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The effect of the plasma shaping (triangularity and elongation) on the continuous spectrum, frequency gaps, and number of eigenmodes is studied. The plasma shaping affects the coupling between Alfvén and slow magnetosonic waves via the geodesic magnetic curvature and the plasma pressure. The Alfvén-slow coupling creates a large number of new gaps in the continuous spectrum below the Alfvén frequency where discrete modes can reside. In ideal magnetohydrodynamic simulations a large number (a few hundred or more) of potential eigenmodes are found. The number of eigenmodes is correlated with the maximum geodesic curvature and a minimum number of possible discrete eigenmodes is found at a negative triangularity of −0.3. It is hypothesized that these possible eigenmodes form a low amplitude and dense discrete spectrum, which can be studied experimentally.

The stress field and heat flux singularities at the vertex of two-dimensional (2D) and three-dimensional (3D) V-notches are, respectively, investigated. By introducing typical terms in the series asymptotic expansions of displacement and temperature fields near the notch tip, the thermoelastic governing equations and radial boundary conditions of a V-notched structure are transformed into characteristic ordinary differential equations with respect to the singular order. These equations can be solved by the interpolating matrix method developed earlier by part of the authors. The singular orders related to the stress field and heat flux can be derived simultaneously and can be specified by the corresponding characteristic angular functions in the present method. The singularities are compared between 2D and 3D thermoelastic specimen containing V-notches. It is found that one singular order will be discarded if a 3D medium is simplified into a 2D one.

This paper considers the problem of minimizing the sum of a smooth convex function and a separable convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal processing, wireless networking and smart grid provisioning. We propose a new algorithm called the proximal block minimization method of multipliers with a substitution to solve this family of problems. The proposed algorithm integrates the block coordinate descent and alternating direction method of multipliers with substitution. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case convergence rate in an ergodic sense, where t denotes the number of iterations. Finally, some preliminary numerical results are reported to support the efficiency of the new algorithm.

Dynamics of Langmuir solitons in the presence of a background density gradient is investigated numerically, including cases with steep gradients to the extent the solitons can disintegrate. The disintegration threshold is explained by regarding the electric field part of the soliton as a point mass moving along the self-generated potential well corresponding to the density cavity. On the other hand, it is demonstrated that the Langmuir solitons are robust when the density gradient is below the threshold. During the acceleration phase toward low density regions, Langmuir solitons adjust themselves to balance the electric field pressure and the negative plasma pressure by expelling the imbalanced portion as density cavities at the sound velocity. When the density gradient is below the disintegration threshold, the electric field part of the soliton bounces back and forth within the potential well suggesting the solitons have internal structures.

The traditional brittle fracture criteria for V-notched structures are established on the base of the singular stress field at a V-notch tip where only two singular stress terms are adopted. The non-singular stress terms also play a significant role in determining the stress and strain fields around a V-notch tip, which in turn could affect the fracture character of V-notched structures predicted by the fracture mechanics criteria. In this paper, the effect of the non-singular stress on the brittle fracture properties for the V-notch problem is discussed. Firstly, the stress field around a V-notch tip is described by the Williams asymptotic expansions. At the same time, the stress field far from the V-notch tip is modeled by the conventional boundary element method since there is no stress singularity. By the combination of the Williams asymptotic expansions and the boundary integral equations, the complete stress field at a V-notch tip including several non-singular stress terms can be obtained. Then, three different brittle fracture criteria are introduced to predict the critical loading and initial crack propagation direction of V-notched structures under mixed-mode loading. Comparing with the existed experimental results, it can be found that the degree of accuracy of the predicted results when taking into account the non-singular stress terms is much higher than the predicted ones neglecting the non-singular stress.

