Parallel Phase Velocity Research Articles

Fast wave current drive in the ion cyclotron frequency range from the single-particle point of view

The quasilinear model is commonly used to determine the heating rate and the current drive efficiency of the fast wave in the ion cyclotron range of frequency. The validity of this model at these frequencies is a controversial issue [Bécoulet et al., Phys. Plasmas 1, 2908 (1994)]. Here this problem is addressed from the single-particle point of view by deriving an approximated Hamiltonian which accounts also for the inhomogeneity of the confining magnetic field. Realistic values of the wave field are calculated by means of the toroidal full-wave code TORIC for typical scenarios of an ASDEX Upgrade [Gruber et al., Nucl. Fusion 41, 1369 (2001)] experiment, and apply the Chirikov criterion to determine the threshold for the development of the intrinsic stochasticity. These results are verified by numerically integrating the Hamiltonian equations. It is found that, due to the discreteness of the parallel phase velocity spectrum of a fast wave at these frequencies, for the parameters of ASDEX Upgrade the intrinsic stochasticity is marginal, especially close to integer and low-rational values of the safety factor. The failure of intrinsic stochasticity to guarantee the validity of the conventional quasilinear model, however, does not imply the onset of nonlinear saturation in the power absorption and in the driven current, since in all realistic situations Coulomb collisions suffice, by a large margin, to ensure the applicability of the linearized Vlasov equation. Under this condition, power and momentum transfer rates to resonant electrons are identical to those predicted by the quasilinear theory.

Formation of electrostatic solitary waves in space plasmas: Particle simulations with open boundary conditions

We study formation process of electrostatic solitary waves (ESW) observed by recent spacecraft via one‐ and two‐dimensional electrostatic particle simulations with open boundaries. The previous simulations have demonstrated that ESW correspond to Bernstein‐Greene‐Kruskal electron holes formed by electron beam instabilities. However, since the previous simulations were performed in uniform periodic systems, wave‐particle interaction of an electron beam instability was taking place uniformly in the systems. In the present study, we inject a weak electron beam from an open boundary into the background plasma to study spatial and temporal development of a bump‐on‐tail instability from a localized source. In the open system, spatial structures of electron holes vary depending on the distance from the source of the electron beam. In an early phase of the simulation run, electron holes that are initially uniform in the direction perpendicular to the magnetic field become twisted through modulation by oblique electron beam modes. As the electron holes propagate along the magnetic field, they are aligned in the perpendicular direction through coalescence. Spatial structures of electron holes in a distant region from the source become one‐dimensional. In a long‐time evolution of the instability, ion dynamics becomes important in determining spatial structures of electron holes. A lower hybrid mode is excited locally in the region close to the source of the electron beam through coupling with electron holes at the same parallel phase velocity. The lower hybrid mode modulates electron holes excited in later phases, resulting in formation of modulated one‐dimensional potentials. Since the perpendicular electric fields of electron holes are carried by the electron holes at the drift velocity of the electron holes, they can be observed even at a distant place from the source.

Interaction between electrostatic whistlers and electron holes in the auroral region

Electron holes have been discovered in several key regions of the magnetosphere in the past few years. These small‐scale structures seem to play an important role in the global dynamics of the magnetosphere, being most often associated with parallel electron beams and strong ion heating, as shown by the Fast Auroral Snapshot (FAST) spacecraft in the auroral region. Electrostatic whistler waves (EWW) in the VLF frequency range are often associated with these electron holes, suggesting that the generation of whistler waves is related to the holes. We present a model of the interaction between EWW and electron holes. Our analysis is based on the mechanical description of the energy exchange between particles and waves; by the use of the Hamiltonian formalism, action‐angle variables, and canonical perturbation theory, we show that trapped electrons, owing to their periodic motion in the potential structure of the electron hole, enter into a resonance with the wave and can destabilize it at large parallel phase velocity relative to the electron thermal velocity. We derive the growth rate of EWW and compare our model with previous ones. Application to FAST observations shows that this linear instability is able to generate EWW with a normalized growth rate γ/ω varying from a few percents at low frequency (above the lower‐hybrid frequency) up to ∼10% at higher frequency (below the electron plasma frequency).

