Nonlinear Wave-particle Interactions Research Articles

Kinetic modeling of nonlinear electron cyclotron resonance heating

A numerical method is proposed for modeling electron cyclotron resonance heating (ECRH) and current drive in fusion devices with, generally speaking, nonlinear wave–particle interaction. Considered is the case of second harmonic extraordinary wave resonance. The method is applied to model the electron distribution function in a simplified magnetic field geometry. Various combined effects of wave–particle interaction and Coulomb collisions are demonstrated. The model is compared to the bounce-averaged quasilinear Fokker–Planck equation for the case of perpendicular propagation of the wave beam with respect to the magnetic field. In addition, the absorption coefficients computed from these two models are compared to the results of both the linear and the adiabatic model. Significant differences between results are found for present-day ECRH power levels and fusion device parameters.

Global Energy Transfer from Pick-up Ions to Solar Wind Protons

It has been known for years now that pick-up ions (PUIs) are produced by ionization of interstellar neutral atoms in the heliosphere and are then convected outwards with the solar wind flow as a separate suprathermal ion fluid. Only poorly known is the thermal behaviour of these pick-ups while being convected outwards. On the one hand they drive waves since their distribution function is unstable with respect to wave growth, on the other hand they also experience Fermi-2 energizations by nonlinear wave-particle interactions with convected wave turbulences. Here we will show that this complicated network of interwoven processes can quantitatively be balanced when adequate use is made of transport-kinetic results according to which pick-up ions essentially behave isothermally at their convection to large solar distances. We derive the adequate heat source necessary to maintain this pick-up ion isothermy and use the negative of that source to formulate the enthalpy flow conservation for solar wind protons (SWPs). This takes care of a consistent PUI-induced heat source guaranteeing that the net energy balance in the SWP–PUI two-fluid plasma is satisfied. With this PUI-induced heat input to SWPs we not only obtain the well-observed SWP polytropy, but we can also derive an expression for the percentage of intitial pick-up energy fed into the thermal proton energy. By a first-order evaluation of this expression we then can estimate that, dependent on the actual PUI temperature, about 40 to 50% of the initial pick-up energy is globally passed to solar protons within the inner heliosphere.

Nonlinear wave-particle interaction upstream from the Earth's bow shock

Abstract. Well-defined ring-like backstreaming ion distributions have been recently reported from observations made by the 3DP/PESA-High analyzer onboard the WIND spacecraft in the Earth's foreshock at large distances from the bow shock, which suggests a local production mechanism. The maximum phase space density for these distributions remains localized at a nearly constant pitch-angle value for a large number of gyroperiods while the shape of the distribution remains very steady. These distributions are also observed in association with quasi-monochromatic low frequency (~ 50 mHz) waves with substantial amplitude (δB/B>0.2). The analysis of the magnetic field data has shown that the waves are propagating parallel to the background field in the right-hand mode. Parallel ion beams are also often observed in the same region before the observation of both the ring-like distributions and the waves. The waves appear in cyclotron resonance with the ion parallel beams. We investigate first the possibility that the ion beams could provide the free energy source for driving an ion/ion instability responsible for the ULF wave occurrence. For that, we solve the wave dispersion relation with the observed parameters. Second, we show that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered on a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions are in good quantitative agreement with the observations

A New Scenario for Type III Solar Radio Emission

This paper describes a new scenario for type III solar radio emission. While the conventional theories emphasize Langmuir waves propagating along the ambient magnetic —eld, the present model stresses extraordinary-mode Bernstein waves with quasi-perpendicular wave vectors. The present model relies on plasma inhomogeneity and wave re—ection to produce the electromagnetic radiation, in contrast to the conventional theories, which rely on nonlinear wave-wave and wave-particle interactions. The essence of the model is that Bernstein waves with frequencies above the X-mode cutoU frequency are —rst excited. Initially these waves can only propagate toward regions with higher density and magnetic —eld. During this process, quasi-electrostatic Bernstein waves spontaneously convert to electromagnetic waves and rapidly reach the local X-mode cutoU frequency. Subsequently, these waves are re—ected and propagate away from the source region. The escaping radiation is observed as the type III emission. It is pointed out that in general, the observed radiation should possess one band in the dynamic spectrum. However, under certain conditions, the present theory is also capable of explaining the appearance of a pair of bands similar to those commonly called the ii fundamental ˇˇ and ii harmonic ˇˇ components in the liter- ature. The present model resolves some of the inconsistencies between the usual plasma emission hypoth- esis and the observed pair emissions. Subject headings: Sun: radio radiationwaves

Nonlinear cyclotron resonant wave-particle interaction in a nonuniform magnetic field

Quasilinear analysis of wave-particle interactions is presented for plasma flowing in a weakly nonuniform magnetic field configuration. The method presented is based on a scale separation between the length scales of quasilinear relaxation and the magnetic field inhomogeneity, allowing one to obtain large scale solutions for both particle distribution functions and wave spectra, without going into the details of the small scale quasilinear relaxation. The numerical example shows the existence of a secondary instability for an initially stable particle distribution function.

