Direction Of Ambient Magnetic Field Research Articles

Parametric coupling of low frequency whistler to Alfven wave in a plasma

The parametric decay of a large amplitude electromagnetic wave in the ion cyclotron range of frequency into a compressional Alfven wave and an electromagnetic sideband wave in a magnetized plasma is investigated. The pump wave propagates in the direction of ambient magnetic field whereas the decay waves propagate at oblique angles. When the pump wave is left circularly polarized the decay is not permitted kinematically as the momentum of pump photon always exceeds the sum of momenta of the decay wave photons. For the right circularly polarized whistler mode pump the decay is permitted with sideband nearly right circularly polarized. The density perturbation associated with the Alfven wave couples with the pump driven oscillatory velocities of ions and electrons to produce a current driving the sideband. The sideband and the pump exert pondermotive force on ions and electrons that drive the Alfven wave. The frequency and growth rate of the Alfven wave increase with the normalized pump frequency. The threshold power density, determined by the collisional damping rates of the decay waves is rather modest.

Titan's induced magnetosphere under non-ideal upstream conditions: 3D multi-species hybrid simulations

A 3D, multi-species hybrid model (kinetic ions, fluid electrons) has been applied to the interaction between Saturn's largest satellite Titan and the plasma in the giant planet's outer magnetosphere. In contrast to the idealized picture deduced from Voyager 1 data, recent observations made by the Cassini magnetometer instrument suggest that the ambient magnetic field is not directed perpendicular to Titan's orbital plane. Therefore, our purpose is to investigate systematically how Titan's induced magnetosphere is affected by a tilt of the upstream magnetic field. In the first part of our study, the structure of Titan's induced magnetosphere is analyzed as a function of the angle between the ambient magnetic field B ̲ 0 and the bulk velocity u ̲ 0 of the corotating plasma flow. Our simulations show that introducing a flow-aligned magnetic field component goes along with an asymmetrization of Titan's magnetotail, in addition to the asymmetry that already arises from the large gyroradii of the ion species involved in the interaction. In the vicinity of Titan, the field lines become strongly twisted, permitting the wakeside magnetic lobe structure to even penetrate into the satellite's geometric plasma shadow. However, despite the increased complexity of Titan's magnetic environment, the overall characteristics of the pick-up tail remain practically the same as in the case of “ideal” magnetic field orientation ( B ̲ 0 ⊥ u ̲ 0 ) . In the second part of our study, we investigate in real-time the transition that Titan's plasma interaction undergoes during a change of the ambient magnetic field direction. In contrast to earlier analyses of Titan's plasma environment under non-stationary upstream conditions, the tilt of the ambient magnetic field is again taken into account. While in the case of B ̲ 0 being perpendicular to u ̲ 0 , the reconfiguration of Titan's induced magnetosphere is mainly governed by reconnection, our simulations suggest that when a flow-aligned field component is included, convection of the field lines around the obstacle's ionosphere plays the key role for the reconfiguration process.

Filamentation of laser in a magnetized plasma under relativistic and ponderomotive nonlinearities

Filamentation of a circularly polarized short pulse laser propagating along the direction of ambient magnetic field in plasma is studied. The nonlinearity arises through the combined effect of relativistic mass variation and ponderomotive force induced electron cavitation. The growth rate is maximum Γmax for an optimum filament size, qopt−1. Γmax and qopt increases with plasma density and ambient magnetic field.

Reply to comment by R. M. Thorne and R. B. Horne on Khazanov et al. [2002] and Khazanov et al. [2006

