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NASA NTRS1984

Strong turbulence of plasma waves

This paper reviews recent work related to modulational instability and wave envelope self-focusing in dynamical and statistical systems. After introductory remarks pertinent to nonlinear optics realizations of these effects, the author summarizes the status of the subject in plasma physics, where it has come to be called 'strong Langmuir turbulence'. The paper treats the historical development of pertinent concepts, analytical theory, numerical simulations, laboratory experiments, and spacecraft observations. The role of self-similar self-focusing Langmuir envelope wave packets is emphasized, both in the Zakharov equation model for the wave dynamics and in a statistical theory based on this dynamical model.

Goldman, M. V.↗

NASA NTRS1994

Nonlinear evolution of a large-amplitude circularly polarized Alfven wave: High beta

The nonlinear dynamics following saturation of the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfven wave is investigated via direct numerical simulation in the case of high plasma beta and no wave dispersion. The magnetohydrodynamic (MHD) code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Turbulent cascades develop after saturation of two coupled oblique three-wave parametric instabilities; one of which is an oblique filamentationlike instability reported earlier. Remnants of the parametric processes, as well as of the original Alfven pump wave, persist during late nonlinear times. Nearly incompressible MHD features such as spectral anisotropies appear as well.

Ghosh, S.↗

NASA NTRS1974

Computational study of nonlinear plasma waves

A low-noise plasma simulation model is developed and applied to a series of linear and nonlinear problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. It is demonstrated that use of the hybrid simulation model allows economical studies to be carried out in both the linear and nonlinear regimes with better quantitative results, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The characteristics of the hybrid simulation model itself are first investigated, and it is shown to be capable of verifying the theoretical linear dispersion relation at wave energy levels as low as .000001 of the plasma thermal energy. Having established the validity of the hybrid simulation model, it is then used to study the nonlinear dynamics of monochromatic wave, sideband instability due to trapped particles, and satellite growth.

Matsuda, Y.↗

NASA NTRS1971

Theory of the unmagnetized plasma.

The Vlasov mathematical model of a plasma, which has come to be thought more useful than any other in describing the dynamical behavior of the majority of plasmas of interest, is first examined. Macroscopic variables and moment equations; linear electrostatics solutions; plasma oscillations, ion acoustic waves, and linear instabilities are treated, as well as external fields, 'test' charges, and nonlinear Vlasov phenomena. Plasmas are statistically described, and attention is given to the kinetic theory of the stable, uniform plasma and the Balescu-Lenard equation; two-time ensemble averages and fluctuation spectra in stable plasmas; the kinetic theory of the unstable plasma; and ensembles of Vlasov plasmas. Some illustrative experiments are described. Four appendixes deal with the electrostatic approximation and transverse waves; solution of the linearized Vlasov equation in a magnetic field; estimates of correlation functions from thermal equilibrium; and equivalence of spatially uniform BBGKY and Klimontovich correlations.

Montgomery, D. C.↗

NASA NTRS1987

Evolution of the axial electron cyclotron maser instability, with applications to solar microwave spikes

The nonlinear evolution of cyclotron radiation from streaming and gyrating electrons in an external magnetic field is analyzed. The nonlinear dynamics of both the fields and the particles are treated fully relativistically and self-consistently. The model includes a background plasma and electrostatic effects. The analytical and numerical results show that a substantial portion of the beam particle energy can be converted to electromagnetic wave energy at frequencies far above the electron cyclotron frequency. In general, the excited radiation can propagate parallel to the magnetic field and, hence, escape gyrothermal absorption at higher cyclotron harmonics. The high-frequency Doppler-shifted cyclotron instability can have saturation efficiencies far higher than those associated with well-known instabilities of the electron cyclotron maser type. Although the analysis is general, the possibility of using this model to explain the intense radio emission observed from the sun is explored in detail.

