Stochastic Heating of Ions by Linear Polarized Alfven Waves

The ion motion in the presence of linear polarized Affvdn waves is studied. For a linearly polarized wave, nonlinear resonances can occur when the amplitude of Alfven wave is large enough. Under certain conditions, these resonances can overlap and thus make the ion motion chaotic. In this process, the plasma can be heated without the limitation of cyclotron resonant condition. Taking into account of a spectrum of waves, the stochastic condition can decrease largely. In addition, the preferential heating can be found in the perpendicular direction.     

Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

The nonlinear dust‐ion‐acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns‐Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z‐axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov–Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg–de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non‐thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non‐thermal electrons, pair‐ions, and dust particles can exist.     

Ion surface cyclotron waves at plasma-metal interfaces

The dispersion properties of slow electromagnetic surface waves propagating across a constant external magnetic field and along a plane plasma-metal interface at harmonics of the ion cyclotron frequency are studied. The motion of the plasma particles is described by a Vlasov-Boltzmann kinetic equation. The effects of the plasma size, the dielectric permittivity of the transition region between the plasma and metal, and the magnitude of the constant external magnetic field on the dispersion characteristics of ion surface cyclotron waves are studied. Zh. Tekh. Fiz. 69, 83–89 (October 1999)     

Nonlinear amplitude osçillations of absolutely unstable electrostatic ion cyclotron waves in an ion beam-plasma system

We have observed experimentally the amplitude oscillations of absolutely unstable electrostatic ion cyclotron waves in an ion beam-plasma system due to nonlinear interaction between the beam ions and electrostatic ion cyclotron waves.     

Effect of beam-plasma interaction on ion transport through a cyclotron injector

The influence of collective effects associated with transverse plasma oscillations excited by a beam of negative ions on the neutralization of the space charge due to fast ions is studied. Conditions for the dynamic deneutralization of an unstable ion beam are refined. Analytic expressions for the plasma ion density distribution and for the stationary electric field in a partially neutralized beam are obtained. The equation of motion of a beam in the self-electric field and in an external magnetic field is used to determine the effect of secondary charged particles on the transport of negative ions through the injector of a cyclotron.     

On the low-threshold parametric mechanism of the anomalous power absorption in electron cyclotron resonance heating experiments in toroidal devices

The experimental conditions that facilitate the excitation of parametric decay instabilities upon the electron cyclotron resonance heating of a plasma at the second harmonic extraordinary wave in tokamaks and stellarators and, as a result, make anomalous absorption of microwave power possible have been analyzed. It has been shown that, in the case of a nonmonotonic radial profile of the plasma density, when the beam of electron cyclotron waves passes near the equatorial plane of a toroidal device, the parametric excitation of electron Bernstein waves, as well as the generation of ion Bernstein waves propagating from the parametric decay region to the nearest ion cyclotron harmonic, where they efficiently interact with ions, is possible. The proposed theoretical model can explain the anomalous generation of accelerated ions observed upon electron cyclotron heating in small and moderate toroidal facilities.     

Nonlinear propagation of ultra-low-frequency electromagnetic modes in a magnetized dusty plasma

A theoretical investigation has been made of nonlinear propagation of ultra-low-frequency electromagnetic waves in a magnetized two fluid (negatively charged dust and positively charged ion fluids) dusty plasma. These are modified Alfvén waves for small value of and are modified magnetosonic waves for large , where is the angle between the directions of the external magnetic field and the wave propagation. A nonlinear evolution equation for the wave magnetic field, which is known as Korteweg de Vries (K-dV) equation and which admits a stationary solitary wave solution, is derived by the reductive perturbation method. The effects of external magnetic field and dust characteristics on the amplitude and the width of these solitary structures are examined. The implications of these results to some space and astrophysical plasma systems, especially to planetary ring-systems, are briefly mentioned. Received 8 July 1999 and Received in final form 11 October 1999     

Features of the dynamics of particles and fields at cyclotron resonances

Some features of the dynamics of particles and fields at cyclotron resonances have been discussed with the focus on chaotic dynamical regimes. It has been shown that the known criterion of the transition of the regular dynamics of particles to chaotic dynamics at cyclotron resonances sometimes describes this transition incorrectly. The reason for such a feature of the criterion has been revealed. The anomalous sensitivity of the dynamics of particles to external fluctuations at autoresonance has been analyzed. A theory of excitation of electromagnetic waves by a beam of phased oscillators under the conditions of isolated nonlinear cyclotron resonance has been developed. It has been shown that the chaotic dynamical regime is due to the periodic change in the structure of the phase portrait of particles in the wave field. It has been shown that higher moments can play a more significant role than lower moments in almost all chaotic dynamical regimes at cyclotron resonances. In this case, the known kinetic diffusion equations should be generalized with the inclusion of these higher moments.     