[1] It is well-known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC wave spatialtemporal-spectral distributions and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping and wave propagation/refraction/reflection, along with wave tunneling and mode conversion and particles. Such a self-consistent RC-EMIC wave model is being progressively developed by Khazanov et al. [2002, 2003a, 2006, 2007]. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density with explicit inclusion of the ray tracing equations. [2] The theoretical formalism for RC ions and RB electrons is well established and is based on gyroaveraged and bounce-averaged kinetic equations that have been developed over the years and systemized in the book by Khazanov [1979]. The application of this formalism to RC ions was continued by Khazanov and Kozyra at the University of Michigan during 1991–1994 and formed a large part of the Ph.D. dissertation work of Fok [1993] and of Jordanova [1995]. Khazanov et al. also applied this formalism to the study of ionosphere-plasmasphere transport of suprathermal electrons [Khazanov et al., 1992, 1994], and global photo [Khazanov et al., 1996; Khazanov and Liemohn, 2002] and plasma sheet [Khazanov et al., 1998] electron transport. This formalism was also generalized to study relativistic electron transport [Khazanov et al., 1999, 2000], as well as different aspects of RC and RB electron formation using various magnetospheric electric and magnetic field topologies [Khazanov et al., 2003b, 2004b, 2004c]. All these above-mentioned studies are the heritage of our RC-EMIC wave model that was presented by Khazanov et al. [2006]. [3] Thorne and Horne [2007, hereinafter referred to as TH2007] call the Khazanov et al. [2002, 2006] results into question in their Comment. The points in contention can be summarized as follows. TH2007 claim that (1) important damping of waves by thermal heavy ions is treated incorrectly in our model, and Landau damping during resonant interaction with thermal electrons is not included; (2) EMIC wave damping due to RC O is not included in our simulation of the 2–7 May 1998 storm; (3) nonlinear processes limiting EMIC wave amplitude are not included in our model; (4) growth of the background electromagnetic fluctuations to a physically significant amplitude must ‘‘occur during a single transit of the unstable region’’ with subsequent damping in the vicinity of the bi-ion latitude, and consequently the bounce-averagedwave kinetic equation employed in the code is not valid. Our reply will address each of these points as well as other criticisms mentioned in the Comment. [4] TH2007 is focused on two of our papers that are separated by 4 years. Significant progress in the selfconsistent treatment of the RC-EMIC wave system has been achieved during those years. The paper by Khazanov et al. [2006] presents the latest version of our model, and in this Reply we refer mostly to this paper.

Potential methods for nonlinear slow magnetoacoustic waves in pressure anisotropic high-β plasmas

We perform a parametric study of highly oblique solitary and periodic nonlinear stationary slow magnetoacoustic waves in the model of McKenzie and Doyle, and Stasiewicz, taking plasma pressure anisotropy into account. The model was proposed for the interpretation of linear magnetic holes, where there is almost no variation in direction of the ambient magnetic field direction. In particular, we focus on magnetic structures in high-β (ratio of kinetic to magnetic pressures) plasmas. We find that gas pressure anisotropy is crucial for the existence of solitary structures in this model for the parameter regime considered. Pressure anisotropy leads to the existence of field enhancing bright solitary structures and field depleting dark solitary structures. To explain the parametric range of the existence of solitary and periodic wave solutions of the model, a pseudo-(Sagdeev) potential is used. We obtain an analytic form for this potential in the case of low Alfvén mach waves. We find that the potential method accurately predicts the parametric range of the existence of solitary waves as calculated by direct numerical simulations.

Linear and nonlinear dust-hydromagnetic waves

A self-consistent and complete theory for linear, weakly nonlinear, and highly nonlinear dust-hydromagnetic waves in a magnetized dust-ion plasma has been presented. Oblique propagation as well as two typical special cases, propagation along and across the ambient magnetic field direction, are considered. The linear dispersion properties are analyzed by using the normal mode analysis. The weakly nonlinear properties are studied by employing the reductive perturbation method, which is valid for small but finite amplitude waves. The highly nonlinear properties are investigated by means of a pseudopotential approach, which is valid for arbitrary amplitude waves. The implications of our results to some space and astrophysical dusty plasmas are briefly mentioned.

Gradient-drift instability in space dusty plasmas

Possible effects of negatively charged dust on the gradient-drift instability in the lower ionosphere are investigated. The presence of localized regions of charged dust with short-scale variations in the dust charge density may lead to the generation of small-scale electron density gradients which can enhance the growth of the instability. In addition, negatively charged dust can influence the instability through its effect on equilibrium charge neutrality, which affects the phase speed of the waves. Using linear kinetic theory, critical electron drifts are estimated. It is found that, if there are perpendicular (to the ambient magnetic field direction) electron density gradients with scale size ∼ several tens of meters in the daytime ionosphere at altitudes ∼90 km , owing to the presence of vertical variations of the dust charge density, waves with wavelengths ∼ a few meters may be driven unstable by electron drifts on the order of the ion thermal speed. Possible applications to dusty plasmas in the low E-region, such as polar mesosphere summer echo regions, are discussed.