Recent experiments in D-T plasmas on the JET and TFTR tokamaks have evaluated a wide range of ITER relevant ion cyclotron heating scenarios. Absorption of fast waves at the second-harmonic tritium resonance has provided bulk ion heating in TFTR supershots and electron heating in JET H-mode discharges. In JET, deuterium minority heating has generated 1.7 MW of fusion power with 6 MW of radio frequency power giving a record steady-state Q-value of 0.22. Strong bulk ion heating has been achieved with He3 minority heating with central ion temperatures up to 13 keV being produced in H-modes with a density of 3.6 × 1019 m-3. Hydrogen, deuterium and He3 minority heating methods have produced plasmas with normalized confinement times greater than or equal to that required by ITER for ignition. These H-modes are characterized by small-amplitude, high-frequency ELMs, each of which transports less than 1.5% of the plasma energy content to the limiters. The heavy minority scheme of tritium in a deuterium plasma has been demonstrated both as a heating scheme and a generator of suprathermal neutrons. On TFTR mode conversion to an ion Bernstein wave has achieved central bulk ion heating in supershots with target ion temperatures greater than 20 keV.

A summary is presented of recent alpha-particle experiments on the tokamak fusion test reactor. Alpha particles are generally well confined in MHD-quiescent discharges, and alpha heating of electrons has been observed. The theoretically predicted toroidicity-induced Alfv?n eigenmode has been seen in discharges of of alpha power, but only in plasmas with weak magnetic shear.

Two-dimensional solutions of compressional Alfven eigenmodes (CAEs) are studied in the cold plasma approximation. For finite inverse aspect ratio tokamak plasmas the two-dimensional eigenmode envelope is localized at the low magnetic field side with the radial and poloidal localization on the order of a/ square root m and a/4 square root m, respectively, where m is the dominant poloidal mode number. Charged fusion product driven Alfven cyclotron instability (ACI) of the compressional Alfven eigenmodes provides the explanation for the ion cyclotron emission (ICE) spectrum observed in tokamak experiments. The ACI is excited by fast charged fusion products via Doppler shifted cyclotron wave-particle resonances. The ion cyclotron and electron Landau dampings and fast particle instability drive are calculated perturbatively for deuterium-deuterium (DD) and deuterium-tritium (DT) plasmas. Near the plasma edge at the low field side the velocity distribution function of charged fusion products is localized in both pitch angle and velocity. The poloidal localization of the eigenmode enhances the ACI growth rates by a factor of square root m in comparison with the previous results without poloidal envelope. The thermal ion cyclotron damping determines that only modes with eigenfrequencies at multiples of the edge cyclotron frequency of the background ions can be easily excited and form an ICE spectrum similar to the experimental observations. Theoretical understanding is given for the results of TFTR DD and DT experiments with valpha 0/vA approximately=1 and JET experiments with valpha 0/vA>1

The spectrum of ion cyclotron emission (ICE) observed in tokamak experiments shows narrow peaks at multiples of the edge cyclotron frequency of background ions. A possible mechanism of ICE based on the fast Alfven Cyclotron Instability (ACI) resonantly excited by high energy charged products (α‐particles or protons) is presented here. Two‐dimensional eigenmode analysis of ACI mode structure and eigenfrequency are obtained in the large tokamak aspect ratio limit. The ACI is excited via wave‐particle resonances in phase space by tapping the fast ion velocity space free energy. The instability growth rates are computed perturbatively from the perturbed fast particle distribution function, which is obtained by integrating the high frequency gyrokinetic equation along the particle orbit. Numerical examples of ACI growth rates are presented for Tokamak Fusion Test Reactor (TFTR) [World Survey of Activities in Controlled Fusion Research [Nuclear Fusion special supplement 1991] (International Atomic Energy Agency...

Hamiltonian systems describing particle motion in a wave with time-dependent (chirped) frequency are studied. The wave is found to form a single-node separatrix ([ital bucket]) moving in the phase space at a rate proportional to that of the frequency change. Particles trapped inside the bucket undergo convection, while untrapped particles colliding with the bucket get a resonant kick, in phase space. In toroidal systems, these effects can result in a large radial convective flux roughly proportional to the size of the bucket and the frequency chirping. Possible applications of this novel mechanism to tokamak plasmas are discussed.