Stochastic heating of plasma at electron cyclotron resonance

It is shown theoretically and experimentally that stochastic heating of plasma electrons is highly efficient. Calculations have shown that over the course of 100 periods of an external microwave field the kinetic energy of the particles reaches values of around 1.0 MeV and the average energy reaches values of the order of 0.3 MeV in the field of two oppositely propagating characteristic (eigen) waves of a cylindrical waveguide, with amplitudes 24 kV/cm in a 1 kG stationary magnetic field. Stochastic instability develops as a result of overlapping of non-linear cyclotron resonances. The experimental results agree with the theory: When these waves are excited by a 0.9 MW external source, above a threshold of 0.45 MW one obtains x rays with a photon energy corresponding to a maximum electron energy of the order of 1 MeV over about 800 periods of the external microwave field. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 806–811 (10 June 1999)     

Sheath motion in a capacitively coupled radio frequency discharge

The sheath motion in a capacitively coupled RF discharge is highly nonlinear. The voltage waveform on a cylindrical probe placed in the sheath region is measured as a function of position and time. A circuit model of the probe-discharge system relates the observed probe voltage to the sheath motion. The equations derived from this circuit model are solved numerically with varying nonlinear sheath motions; the resulting waveforms are compared with the experimental observations to determine the actual sheath motion. The time-varying plasma potential is also determined, indirectly, from the comparison. The authors also report observation of oscillations related to the plasma frequency, whose peak harmonic component can be calculated from a single plasma model. These oscillations can be a useful plasma diagnostic for determining plasma density. The presence of these high-frequency oscillations may significantly enhance the rate of stochastic heating of electrons     

Nonlinear Electrostatic Ion‐Acoustic Waves in the Solar Atmosphere

Basing on recent solar models, the excitation of ion‐acoustic turbulence in the weakly‐collisional, fully and partially‐ionized regions of the solar atmosphere is investigated. Within the frame of hydrodynamics, conditions are found under which the heating of the plasma by ion‐acoustic type waves is more effective than the Joule heating. Taking into account wave and Joule heating effects, a nonlinear differential equation is derived, which describes the evolution of nonlinear ion‐acoustic waves in the collisional plasma.     

Parametric Instability of Surface Waves on the Second Harmonic of Electron Cyclotron Frequency in a Plasma Layer

The parametric instability of surface waves on the second harmonic of electron cyclotron frequency (SWCF) in a plasma filled dielectric wave guide is examined in a kinetic approximation. The studied surface waves are extraordinary polarized modes and propagate across the external steady magnetic field. The amplitude of the electrical pump wave is assumed to be small. Simple expressions for increments of the parametric instability of the SWCF are calculated. The otained results can be used in controlled fusion researches in order to avoid undesirable regimes of plasma periphery heating in that fusion devices which use the resonance electron cyclotron heating method.     

Nonlinear resonance of plasma waves in the thermal irregularities of ionospheric plasma

We study the effect of striction plasma density disturbances on the generation intensity of longitudional cold and plasma oscillations due to polarization of the magnetic field-aligned ionospheric plasma irregularities with δN_o<0 by a powerful radio wave. It is assumed that the plasma density level inside the irregularity intersects the upper-hybrid resonance level, in the vicinity of which the cold oscillations excited directly by a powerful radio wave are transformed to shorter-wave plasma oscillations. We consider the short plasma wave limit to reduce the problem to a system of two coupled equations for the cold wave induction and plasma wave electric field. The first equation is supplemented by a local source equal to the integral of the plasma wave electric field in the resonance region. The second equation involves the cold wave induction at the resonance point and describes the electric field of interacting waves in the resonance vicinity. We use simplifications connected with the small absorption of plasma waves propagating inside the irregularity and weak radiation of these waves outside the irregularity. These conditions correspond to the generation of eigenmodes of plasma oscillations trapped in the irregularity. We have obtained a resonance-type nonlinear equation for the electric field intensity (or energy flux) of eigenmode plasma waves with allowance for striction disturbances of the plasma density profile in the resonance region. It is shown that the striction expulsion of plasma is responsible for the occurrence of coefficients describing the change in the intensity of excitation and radiation of plasma waves at the irregularity boundary. Such an expulsion leads to variations of the efficient generation band of plasma eigenmodes with the total phase increment of the wave in the irregularity. It also leads to a change in the phase shift of the plasma wave reflected from the resonance. These coefficients and the nonlinear phase shift are expressed in terms of real wave functions of the nonlinear Airy equation which describes the electric field of the excited waves in the resonance vicinity when the dissipation is absent. Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 270–297, March, 1998.     

Ion heating with beating electrostatic waves

The nonlinear interaction of a magnetized ion with two beating electrostatic waves (BEW) whose frequencies differ by a cyclotron harmonic can lead, under some conditions [Phys. Rev. E 69, 046402 (2004)], to vigorous acceleration for an ion with arbitrarily low initial velocity. When applied to an ensemble of ions, this mechanism promises enhanced heating over single electrostatic wave (SEW) heating for comparable wave energy densities. The extension of single ion acceleration to heating (SEWH and BEWH) of an ensemble of initially thermalized ions was carried out to compare the processes. Using a numerical solution of the Vlasov equation as a guideline, an analytical expression for the heating level was derived with Lie transforms and was used to show BEWH's superiority over all parameter space.     