Laboratory depositional and compaction-caused inclination errors carried by haematite and their implications in identifying inclination error of natural remanence in red beds

SUMMARY Undetected depositional and/or compaction-caused inclination errors may result in an overestimation of tectonically caused latitudinal offset. Hodych & Buchan used a single-component isothermal remanent magnetization (IRM) acquired in a DC field at a 45 ◦ angle to the bedding to test for inclination errors in Silurian red beds. This approach was criticized by Stamatakos et al. We produced synthetic depositional and compaction-caused inclination errors to test Hodych and Buchan’s approach. Red bed samples collected from the Eocene Suweiyi Formation, Tarim Basin (northwest China) were disaggregated using an ultrasonic cleaner and the sediments were mixed with distilled water to make a sediment slurry. The sediment slurry spontaneously separated into silt-dominated and clay-sized parts, so deposition and compaction experiments were conducted with three categories of slurries: coarse grained, the fine grained and a 1:1 volume ratio mixture of the coarse- and fine-grained slurries. During compaction clay-sized sediments experienced 17 ◦ ‐19 ◦ inclination shallowing at 58 ◦ magnetic field inclination, while coarser sediments showed little laboratory compaction-caused inclination error. Acquisition of IRM, coercivity spectra and unblocking temperature spectra reveal that the magnetic carrier for the fine-grained sample is dominated by pigmentary haematite. A deposition experiment was also conducted with the coarse-grained sediments, which showed a range of depositional inclination error, ∼0 ◦ ‐30 ◦ , carried by larger high unblocking temperature/coercivity particles. The intermediate unblocking temperature (or coercivity) component carried presumably by pigmentary haematite is an accurate record of the ambient magnetic field direction. Our data indicate that the single-component IRM method of Hodych & Buchan can be used to identify and correct for the compaction-caused inclination error of the fine-grained samples, while it failed to detect any depositional inclination error in the coarse-grained samples. Therefore, to better quantify the inclination error in red beds, it is suggested that multiple IRMs be measured in various directions.

Anisotropy of magnetosonic turbulence in the solar wind between 0.1 and 0.4 AU

The anisotropy of the density fluctuations in the solar wind is studied with the assumption that density fluctuations are connected to magnetosonic turbulence. It is shown that the anisotropy of density fluctuations does not coincide with that of the turbulence energy in the case of the fast magnetosonic waves while they are equal for the slow magnetosonic waves. The radial evolution of the two‐dimensional (2‐D) anisotropy ratio in the interplanetary scintillation (IPS) pattern plane due to the change of the ambient magnetic field direction is investigated. In the case of the Parker's spiral magnetic field the radial dependence of the 2‐D anisotropy ratio is shown to be considerably stronger for the fast magnetosonic waves than for the slow magnetosonic waves. The comparison between theoretical estimations and the results of the Kashima high‐frequency IPS measurements shows that the geometric effects are not sufficient to account for the observed radial dependence of the axial ratio, and that the angular distribution of turbulent energy evolves in the region of heliocentric distances between 0.1 and 0.4 AU toward the state enriched by the magnetosonic waves propagating at smaller angles relative to the ambient magnetic field. The nonlinear wave‐wave interactions seem to be responsible for this evolution of the density turbulence spatial power spectrum.

Orientation Behavior of Garden Warblers (Sylvia borin) Under Monochromatic Light of Various Wavelengths

A little more than 30 years ago, a study revealed that migratory European Robins (Erithacus rubecula) could use the earth’s magnetic field for directional orientation (Merkel and Wiltschko 1965, W. Wiltschko 1968). Today, magnetic compass orientation has been demonstrated in more than 15 other species of migratory birds and in homing pigeons, and it seems to be a rather widespread mechanism among birds (R. Wiltschko and Wiltschko 1995). Yet, it is still unclear how birds perceive the geomagnetic field and obtain directional information. One hypothesis under investigation is that magnetoreception occurs via light-dependent processes parallel to the processes of vision in the avian eye (Leask 1977, 1978; Schulten and Windemuth 1986). This hypothesis assumes that incident light elevates certain macromolecules into an excited state, where they may be transferred to an excited triplet state and where further reactions are determined by the direction of the ambient magnetic field. This would mean that light is essential for magnetoreception. Results from early experiments with homing pigeons are in agreement with this prediction. Inexperienced young pigeons derive their home direction from information obtained with their magnetic compass during the outward journey (R. Wiltschko and Wiltschko 1978); pigeons transported to the release site in total darkness respond like birds transported without meaningful magnetic information, which indicates that light is indeed necessary for magnetic compass orientation (W. Wiltschko and Wiltschko 1981). Similar experiments with migratory birds in total darkness proved impossible. Directional tendencies of migrants can be recorded only when the birds show a certain amount of activity, but Zugunruhe (i.e. migratory activity) is suppressed by darkness (Gwinner 1974). However, another approach allows testing the hypothesis of light-dependent magnetoreception in migrants. Leask (1977) suggested that exposing birds to monochromatic light at various wavelengths might modify the excitation transfer probability to the excited triplet state, allowing one