[1] Large-amplitude magnetic pulsations on ion inertial length scales are often observed in space plasmas, but their theoretical explanation is still controversial. We discuss a possible mechanism, different from ideas based on the classical plasma instabilities, for the generation of these pulsations. It is demonstrated that a competition between dispersion and wave steepening processes can lead to the transformation of a large-scale magnetosonic structure into trains of solitons. This kind of longitudinal filamentation is possible for both slow and fast magnetosonic perturbations. Results of numerical simulations are compared with Cluster spacecraft measurements and show that the steepening filamentation mechanism can explain the emergence of a certain class of solitary waves observed in space plasmas.

Characteristics of the high-power reconnection heating were measured for the first time directly by two-dimensional measurements of ion and electron temperatures. While electrons are heated mainly inside the current sheet by the Ohmic heating power, ions are heated mainly by fast shock or viscosity damping of the reconnection outflow in the two downstream areas. The magnetic reconnection converts the energy of reconnecting magnetic field B(p) mostly to the ion thermal energy, indicating that the reconnection heating energy is proportional to B(p)(2).

To explore the causes and risk factors of inpatient death for patients with warfare-related limb trauma. A retrospective study involving 339 patients with warfare-related limb trauma who were admitted to our hospital from 1998 to 2002 was conducted. Autopsy was performed for 15 cases who died in order to investigate the cause of death. Furthermore, based on the clinical features of warfare-related trauma patients, 11 factors were selected for further analysis: X1: causes of trauma, X2: shock after injury, X3: time from injury to hospital admission, X4: injured sites, X5: combined trauma (including head, thorax, abdomen, and vascular injury), X6: number of surgical procedures, X7: foreign body remaining, X8: fracture, X9: amputation, X10: duration of tourniquet homeostasis, X11: infection. All variables were available in all cases, and all parameters were quantified and fed into a computer. Multivariate statistical analysis was performed with a logistic regression model to elucidate the risk factors influencing death. Fifteen of the 339 inpatient cases died (4.4%). The causes were primarily acute renal failure (ARF) (seven cases, 46.7%), pulmonary embolism (PE) (three cases, 20.0%), multiple organ system failure (MOSF) (two cases, 13.3%), and gas gangrene (three cases, 20.0%). There was one case of gas gangrene with concomitant ARF, and one of gas gangrene with MOSF. The primary risk factors influencing death included shock, amputation, and complicating infection (P

Recent research on TFTR has emphasized optimization of performance in deuterium plasmas, transport studies and studies of energetic ion and fusion product physics in preparation for the D-T experiments that will commence in July of 1993. TFTR has achieved full hardware design parameters, and the best TFTR discharges in deuterium are projected to QDT of 0.3 to 0.5.The physics phenomena that will be studied during the D-T phase will include: tritium particle confinement and fueling, ICRF heating with tritium, species scaling with tritium, collective alpha-particle instabilities, alpha heating of the plasma and helium ash buildup. It is important for the fusion program that these physics issues be addressed to identify regimes of benign alpha behavior, and to develop techniques to actively stabilize or control instabilities driver by collective alpha effects.

This paper introduces to you some methods to radlige the digital radiogzaphy, and there respectiae princiales and featuus.

Recent observations of new fast ion beam driven instabilities in MHz frequency range in National Spherical Torus experiments (NSTX) are suggested to be Compressional Alfvin Eigenmodes (CAEs). A new theory of CAEs applicable to low aspect ratio toroidal plasmas is developed based on the ballooning representation for the poloidal dependence of the perturbed quantities. In agreement with observations, the analytical theory predicts that CAEs are discrete modes with frequencies correlated with the characteristic Alfvin velocity of the plasma. Plasma equilibrium structure is essential to determine accurately the dispersion of CAEs. The mode structure is localized in both the minor radius and the poloidal directions on the low magnetic field side.