Dust-lower-hybrid instability in the presence of dust charge fluctuation in a streaming dusty plasma

A detailed theoretical investigation has been made on the properties and excitation of low-frequency and low-phase-velocity electrostatic dust-modes in a magnetized dusty plasma including the streaming of ions, dust charge fluctuation, and the kinetic effects using the Vlasov–Poisson analysis. In the case of high-density dusty plasma, the dust-lower-hybrid (dlh) mode propagating nearly transverse to the external static magnetic field is obtained. On the other hand, for the low-density dusty plasma, the dust-acoustic (DA) wave propagating nearly perpendicular to the external magnetic field has been obtained. It is found that in any case of the above dust-modes, the Landau damping linearly adds to the damping due to dust charge fluctuation. These low-frequency modes can be excited when the ion streaming velocity exceeds the parallel phase velocity of the mode provided the damping due to the dust charge fluctuation is smaller than the Landau damping term of the respective mode. Moreover, it is found that the DA mode is damped rapidly compared to the dlh-mode through charge fluctuation and Landau damping processes.

Kinetic Alfvén wave instability in a dusty plasma

On account of the presence of a dust beam parallel to the direction of the uniform magnetic field, the dust-kinetic Alfvén wave becomes unstable and grows in amplitude when the drift velocity of dust particles exceeds the parallel phase velocity of the wave. The instability growth rate depends on the temperature and density of the plasma ions/electrons, the Alfvén speed, and the dust flow velocity along the magnetic field lines.

Lower-Hybrid Instability with Ion Streaming and Dust-Charge Fluctuation in a Dusty Plasma

Using Vlasov-kinetic model, a dispersion relation of the low-frequency and electrostatic lower-hybrid wave is obtained accounting for the streaming of ions and dust charge fluctuations in a finite temperature and collisionless magnetized dusty plasma. It is found that the damping of this mode is the sum of the Landau damping and the charge fluctuation effect. This lower-hybrid mode can be excited when the ion streaming velocity in the direction of the magnetic field exceeds the parallel phase velocity of the mode and when the magnitude of the Landau damping exceeds the magnitude of the damping due to the dust charge fluctuation. Thus, the lower-hybrid-like mode in a dusty plasma will be damped rapidly by the unmagnetized ions compared to that due to the dust charge fluctuation process.

Cyclotron effects on wave dispersion in pulsar plasmas

Dispersion in an intrinsically relativistic, one-dimensional, electron–positron pair plasma (a pulsar plasma) is treated exactly, generalizing earlier results that applied in the low-frequency limit and that neglected the cyclotron resonance. The general theory involves two additional relativistic plasma dispersion functions, evaluated at the normal and anomalous Doppler resonances. These two functions are associated with the non-gyrotropic and gyrotropic parts of the response respectively. The functions are evaluated for bell-type and Jüttner distributions. Wave dispersion is discussed for a non-gyrotropic pulsar plasma with a highly relativistic Alfvén speed. Emphasis is placed on crossings of the light line, defined in terms of the parallel phase velocity. Subluminal waves exist only for sufficiently small angles of propagation, and are confined to frequencies below about the mean gyrofrequency of the relativistic particles.

Nonlinear Model for Coherent Electric Field Structures in the Magnetosphere

A new pseudo-three-dimensional electron hole in a magnetized plasma is possible when the low-frequency ion dynamics is taken into account. The newly found nonlinear Bernstein-Greene-Kruskal stationary solution, whose parallel phase velocity ranges between almost zero and the electron thermal speed, has the form of a cylinder that is tilted relative to the magnetic field. These structures are interpreted as three-dimensional electron holes coupled with hydrodynamic vortices, and provide a possible theoretical explanation for the POLAR and FAST satellite observations of coherent structures characterized by bipolar spikes of the parallel electric field and large perpendicular ion kinetic energies.

Solar3He‐rich Events and Electron Acceleration in Two Stages

The heating, acceleration, and enhancement of electrons in solar 3He-rich events are studied according to the two-stage acceleration model proposed for the enhancement of 3He and heavy ions. First, electrostatic ion cyclotron instabilities destabilized by electron currents are theoretically and numerically investigated for a plasma consisting mainly of H, 4He, and electrons. Since the parallel phase velocities of the ion cyclotron waves are smaller than around the electron thermal velocity, electrons can have strong Landau resonance (?r-k?ve, ?=0) with the ion cyclotron waves. Here ?r and k? are, respectively, the real frequency and wavenumber parallel to the external magnetic field and ve, ? is the parallel electron velocity. Second, preferential heating of electrons by the ion cyclotron waves is studied through the quasi-linear theory. It is shown that H cyclotron waves are very efficient at heating electrons through the Landau resonance. Third, these preheated electrons can be further accelerated to high energies in the Fermi acceleration process. The abundance ratio (e/H) of high-energy electrons and protons is estimated. The abundance ratio is very high when electrons are sufficiently heated relative to protons and agrees well with observations. Therefore, the present two-stage model explains all aspects of acceleration (3He, electrons, and heavy ions) in flares in a self-consistent way.