Vlahos, Loukas↗

NASA NTRS2011

Consequences of the Ion Cyclotron Instability in the Inner Magnetospheric Plasma

The inner magnetospheric plasma is a very unique composition of different plasma particles and waves. Among these plasma particles and waves are Ring Current (RC) particles and Electromagnetic Ion Cyclotron (EMIC) waves. The RC is the source of free energy for the EMIC wave excitation provided by a temperature anisotropy of RC ions, which develops naturally during inward E x B convection from the plasma sheet. The cold plasmasphere, which is under the strong influence of the magnetospheric electric field, strongly mediates the RC-EMIC waves-coupling process, and ultimately becomes part of the particle and energy interplay, generated by the ion cyclotron instability of the inner magnetosphere. On the other hand, there is a strong influence of the RC on the inner magnetospheric electric and magnetic field configurations and these configurations, in turn, are important to RC dynamics. Therefore, one of the biggest needs for inner magnetospheric plasma physics research is the continued progression toward a coupled, interconnected system, with the inclusion of nonlinear feedback mechanisms between the plasma populations, the electric and magnetic fields, and plasma waves.

Khazanov, George V.↗

NASA NTRS2000

Theory of Type 3 and Type 2 Solar Radio Emissions

The main features of some current theories of type III and type II bursts are outlined. Among the most common solar radio bursts, type III bursts are produced at frequencies of 10 kHz to a few GHz when electron beams are ejected from solar active regions, entering the corona and solar wind at typical speeds of 0.1c. These beams provide energy to generate Langmuir waves via a streaming instability. In the current stochastic-growth theory, Langmuir waves grow in clumps associated with random low-frequency density fluctuations, leading to the observed spiky waves. Nonlinear wave-wave interactions then lead to secondary emission of observable radio waves near the fundamental and harmonic of the plasma frequency. Subsequent scattering processes modify the dynamic radio spectra, while back-reaction of Langmuir waves on the beam causes it to fluctuate about a state of marginal stability. Theories based on these ideas can account for the observed properties of type III bursts, including the in situ waves and the dynamic spectra of the radiation. Type 11 bursts are associated with shock waves propagating through the corona and interplanetary space and radiating from roughly 30 kHz to 1 GHz. Their basic emission mechanisms are believed to be similar to those of type III events and radiation from Earth's foreshock. However, several sub-classes of type II bursts may exist with different source regions and detailed characteristics. Theoretical models for type II bursts are briefly reviewed, focusing on a model with emission from a foreshock region upstream of the shock for which observational evidence has just been reported.

Robinson, P. A.↗

NASA NTRS2017

Critical Fluctuations in Beam-Plasma Systems and Solar Type III Radio Bursts

The type III radio bursts are the most intense radio emissions from the sun. In Figure 1, we present a typical type III burst observed by the STEREO spacecraft. Ginzburg and Zheleznyakov (1958) were the first to suggest that Langmuir waves excited by the solar flare accelerated electrons are the source of these bursts. The in situ detection of electron beams and Langmuir waves in association with type III bursts together with tracking of type III burst sources in the interplanetary medium confirmed this plasma hypothesis. However, the dynamics of type III electron beams and their interaction with the ambient plasma through the excited Langmuir waves is an unsolved problem. In order that the electron beams don't lose their energy by resonantly interacting with Langmuir waves, various nonlinear processes, such as the induced scattering of Langmuir waves off the background ions in weak turbulence regime and oscillating two-stream instability in strong turbulence regime were invoked. However, the observed electron density fluctuations do not allow Langmuir waves to grow to very high intensities as pointed out by several authors. As far as the conversion of Langmuir wave energy into electromagnetic energy is concerned, there is no consensus either for the fundamental or for the second harmonic emission. In this paper, we address these issues in terms of critical fluctuations near the boundary of the beam-plasma instability which is analogous to the anomalously growing fluctuations near the phase transition points called critical points. We show that this phenomenon can account for the survival of electron beams over large distances as well as the intensities of Langmuir waves excited during this phase transition regime are sufficient to explain the peak intensities of the fundamental as well as harmonic emissions

Fluctuations↗

NASA NTRS1994

Magnetotail dynamics under isobaric constraints

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Birn, Joachim↗

NASA NTRS1994

Electrotastic Solitary Waves (ESW) in the magnetotail: BEN wave forms observed by GEOTAIL

Wave forms of BEN (Broadband Electrostatic Noise) in the geomagnetic tail were first detected by the Wave Form Capture reciever on the GEOTAIL spacecraft. The results show that most of the BEN in the plasma sheet boundary layer (PSBL) are not continuous broadband noise but are composed of a series of solitary pulses having a special form which we term 'Electrostatic Solitary Waves (ESW)'. A nonlinear BGK potential model is proposed as the generation mechanism for the ESW based upon a simple particle simulation which considers the highly nonlinear evolution of the electron beam instability. The wave forms produced by this simulation are very similar to those observed by GEOTAIL and suggest that the nonlinear dynamics of the electron beam play an essential role in the generation of ESW.