The sawtooth period in JET ELM-free H-Mode plasmas is increasing with Neutral Beam Injection (NBI) power. For injected power PNBI 12MW no large sawtooth crash is observed during the ELM-free period. However, as the edge stability is improved and external kink modes and ELMs are delayed, a possible sawtooth crash at a high plasma beta becomes a concern. In JET DT experiments, delaying sawteeth was found to be crucial in the quest for high fusion power. Fast particles are known to provide stabilizing effect on sawteeth, however, sawtooth stabilization by NBI ions is not clearly understood, since NBI ions are usually not ''fast'' enough to stabilize the m/n = 1/1 internal kink mode which is believed to cause the crash. In order to understand the observed sawteeth stabilization in tokamak experiments with NBI heating, the internal kink m/n = 1/1 mode stability of JET plasmas was modeled using the NOVA-K code, which is also benchmarked with the nonperturbative version of NOVA and the M3D code. Comparison of m/n = 1/1 mode stabilization by NBI ions in JET and TFTR and application of the nonlinear stabilization criteria is given.

During the past two years, deuterium-tritium (D-T) plasmas in the Tokamak Fusion Test Reactor (TFTR) have been used to study fusion power production,isotope effects associated with tritium fueling, and alpha-particle physics in several operational regimes. The peak fusion power has been increased to 10.7 MW in the supershot mode through the use of increased plasma current and toroidal magnetic field and extensive lithium wall conditioning. The high-internal-inductance (high -li) regime in TFTR has been extended in plasma current and has achieved 8.7 MW of fusion power. Studies of the effects of tritium on confinement have now been carried out in ohmic, NBI- and ICRF-heated L-mode and reversed-shear plasmas. In general, there is an enhancement in confinement time in D-T plasmas which is most pronounced in supershot and high-li discharges, weaker in L-mode plasmas with NBI and ICRF heating and smaller still in ohmic plasmas. In reversed-shear discharges with sufficient deuterium-NBI heating power, internal transport barriers have been observed to form, leading to enhanced confinement. Large decreases in the ion heat conductivity and particle transport are inferred within the transport barrier.It appears that higher heating power is required to trigger the formation of a transport barrier with D-T NBI and the isotope effect on energy confinement is nearly absent in these enhanced reverse-shear plasmas. Many alpha-particle physics issues have been studied in the various operating regimes including confinement of the alpha particles, their redistribution by sawteeth, and their loss due to MHD instabilities with low toroidal mode numbers. In weak-shear plasmas, alpha-particle destabilization of a toroidal Alfven eigenmode has been observed.

A nonlinear kinetic-MHD model for studying low frequency multiscale phenomena has been developed by taking advantage of the single fluid MHD model`s simplicity and by properly accounting for core ion finite Larmor radius (FLR) effects and major kinetic effects of energetic particles. The kinetic-MHD model treats the low energy core plasma by a generalized MHD description and energetic particles kinetically; the coupling between the dynamics of these two components of plasmas is through the plasma pressure. The generalized MHD model for core plasma includes core ion FLR effects which provide a finite parallel electric field, a modified perpendicular velocity from the {bold E} {times} {bold B} drift, and a gyroviscosity tensor, which are neglected in the usual single fluid MHD description. The perturbed core plasma electron and ion densities, velocity and pressure tensor are determined from both the low frequency and high frequency gyro-kinetic equations. From the quasineutrality condition, we obtain the parallel electric field, which arises from the ion gryoradius effects. The kinetic-MHD model is closed by generalized pressure laws for the core and energetic plasmas. When ion gryoradius radius is on the order of the plasma equilibrium scale length, the Vlasov description may be adopted to describe the energetic particle dynamics. From the kinetic-MHD model we derive eigenmode equations for low frequency waves such as shear/kinetic Alfven waves (KAW) and ballooning-mirror modes. The kinetic-MHD model has been successfully applied to study ballooning-mirror instabilities to understand the field-aligned structure and instability threshold of compressional Pc 5 waves in the ring current region. It is also demonstrated that the ion FLR effects in the dispersion relation of KAWs are properly retained; note that these are not properly included in the popularly employed two-fluid equations because the gryoviscosity contribution is usually not retained. 18 refs., 2 figs.