Dust-lower-hybrid instability in a dusty plasma with a background of neutral atoms and streaming electrons and ions

The dispersion relation and damping of an electrostatic dust-lower-hybrid mode has been derived using both the fluid and kinetic models of plasmas in magnetized dusty plasmas with a background of neutral atoms and streaming electrons and ions. This mode can be excited in a laboratory experiment when the streaming velocity of electrons and ions in the direction of the magnetic field exceeds the parallel phase velocity.

Enhanced Axial Loss of Electrons from a Tandem Mirror Induced by an Alfvén Ion Cyclotron Wave

Increases in the flux and temperature of end-loss electrons are observed following excitation of an Alfv\'en ion cyclotron (AIC) mode in the GAMMA 10 tandem mirror. Electron loss power carried to an end wall becomes more than twice as large as that without the AIC mode. The increases in the electron flux and temperature are observed only when the parallel phase velocity of the AIC mode matches with the electron thermal velocity, strongly suggesting that the parallel electron acceleration is due to electron Landau damping of the AIC mode.

Coherent nonlinear electromagnetic drift-mode structures

The nonlinear dynamics of an inhomogeneous plasma with hot electrons and cold ions, in the frequency range below the ion cyclotron and magnetosonic frequencies, is studied in the presence of magnetic shear. Both the finite electron mass and electron stress-tensor effects are accounted for, permiting arbitrary parallel phase velocities. A class of nonlinear travelling solutions is found, which are fully determined by the boundary conditions in the infinity, even on closed nonlinear characteristics. For the typical tokamak scaling β < (Ln/Ls)2, two different regimes are distinguished. In the shear Alfvén regime, β ≪ me/mi, the solution has the form of a complex vortex chain, possessing both the magnetic and flow components, supported by a self-organized, localized plasma flow and poloidal field. In the drift-wave regime, me/mi ≪ β ≪ 1, the solution is a nonlinear electromagnetic drift wave, whose amplitude is determined by its wavelength and the angle of propagation.

Interferometric determination of broadband ELF wave phase velocity within a region of transverse auroral ion acceleration

Broadband electric field fluctuations with typical amplitudes of 10–20 mV/m peak‐to‐peak and frequencies from 0 Hz to 3 kHz (BB‐ELF) were observed coincident with a region of ≤200 eV transverse H+ acceleration (TAI) near the poleward edge of the pre‐midnight aurora. The coherence and phase velocity of the electric fields were measured using a interferometric antenna array over the frequency range of ≈ 100 Hz to 3 kHz. These electric field fluctuations were found to have the following characteristics: 1) incoherence perpendicular to the geomagnetic field, 2) coherence parallel to the the geomagnetic field, 3) parallel phase velocity (ω/k∥) of 30–35 km/s upwards, 4) 0 &lt; |k∥/k⟂| &lt; 0.22. We show that these properties are compatible with the emission being electrostatic H+ cyclotron (EHC) waves. We also discuss possible generation mechanisms for the waves, and their relationship to the TAI.

On the kinetic dispersion relation for shear Alfvén waves

Kinetic Alfvén waves have been invoked in association with auroral currents and particle acceleration since the pioneering work of Hasegawa [1976]. However, to date, no work has considered the dispersion relation including the full kinetic effects for both electrons and ions. Results from such a calculation are presented, with emphasis on the role of Landau damping in dissipating Alfvén waves which propagate from the warm plasma of the outer magnetosphere to the cold plasma present in the ionosphere. It is found that the Landau damping is not important when the perpendicular wavelength is larger than the ion acoustic gyroradius and the electron inertial length. In addition, ion gyroradius effects lead to a reduction in the Landau damping by raising the parallel phase velocity of the wave above the electron thermal speed in the short perpendicular wavelength regime. These results indicate that low‐frequency Alfvén waves with perpendicular wavelengths greater than the order of 10 km when mapped to the ionosphere will not be significantly affected by Landau damping. While these results, based on the local dispersion relation, are strictly valid only for short parallel wavelength Alfvén waves, they do give an indication of the importance of Landau damping for longer parallel wavelength waves such as field line resonances.