Amplification of extra-ordinary mode wave in the presence of kinetic Alfvén wave turbulence

The amplification mechanism of extra-ordinary mode radiation in the presence of kinetic Alfven wave turbulence driven by an electron beam is studied. It is shown that plasma maser process may be responsible for the amplification of the extra-ordinary mode through up-conversion of turbulent energy via nonlinear wave particle interaction. The relevance of this investigation to space plasmas is discussed.

The HAGIS self-consistent nonlinear wave-particle interaction model

The problem of modelling the self-consistent interaction of an energetic particle ensemble with a wave spectrum specific to magnetically confined plasmas in a torus is discussed. Particle motion in a magnetic field coordinate system, whose surfaces are perturbed by a spectrum of finite amplitude magnetohydrodynamical (MHD) waves, is described using a Hamiltonian formulation. Employing the δƒ method enables the simulation particles to only represent the change in the total particle distribution function and consequently possesses significant computational advantages over standard techniques. Changes to the particle distribution function subsequently affect the wave spectrum through wave-particle interactions. The model is validated using large aspect-ratio asymptotic limits as well as through a comparison with other numerical work. A consideration of the Kinetic Toroidal Alfvén Eigenmode instability driven by fusion born α-particles in a D-T JET plasma illustrates a use of the code and demonstrates nonlinear saturation of the instability, together with the resultant redistribution of particles both in energy and across the plasma cross section.

Pulsations of precipitating energetic electrons: ACTIVE satellite data

We present the patterns of high frequency energetic electron (~ 20 to ~ 300 keV) pulsations in middle latitudes, in subauroral and auroral regions, based on low altitude nearly polar orbiting satellite (Intercosmos-24, project ACTIVE) measurements. Two detectors with different orientations allowed the fluxes within and outside the loss cone to be compared. The trapped electrons do not exhibit the strong pulsations observed within the bounce loss cone. The pitch angle diffusion coefficient changes significantly on time scales comparable to or even shorter than the bounce period of electrons. The same is valid for changes of precipitating electron energy spectra. There are indications that both pitch angle and energy diffusion are in operation. VLF emissions at f < 3.5 kHz with a complicated structure are observed simultaneously with the electron pulsations, but there is no clear correlation between waves and particles. If the characteristics of the electron pulsations and VLF emissions are of a temporal character, they are qualitatively consistent with the models of nonlinear wave particle interactions, or with the concept of a flowing cyclotron maser. However, the pulsations may originate from fine spatial structure. Variability of the precipitation flux implies short time and/or small scale changes of ionization at altitudes down to 70 km.

Whistler mode wave coupling effects on electron dynamics in the near Earth magnetosphere

Nonlinear electron whistler mode wave particle interactions in the near earth magnetosphere suggest several candidate mechanisms for phase space diffusion of electrons into the loss cone to provide a source of auroral precipitating electrons. A unidirectional whistler mode wave propagating parallel to the background magnetic field and interacting with an electron can be shown to produce resonance (trapping of electrons) but the process is not stochastic. Chaos can be introduced by resonance between electrons that mirror many times in the earth's field, and a whistler wavefield. Here, we show that an electron interacting with two oppositely directed, parallel propagating whistler mode waves exhibits stochastic behaviour in addition to resonance. The background field is uniform, so that stochasticity arises solely due to the presence of the wavefield without requiring bounce motion of electrons between mirror points. Stochasticity first appears for wave amplitudes not inconsistent with observations at disturbed times in the near earth magnetosphere and therefore may contribute to pitch angle diffusion.