Two-dimensional solutions of compressional Alfven eigenmodes (CAE) are studied in the cold plasma approximation. For finite inverse aspect ratio tokamak plasmas the two-dimensional eigenmode envelope is localized at the low magnetic field side with the radial and poloidal localization on the order of a/{radical}m and a/(fourth root of m), respectively, where m is the dominant poloidal mode number. Charged fusion product driven Alfven Cyclotron Instability (ACI) of the compressional Alfven eigenmodes provides the explanation for the ion cyclotron emission (ICE) spectrum observed in tokamak experiments. The ACI is excited by fast charged fusion products via Doppler shifted cyclotron wave-particle resonances. The ion cyclotron and electron Landau dampings and fast particle instability drive are calculated perturbatively for deuterium-deuterium (DD) and deuterium-tritium (DT) plasmas. Near the plasma edge at the low field side the velocity distribution function of charged fusion products is localized in both pitch angle and velocity. The poloidal localization of the eigenmode enhances the ACI growth rates by a factor of {radical}m in comparison with the previous results without poloidal envelope. The thermal ion cyclotron damping determines that only modes with eigenfrequencies at multiples of the edge cyclotron frequency of the background ions can be easily excited and form an ICE spectrum similar to the experimental observations. Theoretical understanding is given for the results of TFTR DD and DT experiments with {upsilon}{sub {alpha}0}/{upsilon}{sub A} 1.

The toroidicity-induced Alfvin eigenmodes (TAE) with radially extended structure are found to be stable in the Tokamak Fusion Test Reactor Deuterium-Tritium plasmas. A core localized TAE mode is shown to exist near the center of the plasma at small magnetic shear and finite plasma beta, which can be destabilized by energetic alpha particles on TFTR. With additional instability drive from fast minority ions powered by ICRH, both the global and the core localized TAE modes can be readily destabilized.

Recently, the TS-3 and TS-4 tokamak merging experiments revealed significant plasma heating during magnetic reconnection. A key question is how and where ions and electrons are heated during magnetic reconnection. Two-dimensional measurements of ion and electron temperatures and plasma flow made clear that electrons are heated inside the current sheet mainly by the Ohmic heating and ions are heated in the downstream areas mainly by the reconnection outflows. The outflow kinetic energy is thermalized by the fast shock formation and viscous damping. The magnetic reconnection converts the reconnecting magnetic field energy mostly to the ion thermal energy in the outflow region whose size is much larger than the current sheet size for electron heating. The ion heating energy is proportional to the square of the reconnection magnetic field component . This scaling of reconnection heating indicates the significant ion heating effect of magnetic reconnection, which leads to a new high-field reconnection heating experiment for fusion plasmas.