New aspects of whistler waves driven by an electron beam studied by a 3-D electromagnetic code

We have restudied electron beam driven whistler waves with a 3-D electromagnetic particle code. In the initialisation of the beam-plasma system, “quiet start” conditions were approached by including the poloidal magnetic field due to the current carried by beam electrons streaming along a background magnetic field. The simulation results show electromagnetic whistler wave emissions and electrostatic beam modes like those observed in the Spacelab 2 electron beam experiment. It has been suggested in the past that the spatial bunching of beam electrons associated with the beam mode may directly generate whistler waves. However, the simulation results indicate several inconsistencies with this picture: (1) the parallel (to the background magnetic field) wavelength of the whistler wave is longer than that of the beam instability, (2) the parallel phase velocity of the whistler wave is smaller than that of the beam mode, and (3) whistler waves continue to be generated even after the beam mode space charge modulation looses its coherence. The complex structure of the whistler waves in the vicinity of the beam suggest that the transverse motion (gyration) of the beam and background electrons is involved in the generation of the whistler waves.

On the stability of shear-Alfvén vortices

Linear stability of shear-Alfvén vortices is studied analytically, using the Lyapunov method. Vortices belonging to the drift mode, which is a generalization of the standard Hasegawa–Mima vortex to the case of large parallel phase velocities, are proved to be unstable. In the case of the convective-cell mode, short perpendicular-wavelength perturbations are stable for a broad class of vortices. Eventually, instability of convective-cell vortices may occur on the perpendicular scale comparable with the vortex size, but it is followed by a simultaneous excitation of coherent structures with a better localization than the original vortex.

New aspects of whistler waves driven by an electron beam studied by a 3‐D electromagnetic code

We have restudied electron beam driven whistler waves with a 3‐D electromagnetic particle code. The simulation results show electromagnetic whistler wave emissions and electrostatic beam modes like those observed in the Spacelab 2 electron beam experiment. It has been suggested in the past that the spatial bunching of beam electrons associated with the beam mode may directly generate whistler waves. However, the simulation results indicate several inconsistencies with this picture: (1) whistler waves continue to be generated even after the beam mode space charge modulation looses its coherence, (2) the parallel (to the background magnetic field) wavelength of the whistler wave is longer than that of the beam instability, and (3) the parallel phase velocity of the whistler wave is smaller than that of the beam mode. The complex structure of the whistler waves in the vicinity of the beam suggest that the transverse motion (gyration) of the beam and background electrons is also involved in the generation of whistler waves.

The absorption mechanisms of whistler waves in cool, dense, cylindrically bounded plasmas

It can be shown that whistler waves with low parallel phase velocity can be subject to strong cyclotron damping, even when the wave frequency is well below the cyclotron frequency. This resonance arises as a result of the Doppler effect which is proportional to the plasma density and increases the frequency experienced by electrons moving in the opposite direction to the wave. In this paper the dispersion relation of whistler waves in a cylindrically bounded plasma is obtained and then solved. This geometry is desirable for its relevance to experiment and also for comparison with theoretical results by other authors. In addition to cyclotron damping, Landau damping as well as electron–ion, electron–electron, and electron–neutral collisions are all included thus enabling the relative importance of these damping mechanisms to be evaluated. The dispersion relation that is obtained is used to explore the transition from Landau dominated damping to cyclotron dominated damping.

Observation and analysis of a two-parallel-temperature electron tail during lower-hybrid current-drive on a tokamak

A ‘‘two-parallel-temperature’’ feature of the fast-electron distribution function has been observed during lower-hybrid current-drive experiments on the Versator-II tokamak (B. Richards, Ph.D. thesis, Massachusetts Institute of Technology, 1981). Computational modeling predicts this feature and indicates that the colder tail is initiated by low-power, high-N∥ waves from the sidelobes of the antenna N∥ spectrum. The modeling indicates these waves bridge the ‘‘spectral gap,’’ enabling current drive even though the wave parallel phase velocity greatly exceeds the electron thermal velocity for the majority of the wave power.

Ion temperature gradient driven impurity modes

The presence of two (or more) species of ions in an inhomogeneous magnetically confined plasma can present opportunities for a new class of drift-type modes to become unstable. When the thermal velocity of a minority ion species (the impurity) is much smaller than that of the primary species, waves with parallel phase velocities intermediate between the two thermal velocities can be driven unstable by a source of the free energy (for example density or temperature gradient) and by Landau damping. Their linear stability theory and quasi-linear particle and heat transport are discussed in the context of shearless slab geometry. Also discussed is the simultaneous appearance of two unstable modes, one propagating in the ion diamagnetic direction and the other in the electron direction. When the effective impurity concentration is finite, the threshold for the ion temperature gradient instability is dramatically increased