AMPTE observations of mirror mode waves in the magnetosheath: Wavevector determination

A unique method has been developed to completely determine the wavevector of a mirror mode wave using data from two closely spaced (separation less than wavelength/2) spacecraft. The method is based on the fact that mirror mode waves are linearly polarized and have zero frequency in the plasma rest frame. The method has been tested using Active Magnetospheric Particle Tracer Explorers United Kingdom Subsatellite (AMPTE UKS) and Ion Release Module (AMPTE IRM) high‐resolution magnetic field data from an interval of mirror mode waves observed in the middle magnetosheath on September 21, 1984. The results are also compared to those obtained using other methods of wavevector determination. The wavevectors estimated during the event are highly oblique to the ambient magnetic field direction as is expected from mirror wave theory. The application of the wavevector determination technique to further studies, such as studying the effect of finite electron temperature on mirror wave characteristics, is discussed.

Feasibility studies of TFMMIP and TFEM surveying with Sub-Audio Magnetics

The Sub-Audio Magnetics (SAM) technique measures parameters related to electrical and magnetic characteristics of the sub-surface. A galvanic and/or electromagnetic source is used to excite current flow within the sub-surface. Measurements are taken with a rapid sampling, total field magnetometer while continuously traversing within the survey area.By selecting the transmitted waveform appropriately, magnetic signals related to separate physical phenomena become distinguishable and can be observed within the measured magnetic field variations. Signal processing techniques are then used to obtain the following measurements:• Total Magnetic Intensity (TMI)• Total Field Magnetometric Resistivity (TFMMR)• Total Field Magnetometric Induced Polarisation (TFMMIP)• Total Field Electromagnetics (TFEM)The measurements indicated are used to map variations in sub-surface resistivity, changeability and magnetic properties. While software and hardware limitations have previously restricted measurements to the TMI and TFMMR parameters, ongoing development of acquisition and processing software now allows all four parameters to be measured, potentially from a single survey.Application of the SAM method to the Flying Doctor Lead/Zinc/Silver deposit showed that the mineralisation produced significant anomalous responses within the TFMMR. TFMMIP and TFEM parameters. Surface TFMMR and TFMMIP data are transformed to equivalent Magnetometric Resistivity (MMR) and Magnetometric Induced Polarisation (MIP) data, removing the data’s dependence on the direction of the Earth's ambient magnetic field direction.A survey over an unexploded ordnance (UXO) test site showed that Total Magnetic Intensity (TMI) and transient electromagnetic (TFEM) data may be simultaneously acquired and used to locate these types of targets.

Dating of thaw depths in permafrost terrain by the palaeomagnetic method: experimental acquisition of a freezing remanent magnetization

SUMMARY The acquisition of a freezing remanent magnetization (FRM) has been studied in controlled magnetic and thermal environments by successive freezing and thawing (- 18 to + 20 C) of samples of natural sediments from a frost polygon near Ny Alesund, Spitsbergen. Successive freeze-thaw cycles cause a significant decrease in the intensity of the initially induced shock remanent magnetization (SRM), associated with directional trends towards the ambient magnetic field direction during the freezing phase. A slow increase in intensity commences after seven to 10 freeze-thaw cycles. The acquisition of a FRM in samples carrying an isothermal remanent magnetization shows a significantly smaller reduction in intensity and only minor directional variations. This result indicates that only a fraction of the magnetic grains in a natural sediment contributes to the natural remanent magnetization. Insignificant changes in lengths and directions of the principal susceptibility ellipsoid axes also indicate that magnetic fabric and remanent magnetization are carried by partly different populations of magnetic grains. The acquisition of a FRM in nature has yet to be explored. If such a process is confirmed, however, it has the potential for obtaining age estimates of ancient thaw depths and for providing insights into material transport processes in frost polygons.