The electric field in the reconnecting current sheet of the 2003 October 29 X10 flare is estimated to be a few kV m–1 in this study, based on the rate of change in the photospheric magnetic flux in the newly brightened areas of Transition Region and Coronal Explorer (TRACE) UV ribbons. For comparison, the motion speed of Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) hard X-ray (HXR) footpoints and the photospheric magnetic field strength are also used for the electric field calculation. This X10 flare event is selected due to its distinct two-phase HXR kernel motion, two arcade systems with different magnetic shear, and the high cadence and complete coverage of the TRACE 1600 A Michelson Doppler Imager (MDI) magnetogram and RHESSI HXR observations. We pay particular attention to the electric field characteristics in different flare phases, as well as the temporal correlation with the HXR emission and its power-law spectral index and the photospheric magnetic field strength. We found that in the early impulsive phase, the reconnection electric field peaks just before the HXR emission peaks and the energy spectrum hardens. The result is consistent with the scenario that more particles are accelerated to higher energies by larger reconnection electric fields and then precipitate into the lower chromosphere to produce stronger HXR emissions. Such a particle acceleration mechanism plays its most significant role in the impulsive phase of this flare. In addition, our results provide evidence that the highly sheared magnetic field lines are mapped to the magnetic reconnection diffusion region to produce a large reconnection electric field.

Fertility declines in China are evident, however disagreement occurs over what the determinants are. This study examines the impact of changes in marriage patterns and marital fertility patterns in China during 1953-81. Coale's indirect standardization procedure is used, and results show wide fluctuations during 1949-64, a slight decline during 1965-68, a sharp decline during the 1970s, and a slight increase in the early 1980s. The decline in 1967 marks the beginning of the Cultural Revolution. The decline during the 1970s marks the "later, longer, fewer" campaign. Marital fertility and overall fertility follow the same curve, which suggests that marital fertility has a greater impact on fertility than nuptiality. 74.4% of total fertility during 1953-81 is accounted for by changes in marital fertility. 25.6% of total fertility is attributed to the decline in marital fertility. The proportion ever married inhibits potential fertility more during 1961-81 than during 1953-60 (30% vs. 20%). Changes in the overall fertility rate are more dramatic than changes in the index of marital fertility. For example, the decline was from 0.46 to 0.29 in general fertility compared to a decline from 0.53 to 0.41 for marital fertility. It is reasoned that marital fertility declined due to family limitation. Data are obtained from the 1982 One-Per-Thousand Sample Fertility Survey on the retrospective histories of childbearing and marriage among women aged 15-67 years. A conclusion is made that research should focus on examining the underlying determinants of marital fertility. After the 1970s a variety of factors influenced fertility including family planning policy during the 1970s and in 1979, institutional developments, and social changes in education, employment, women's status, and health services. Behavioral and psychological factors also have an impact on fertility decisions.

Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC), consisting of six Low Earth Orbit (LEO) Global Position System (GPS) receivers, on board the Formosat Satellite 3 (FORMOSAT-3) is providing dense observations of density, refractivity, temperature and water vapor profiles of the neutral atmosphere since middle of July 2006. Special radiosonde (Väisälä) campaign was conducted at Gadanki (13.48°N, 79.18°E), a tropical site in India, during July 2006 to March 2007 to validate these meteorological parameters. Co-located Nd: YAG Rayleigh lidar was also operated during the overpass of COSMIC and is utilized to validate the temperatures in the height range of 30 to 40 km. Atotal of 142 overpasses occurred during the above mentioned period within 300 km distance from Gadanki out of which 41 overpasses occurred within a time difference of ±4 hours of radiosonde launch. In addition, 18 overpasses occurred within the time difference of ±4 hours of lidar operation. A detailed comparison has been made with all these overpasses for the refractivity, temperature and water vapor obtained from COSMIC. The water vapor comparison has shown generally a good agreement with a mean difference of 5 - 10% below 6 - 7 km. Although there is a colder bias between COSMIC and radiosonde, a very good comparison in temperature is also found between 10 and 27 km with a mean difference of less than 1 K (RMS difference is only 0.64 K). There exists a large difference in temperature of about 8 K between 30 and 40 km (between COSMIC and lidar). Possible reasons for these large differences are given. There was one event that occurred just over Gadanki for which a detailed comparison has been made with special emphasis on water vapor retrievals. Sensitivity test is also done on the fractional difference in N for the event that occurred on 24 July 2006 between COSMIC (1D-var) and radiosonde and found that pressure plays a key role than temperature in determining the refractivity.