Mode-Coupling and Nonlinear Landau Damping Effects in Auroral Farley-Buneman Turbulence

The fundamental problem of Farley-Buneman turbulence in the auroral E-region has been discussed and debated extensively in the past two decades. In the present paper we intend to clarify the different steps that the auroral E-region plasma has to undergo before reaching a steady state. The mode-coupling calculation, for Farley-Buneman turbulence, is developed in order to place it in perspective and to estimate its magnitude relative to the anomalous effects which arise through the nonlinear wave-particle interaction. This nonlinear effect, known as nonlinear “Landau damping” is due to the coupling of waves which produces other waves which in turn lose energy to the bulk of the particles by Landau damping. This leads to a decay of the wave energy and consequently a heating of the plasma. An equation governing the evolution of the field spectrum is derived and a physical interpration for each of its terms is provided.

Solar Energetic Particles: Sampling Coronal Abundances

In the large solar energetic particle (SEP) events, coronal mass ejections (CMEs) drive shock waves out through the corona that accelerate elements of the ambient material to MeV energies in a fairly democratic, temperature-independent manner. These events provide the most complete source of information on element abundances in the corona. Relative abundances of 22 elements from H through Zn display the well-known dependence on the first ionization potential (FIP) that distinguishes coronal and photospheric material. For most elements, the main abundance variations depend upon the gyrofrequency, and hence on the charge-to-mass ratio, Q/A, of the ion. Abundance variations in the dominant species, H and He, are not Q/A dependent, presumably because of non-linear wave-particle interactions of H and He during acceleration. Impulsive flares provide a different sample of material that confirms the Ne:Mg:Si and He/C abundances in the corona.

Nonlinear wave-particle interaction and conditions for the applicability of quasilinear theory

In this paper it is shown that the usual conditions of the broad wave packet and overlapping of the trapping intervals of neighboring harmonics are not sufficient for the applicability of the quasilinear theory. The additional important condition is phase randomization in wave-wave interaction. In order for this randomization to occur during a time of wave evolution, i.e. of the inverse growth rate, the mismatch between the frequency of the three-wave nonlinear driver and that of the plasma eigenmode must exceed significantly the growth rate. If this condition is not fulfilled, quasilinear theory is applicable only for wave spectra smoothed by a procedure of averaging over neighboring harmonics inside the trapping interval. Experimental tests done with a warm beam moving through a traveling tube qualitatively support this point of view. At the same time, as it is shown in the paper, nonlinear interaction of waves has the tendency for steepening and modulation of the spectral energy density at a typical k scale of the order of inverse trapping length.

Self-consistent simulation studies of non-linear electron-whistler wave-particle interactions

We present results from self-consistent one-dimensional electromagnetic particle-in-cell simulation studies of non-linear electron-whistler wave-particle interactions. In contrast to analytical treatments that assume a constant amplitude, monochromatic wave field, effects on the wave fields due to an evolving electron distribution are self-consistently represented in our simulations (over a wide frequency range from 0.04 ω ce to ∼100 ω ce). We analyse the phase space trajectories of the entire set of simulation electrons (many thousands) through application of the delay-coordinate technique. This enables us to establish the trapping frequencies of electrons directly from the trajectories. Additional details in the phase space structure and dynamical changes in the properties of the trajectories are also obtained. Results from two different simulations, in which the wave spectrum is eventually dominated by a single whistler wave mode of relatively large amplitude ( B w B 0 ∼0.2–0.3 ), show: (i) the phase space trapping of large numbers of simulation electrons (thousands) with characteristic frequencies around the expected primary trapping resonance frequency estimated from the observed wave amplitude; (ii) more than one strong characteristic frequency component in trapped electron phase space motion; (iii) the dynamics of the trapped process is time dependent, there being an evolutionary shift in time of trapped electron phase space trajectoris towards lower characteristic frequencies. We suspect that (ii) is due to the presence of higher order trapping resonances under the relatively large wave amplitude, whilst (iii) is not explained by time independent analytical treatments that neglect the effects of particles on the wave field.

Some physical considerations for unusual atmospheric lights observed in Norway

In this paper, some unusual atmospheric lights observed in Norway have been explained as the results of nonlinear wave-particle interactions based on turbulent plasma theory and wave-vortex interaction as well as laboratory experiments on rocks. The paper also points out that the atmospheric lights have provided evidence for the vortex structure of fireballs and for the physical mechanism of wave-particle interaction for the formation of plasma ball lightning and solitons.

Nonlinear Landau damping in quark-gluon plasma.

The semiclassical kinetic equations for the quark-gluon plasma (QGP) are discussed by the multiple time-scale method. The mechanism of nonlinear Landau damping owing to non-Abelian and nonlinear wave-particle interactions in QGP is investigated, and the nonlinear Landau damping rate for the longitudinal color eigenwaves in the long-wavelength limit is calculated.