Anisotropy of inertial range turbulence in the polar heliosphere

A variance analysis of high frequency, inertial range fluctuations in the polar magnetic field as recorded by the Ulysses spacecraft indicates that they are largely transverse to the ambient magnetic field direction and highly anisotropic. Despite large changes in the mean field direction caused by the presence of large amplitude Alfvén waves, alignment of minimum variance vectors of 5 minute intervals of linearly detrended data with the mean field direction was good, with around 75% of minimum variance vectors lying within 26° of the mean field direction during a typical 5 day interval. Such fluctuations transverse to the mean field have anisotropies—the ratio of power transverse to the field to that parallel—of around 30. We find a small tendency for the field‐transverse fluctuations to become more isotropic with distance. Intervals whose minimum variance directions are not field‐aligned appear to be indicative of a significantly different type of fluctuations, with higher total variances and lower anisotropy.

One‐ and two‐dimensional simulations of whistler mode waves in an anisotropic plasma

We present results from self‐consistent, one‐ and two‐dimensional, electromagnetic simulations of the electron whistler mode instability relevant to the near‐Earth nightside plasma sheet region during geomagnetically disturbed times. Specifically, we study the evolution of energetic, anisotropic (T⊥ > T∥) electron distributions that are injected into the nightside ring current region at geomagnetically disturbed times, the resulting growth of electron whistler mode waves, and subsequent electron pitch angle diffusion via electron whistler wave‐particle interactions. Growth of whistler mode waves from an initial pitch angle anisotropy (T⊥ ≈ 4 T∥) is studied in the strong pitch angle diffusion regime (defined as having scattering times much shorter than a typical electron bounce time in the near Earth's dipolar field). The quasi‐linear and subsequent nonlinear evolution of waves and the corresponding migration of electrons in velocity space is followed over timescales such that ion motion may be neglected. Our simulations contain wave frequencies and growth rates that are a significant fraction of the electron gyrofrequency (ω ∼ 0.5ωce, γ ∼ 0.1ωce being typical) and the simultaneous evolution of waves propagating both parallel and nonparallel to the ambient magnetic field direction. Effects due to these are not usually accounted for in applications of quasi‐linear theory to the problem of electron whistler wave‐particle interactions, so that our self‐consistent simulations of the electron whistler instability provide an important insight into the applicability of quasi‐linear theory to the velocity space diffusion of electrons due to electron whistler wave‐particle interactions. We examine the dependence of whistler mode wave growth rates, nonlinear wave mode saturation, and pitch angle diffusion rates on the β value of the hot electron species which contains the resonant population, and we compare the differences between results of one‐ and two‐dimensional simulations. In general, we have found significantly larger average growth rates in a one‐dimensional than in a two‐dimensional geometry, by up to a factor of ∼2–3, with the difference between such growth rates becoming larger as β increases. As a result, we find pitch angle diffusion rates are significantly larger (by up to a factor of ∼10) in a one‐dimensional geometry, and pitch angle diffusion rates increase as β increases. During the early wave growth period of the instability, pitch angle diffusion rates Dα have been found to scale to magnetic wave energy Bw², approximately Dα ∝ Bw². We also show that in the self‐consistently evolved system (containing several wave modes), the pitch angle diffusion is still consistent with a usual quasi‐linear approach in which resonant particles are taken to diffuse along surfaces of constant wave frame energy.

SSC-associated magnetic variations at the geosynchronous altitude

SSC events at the geosynchronous altitude have been studied using data obtained from the geosynchronous satellites SMS/GOES, as well as data obtained on the ground for the period from 1976 to 1980. Two characteristic local time dependencies are found for the SSC associated phenomena at the geosynchronous altitude. In the compressional component (parallel to the ambient magnetic field direction), the SSC associated signature is very large in the noon-side, while it becomes smaller with increasing distance from the noon-side and is very small or zero in the midnight-side. In the transverse component (east-west direction), the direction of the initial movement of Psc changes drastically across the noon and the midnight. The direction is eastward in the morning-side, while it is westward in the evening-side. These observational results will be examined quantitatively in the present study.