Accurate, consistent, and stable observations from different satellite missions are crucial for climate change detection. In this study, we use Global Positioning System (GPS) Radio Occultation (RO) data from the early phase of the FORMOSAT-3/Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) mission, which was successfully launched on 15 April 2006, to inter-calibrate Temperature in the Lower Stratosphere (TLS) taken from Advanced Microwave Sounding Unit (AMSU) microwave measurements from different satellites for potential improvements of stratospheric temperature trend analysis. Because of the limited number of COSMIC soundings in the early phase of the mission, these results are considered preliminary. In this study, we use COSMIC RO data to simulate microwave brightness temperatures for comparison with AMSU Ch9 measurements (e.g., TLS) on board NOAA15, 16, and 18. Excellent correlation was found between synthetic COSMIC brightness temperatures (Tbs) and Tbs from NOAA15, NOAA16, and NOAA18, respectively. However, systematic differences on the order of 0.7 to 2 K were found between COSMIC and AMSU observations over Antarctica. Our results demonstrate that synthetic COSMIC Tbs are very useful in identifying inter-satellite offsets among AMSU measurements from different satellites. To demonstrate the long-term stability of GPS RO data, we compare COSMIC dry temperature profiles to those from collocated CHAMP profiles, where CHAMP was launched in 2001. The fact that the CHAMPand COSMIC dry temperature difference between 500 and 10 hPa ranges from -0.35 K (at 10 hPa) to 0.25 K (at 30 hPa) and their mean difference is about -0.034 K demonstrates the long-term stability of GPS RO signals. In order to demonstrate the potential usage of the GPS RO calibrated AMSU Tbs to inter-calibrate other overlapping AMSU Tbs, we examine the uncertainty of the calibration coefficients derived from AMSU-GPS RO pairs. We found the difference between COSMIC calibrated AMSU Tbs and those from CHAMP to be in the range of __0.07 K with a 0.1 K standard deviation. This demonstrates the robustness of the calibration coefficients found from AMSU-GPS RO pairs and shows the potential to use the calibrated AMSU Tbs to calibrate other overlapping AMSU Tbs where no coincident GPS RO data are available.

Based on a two-fluid plasma model where the electron mass and the displacement current are neglected, the eigenmode properties such as the frequency and the compressibility are studied. It is found that these properties strongly depend on the two-fluid parameter kli, where k is the wave number of a mode and li is the ion skin depth. Especially it is found that as the two-fluid parameter kli increases beyond unity, the Alfven wave, which is an incompressible mode in the magnetohydrodynamics (MHD) limit, becomes compressible and its phase velocity approaches to the acoustic speed. The slow magnetosonic wave, which is compressible in the MHD limit, becomes incompressible as kli increases. Implications of these results are also discussed.

A second order splitting scheme is developed to integrate the three dimensional Vlasov equation for a plasma in a magnetic field. The integration of the Vlasov equation is divided into a series of intermediate steps and Fourier interpolation and the ASD method with a third order Taylor expansion are used to integrate the fractional equations. Numerical experiments related to cyclotron waves in 2 and 2/sup 1///sub 2/ D are demonstrated with high accuracy and efficiency. The computer storage requirements are modest; for example, a typical 2D nonlinear electron plasma simulation requires only 4000 ''particles.''

Both one‐ and two‐dimensional particle simulation models have been used to study the nonlinear behavior of the electrostatic hydrogen cyclotron instabilities driven by the electron current along the magnetic field. It is found that the instability saturates as a result of electron velocity space diffusion along the magnetic field. The cyclotron waves remain highly coherent in the nonlinear stage. When the electron drift speed is comparable to the thermal speed, substantial ion heating as well as particle cross‐field diffusion comparable to Bohm diffusion has been observed. Comparisons of the simulation results with the theoretical predictions and the observations in both laboratory and space plasmas are discussed.