtained. Thus, modulation instability of the intense laser beam in electron-positron plasma is studied and the temporal growth rate of the instability is derived. The analysis shows that the growth rate of modulation instability is increased significantly near the critical surface in a laser-plasma.     

Modulation instability by intense laser beam in magnetized plasma

Modulation instability of an intense right-hand elliptically polarized laser beam propagating through magnetized plasma is investigated by a new method. The nonlinear dispersion relation, in which the relativistic and ponderomotive nonlinearities are taken into account, is obtained for the laser radiation in magnetized plasma by the Lorentz transformation. The Karpman equation is firstly generalized to the case of three dimensions with three field components. When the nonlinear frequency shift of the electromagnetic field in plasma is involved, the nonlinear evolution equation for the slowly varying envelope of the laser field is obtained. Thus, modulation instability of the intense laser beam in magnetized plasma is studied and the temporal growth rate of the instability is derived. The analysis shows that the peak growth rate of self-modulation instability is increased due to the axial magnetization of plasma. It is also shown that the growth rate of modulation instability is increased significantly near the critical surface in a laser-plasma.     

Nonplanar dust ion-acoustic solitary and shock waves in a dusty plasma with electrons following a vortex-like distribution

Properties of nonplanar (viz. cylindrical and spherical) dust ion-acoustic (DIA) solitary and shock waves propagating in a dusty plasma containing charge fluctuating stationary dust, inertial warm ions, and non-isothermal electrons following a vortex-like distribution, are investigated by the reductive perturbation method. It has been shown that all the basic features of the DIA solitary and shock waves are significantly modified by the effects of vortex-like electron distribution, dust charge fluctuation, and nonplanar cylindrical and spherical geometries. The implications of our results in some space and laboratory dusty plasma environments are briefly discussed.