Stimulated plasma waves in the ionosphere

The results of 15 years of plasma resonance observations from rocket‐ and satellite‐borne topside sounders are summarized. The major resonances are observed at the electron plasma frequency ƒN, the electron cyclotron frequency ƒH, the upper hybrid frequency ƒT = (ƒ2N+ƒ2H)1/2, the harmonics 2ƒT and nƒH with n > 1, and two series of resonances that appear between nƒH∶ the ƒQn resonances observed above ƒT (at the maximum frequency of the Bernstein modes) and the ƒDn resonances observed below ƒT (called the diffuse resonances). Most of the resonances can be interpreted in terms of the reception of longitudinal plasma waves stimulated by the sounder pulse. In some cases these waves, which travel with low group velocity (of the order of the electron thermal velocity or less) are received after being reflected in the nearby medium (within a distance of several kilometers). The reflections are due to the extreme sensitivity of the dispersion curves near the resonant frequencies to small changes in electron density (for the ƒN and ƒT resonances) or to small changes in magnetic field strength (for the lower‐order nƒH resonances). In other cases (ƒQn resonances and the higher‐order nƒH resonances) the signal reception is due to the matching of a component of the wave group velocity to the satellite velocity rather than to a wave reflection process. The ƒDn resonances involve a sounder‐stimulated electron temperature anisotropy leading to the Harris instability of the Bernstein modes and a nonlinear coupling between these wave‐modes. Since the interpretation of all of the resonances depends on warm plasma theory, the observations can be used to obtain the electron temperature T⊥ and T∥ (corresponding to electron motions perpendicular and parallel to the ambient magnetic field direction, respectively) as well as the electron density and the magnetic field intensity. These measurements pertain to a large volume (hundreds of meters to kilometers) around the antenna and thus are not seriously affected by spacecraft/plasma interactions. The results of the investigations of artificially stimulated plasma waves by sounder pulses have been applied to the interpretation of naturally occurring wave phenomena such as the (n+1/2)ƒH magnetospheric VLF emissions, the terrestrial kilometric radiation, and the Jovian decametric radiation. Among the major unexplained plasma resonance phenomena are the resonances observed at ƒH and 2ƒT, and the numerous ion effects associated with the electron plasma resonances. The advent of the Space Shuttle with subsatellites will enable active‐controlled experiments to be conducted with highly flexible radio‐frequency instrumentation in order to investigate problems of interest to many geophysical and astrophysical phenomena such as wave mode coupling and the evolution of nonlinear and plasma wave instability processes.

Distributions of tangential discontinuity in the corotating solar wind structure

Distributions of the tangential discontinuity (TD) in the solar wind sector structure are investigated on the basis of the magnetic field data and the ion plasma parameters from the Explorer 33 satellite from 23 January to 23 March 1968. The TD is separated from the observed field fluctuations by calculating the direction of the plasma flow and also the direction of the minimum field fluctuation with respect to the ambient magnetic field direction. It is found that the TD is formed by the thin layered field-aligned currents (the current sheets), and that the TD is predominantly built up in the leading edge of the solar wind where the compression of the plasma and the magnetic field takes place. It is suggested that the current sheets might be locally generated in the leading edge in the turbulent conditions arising from collisions between the fast- and the slow-stream of the solar sector structure.

Nonlinear mode-mode coupling of Alfven waves in the interstellar medium

A set of differential equations is set up to describe the temporal and spatial evolution of transverse and longitudinal waves under mode-mode coupling in a relativistic plasma embedded in an ambient magnetic field. The plasma consists of immobile protons, thermal electrons and cosmic ray protons. The cosmic rays are assumed to be streaming along the ambient magnetic field direction with a bulk velocity larger than the Alfven velocity. An Alfven wave couples with another transverse and one longitudinal wave. The temporal mode-mode coupling effects on the nonlinear behaviour of the Alfven wave (which is unstable using linear theory in the absence of mode-mode coupling) have been examined. Under certain conditions, it is found that the linear instability of the Alfven wave is 'quenched'. Upon inserting numerical parameters appropriate to the cosmic ray gas in the galactic disk it is shown that when the initial energy of perturbation is 10-2 of the ambient field energy, the rate of quenching is the same order as the linear e-folding time (10 approximately 102 yr when the streaming velocity of the cosmic ray is approximately 108 cm/sec).

Short-life mode of electrostatic electroncyclotron harmonic waves

Dispersion curves of electrostatic electron cyclotron harmonic waves with a phase exp {i(k. r – ωt)}, where ω and k are the angular frequency and wave vector, respectively, are calculated numerically for a case of real ω and complex k that is pertinent for a case of pulsed short dipole excitation of plasma waves. Oblique propagation with respect to the ambient magnetic field direction is considered. There are positive κi and negative κi modes, where k is the imaginary part of the wave number κ = ∣κ∣ in the solutions. The energy propagates in opposite directions in the two modes, and the waves are always subjected to thermal damping. The positive κi mode usually indicates a large κi value (i.e. a large attentuation rate); and it is here called the ‘short-life’ mode.