Matsumoto, H.↗

NASA NTRS1994

Nonlinear evolution of a large-amplitude circularly polarized Alfven wave: Low beta

The nature of turbulent cascades arising from the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfven wave is investigated via direct numerical simulation for the case of low plasma Beta and no wave dispersion. The magnetohydrodynamic code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Anisotropic turbulent cascades, similar to those found in early incompressible two-dimensional simulations, occur after nonlinear saturation of the parallel propagating decay instability. The turbulent spectrum can be divided into three regimes: the lowest wave numbers are dominated by lower sideband remnants of the parametric process, intermediate wave numbers display nearly incompressible dynamics, and the highest wave numbers are dominated by acoustic turbulence.

Ghosh, S.↗

NASA NTRS1995

Effects of highly intermittent magnetic fields and plasma flows on solar wind dynamics

Filamentary magnetic fields and intermittent mass flows with highly variant physical parameters as observed in coronal holes provide, from a theoretical point of view, natural conditions for strongly nonlinear dynamics. The presence of sheared mass flows along fine scale magnetic structures results in strong nonlinear instability, most important of which is the explosive instability. We specify the physical conditions for several different manifestations of the onset of explosive instability and its further evolution: (1) fully developed explosive instability - explosive release of the energy; (2) shock formation - stabilization of instability by small scale spatial inhomogeneities leads to formation of subsequent shocks having a number of peculiarities that is determined by the interplay of thermal and viscous losses (for example, in predominance of thermal losses the isothermal jump occurs); and (3) solitary waves - stabilization of explosive instability by nonlinear dispersion effect leads to formation of a 'gas' of solitons which are later either damped away with characteristic time and energy input or evolve to solitons with explosively growing amplitudes. Each scenario is completely determined by the physical parameters of the medium, thus producing a quite uneven distribution of energy in a coronal hole and, respectively, an uneven outward propagation of the energy flux.

Ryutova, M.↗

NASA NTRS2004

Particle Acceleration, Magnetic Field Generation, and Emission in Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (m) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient parallel magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. New simulations with an ambient perpendicular magnetic field show the strong interaction between the relativistic jet and the magnetic fields. The magnetic fields are piled up by the jet and the jet electrons are bent, which creates currents and displacement currents. At the nonlinear stage, the magnetic fields are reversed by the current and the reconnection may take place. Due to these dynamics the jet and ambient electron are strongly accelerated in both parallel and perpendicular directions.

Nishikawa, Ken-IchiI.↗

NASA NTRS2005

Particle Acceleration, Magnetic Field Generation in Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient parallel magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. New simulations with an ambient perpendicular magnetic field show the strong interaction between the relativistic jet and the magnetic fields. The magnetic fields are piled up by the jet and the jet electrons are bent, which creates currents and displacement currents. At the nonlinear stage, the magnetic fields are reversed by the current and the reconnection may take place. Due to these dynamics the jet and ambient electron are strongly accelerated in both parallel and perpendicular directions.

Nishikawa, Ken-Ichi↗

NASA NTRS1998

Constraints on Nonlinear and Stochastic Growth Theories for Type 3 Solar Radio Bursts from the Corona to 1 AU

Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for modulational instability or parametric decay to proceed in type III sources at any heliocentric distance: theories for type III bursts based on modulational instability or parametric decay are therefore not viable in general. In contrast, the constraint on SGT can be satisfied and random phase ES decay can proceed at all heliocentric distances under almost all circumstances. (The contrary circumstances involve unusually slow, broad beams moving through unusually hot regions of the Corona.) The analyses presented here strongly justify extending the existing SGT-based model for interplanetary type III bursts (which includes SGT physics, random phase ES decay, and specific electromagnetic emission mechanisms) into a general theory for type III bursts from the corona to beyond 1 AU. This extended theory enjoys strong theoretical support, explains the characteristics of specific interplanetary type III bursts very well, and can account for the detailed dynamic spectra of type III bursts from the lower corona and solar wind.

Cairns, Iver H.↗