Parametric Mechanism of Anomalous Microwave Power Absorption in Experiments on Electron Cyclotron Heating in Toroidal Magnetic Traps

The nonlinear stage of the parametric decay instability of an extraordinary wave is analyzed in the presence of a nonmonotonic density profile. The decay excites an electron Bernstein wave, which is localized in the vicinity of a local density maximum, and an ion Bernstein wave, which leaves a nonlinear interaction region and is absorbed by ions in the vicinity of the harmonics of the ion cyclotron frequency. The main mechanism of instability saturation is considered to be a cascade of decays of a primary daughter electron Bernstein wave, which leads to the excitation of localized secondary electron Bernstein waves and ion cyclotron (Bernstein) waves. The localization of electron Bernstein waves causes a significant decrease in the secondary- decay excitation threshold, which is thought to provide saturation of the primary instability at the lowest level. The saturation of the primary parametric decay instability of a pump wave and the anomalous absorption of the pump power are analytically estimated. A numerical simulation is performed using the parameters that are typical of the experiments on the electron cyclotron resonance heating of plasma at the second resonance harmonic in TCV tokamak.     

Effect of magnetic field on the thermal nonlinearity of surface waves in plasma-metal structures

A study is made into the effect of the nonlinear mechanism of plasma electron heating on the dispersion properties of potential surface waves propagating along the interface between a metal and finite-pressure magnetoactive plasma. An external steady magnetic field is directed normally to the interface. Different mechanisms of electron energy loss are treated in a weak heating approximation. The energy balance equation is used to determine the spatial distribution of the plasma electron temperature under conditions of nonlocal heating. The effect of the plasma parameters on the nonlinear shift of the wavenumber and on the spatial damping factor of surface waves is investigated. The results obtained are valid for both semiconductor and gaseous plasmas.     

The Darwin Direct Implicit Particle-in-Cell (DADIPIC) Method for Simulation of Low Frequency Plasma Phenomena

We describe a new algorithm for simulating low frequency, kinetic phenomena in plasmas. Darwin direct implicit particle-in-cell (DADIPIC), as its name implies, is a combination of the Darwin and direct implicit methods. Through the Darwin method the hyperbolic Maxwell's equations are reformulated into a set of elliptic equations. Propagating light waves do not exist in the formulation so the Courant constraint on the time step is eliminated. The direct implicit method is applied only to the electrostatic field with the result that electrostatic plasma oscillations do not have to be resolved for stability. With the elimination of these constraints spatial and temporal discretization can be much larger than that possible with explicit, electrodynamic PIC. We discuss the algorithms for pushing the particles and solving for the fields in 2D cartesian geometry. We also detail boundary conditions for conductors and dielectrics. Finally, we present two test cases, electron cyclotron waves and collisionless heating in inductively coupled plasmas. For these test cases DADIPIC shows agreement with analytic kinetic theory and good energy conservation characteristics.     

Low-threshold absolute parametric decay instabilities in experiments on electron cyclotron resonance heating in tokamaks

We have analyzed experimental conditions for the excitation of absolute parametric decay instabilities accompanying the electron cyclotron resonance heating (ECRH) of plasma at the second harmonic of resonance in tokamaks. It has been shown that, in the case of a nonmonotonic radial profile of the plasma density, when a heating beam passes near the equatorial plane of a tokamak, the parametric excitation of resonances of ion Bernstein waves accompanied by the generation of the backscattered microwave radiation can occur. The threshold of absolute instability thus developed is determined by the dissipation of an ion Bernstein wave and can be exceeded in current experiments on the ECRH of a plasma in tokamaks.     

Solitary electromagnetic pulses detected with super-Alfvénic flows in Earth's geomagnetic tail

Solitary nonlinear (deltaB/B>1) electromagnetic pulses have been detected in Earth's geomagnetic tail accompanying plasmas flowing at super-Alfvénic speeds. The pulses in the current sheet had durations of approximately 5 s, were left-hand circularly polarized, and had phase speeds of approximately the Alfvén speed in the plasma frame. These pulses were associated with a field-aligned current J(parallel) and observed in low density (approximately 0.3 cm(-3)), high temperature (T(e) approximately T(i) approximately 3x10(7) K), and beta approximately 10 plasma that included electron and ion beams streaming along B. The wave activity was enhanced from below the ion cyclotron frequency to electron cyclotron and upper hybrid frequencies. The detailed properties suggest the pulses are nonlinearly steepened ion cyclotron or Alfvén waves.     

Experimental observations of mode-converted ion cyclotron waves in a tokamak plasma by phase contrast imaging

The process of mode conversion, whereby an externally launched electromagnetic wave converts into a shorter wavelength mode(s) in a thermal plasma near a resonance in the index of refraction, is particularly important in a multi-ion species plasma near the ion cyclotron frequency. Using phase contrast imaging techniques (PCI), mode-converted electromagnetic ion cyclotron waves have been detected for the first time in the Alcator C-Mod tokamak near the H-3He ion-ion hybrid resonance region during high power rf heating experiments. The results agree with theoretical predictions.