The influence of pick-up ion-induced wave pressures on the dynamics of the mass-loaded solar wind

The solar wind at larger distances is known to be a multicomponent plasma. The different components, solar ions, pick-up ions, and anomalous ions, are without collisional coupling but they are all coupled to the intrinsic wave turbulences by nonlinear wave-particle interactions. Since quite a long time it is not understood why dynamical processes associated with the loading of the primary solar wind by secondary pick-up ions neither lead to a recognizable heating nor to a deceleration of the solar wind at larger distances. While the inefficient heating seems to be explained by the fact that pick-up ions do not assimilate quickly enough to the solar wind distribution function, the unobservable deceleration of the distant solar wind always remained mysterious. Different from all theoretical approaches up to now, here we intend to show that the wave-induced pick-up ion pressure has to be introduced into the equations of motion in an adequate non-polytropic form to correctly describe the multicomponent plasma dynamics. If this is done it becomes clear that the deceleration of the solar wind is considerably reduced or even vanishing.

Nonlinear growth rate of Langmuir waves in the case of a wide spectrum

A nonlinear equation for the evolution of a Langmuir harmonic in a wide spectrum is derived in a consistent manner. This equation substitutes the usual quasilinear growth rate of the weak plasma turbulence theory. The derivation is based on the determination of the resonant particle distribution through the solution of the exact nonlinear equations of motion in a given field, composed of all effectively acting harmonics. The method requires a slow variation of the harmonic amplitudes over the nonlinear characteristic time of resonant interaction, and small enough amplitudes for the averaging method to be applicable. Two nonlinear terms appear in this equation: one is proportional to the particular harmonic considered, the other is a contribution from the whole effective spectrum around this harmonic. From this last term, it follows that a wave with negligible initial amplitude can grow spontaneously through the nonlinear wave–particle interaction.

Wave-particle chaos in the magnetosphere

The nonlinear interaction between the bounced motion of a proton and the kinetic Alfvén wave excited in the magnetosphere is studied. Using the Poincaré surface of section technique, the motion of the proton is traced numerically in phase space. With suitable initial conditions, particle trajectories are calculated for several values of the wave amplitudes under the paraxial approximation of the ambient field. The trajectories show chaotic behavior at some finite amplitude of the wave. The threshold electrostatic field computed for the onset of wave-particle chaos is less than the expected parallel electric field associated with the kinetic Alfvén wave. This suggests that nonlinear wave-particle interactions can lead to chaos and subsequent instability of the bounced motion of the proton.

Simulations of wave–particle interactions in stimulated Raman forward scattering in a magnetized plasma

Stimulated Raman forward scattering in a high-temperature, magnetized plasma is investigated with relativistic Vlasov–Maxwell simulations and with envelope and test particle calculations. The parameters correspond to Raman current drive by free-electron lasers in reactor grade tokamak plasmas. The phase velocity of the Raman excited plasma wave is large, and therefore the Landau damping is initially weak. The electron plasma wave grows to a large amplitude and accelerates electrons to high energies. Simultaneous pump depletion weakens the driving ponderomotive force, which leads to a collapse of the plasma wave if the number of the interacting electrons is large enough. Spatially the wave–particle interaction takes place in a distance of a few wavelengths of the plasma wave. The electron energies can largely exceed the kinetic energy at the phase velocity of the electron plasma wave. Short-wavelength amplitude modulations of the plasma wave appear at high amplitudes. Efficient generation of the nonresonant anti-Stokes wave and of the second Stokes wave are also observed. Analytical growth rates and envelope calculations explain well the early evolution of the Raman process. Later on, nonlinear wave–particle interactions and relativistic effects start to dominate, and the system is not satisfactorily described by simple envelope equations.

Magnetohydrodynamic turbulence dissipation and stochastic proton acceleration in solar flares

The Alfven and fast magnetosonic wave MHD modes can stochastically accelerate protons from super-Alfvenic to ultrarelativistic energies in solar flares. It is the Landau resonance, however, which generates most of the magnetosonic wave energy being dissipated on electron heating rather than on stochastic proton acceleration. Alfven waves are also subject to a nonlinear wave-particle interaction, and nonlinear Landau damping can selectively and efficiently heat the ambient protons to preaccelerate many to super-Alfvenic speeds. A spectrum of Alfven waves can therefore energize protons from low-temperature thermal to ultrarelativistic energies through a combination of linear and nonlinear particle-wave interactions.