Parallel Phase Velocity Research Articles

A Hamiltonian gyrofluid model based on a quasi-static closure

A Hamiltonian six-field gyrofluid model is constructed, based on closure relations derived from the so-called ‘quasi-static’ gyrokinetic linear theory where the fields are assumed to propagate with a parallel phase velocity much smaller than the parallel particle thermal velocities. The main properties captured by this model, primarily aimed at exploring fundamental problems of interest for space plasmas such as the solar wind, are its ability to provide a reasonable agreement with kinetic theory for linear low-frequency modes, and at the same time to ensure a Hamiltonian structure in the absence of explicit dissipation. The model accounts for equilibrium temperature anisotropy, ion and electron finite Larmor radius corrections, electron inertia, magnetic fluctuations along the direction of a strong guide field and parallel Landau damping, introduced through a Landau-fluid modelling of the parallel heat transfers for both gyrocentre species. Remarkably, the quasi-static closure leads to exact and simple expressions for the nonlinear terms involving gyroaveraged electromagnetic fields and potentials. One of the consequences is that a rather natural identification of the Hamiltonian structure of the model becomes possible when Landau damping is neglected. A slight variant of the model consists of a four-field Hamiltonian reduction of the original six-field model, which is also used for the subsequent linear analysis. In the latter, the dispersion relations of kinetic Alfvén waves and the firehose instability are shown to be correctly reproduced, relatively far in the sub-ion range (depending on the plasma parameters), while the spectral range where the slow-wave dispersion relation and the field-swelling instabilities are precisely described is less extended. This loss of accuracy originates from the breaking of the condition of small phase velocity, relative to the parallel thermal velocity of the electrons (for kinetic Alfvén waves and firehose instability) or of the ions (in the case of the field-swelling instabilities).

Whistler Waves Driven by Field‐Aligned Streaming Electrons in the Near‐Earth Magnetotail Reconnection

AbstractWe analyze Magnetospheric Multiscale Mission observations of whistler waves and associated electron field‐aligned crescent distribution in the vicinity of the magnetotail near‐Earth X‐line. The whistler waves propagate outward from the X‐line in the neutral sheet. The associated field‐aligned streaming electrons exhibit a crescent‐like shape, with an inverse slope (df/d|v|||>0) at 1–5 keV. The parallel phase velocity of the waves is in the range (1–5 keV) of the inverse slope of the field‐aligned crescents in the velocity space. We demonstrate that the observed whistler waves are driven by the electron field‐aligned crescents through Landau resonance. The cyclotron resonance is at the high‐energy tail with negligible free energy of pitch angle anisotropy in these events.

Driven thermal waves and determination of the thermal conductivity in a magnetized plasma

Results are presented from a basic heat transport experiment using a magnetized electron temperature filament that behaves as a thermal resonator. A small, crystal cathode injects low-energy electrons along the magnetic field into the afterglow of a large preexisting plasma forming a hot electron filament embedded in a colder plasma. A series of low amplitude, sinusoidal perturbations are added to the cathode discharge bias that create an oscillating heat source capable of driving thermal waves. Langmuir probe measurements demonstrate driven thermal oscillations and allow for the determination of the amplitude and parallel phase velocity of the thermal waves over a range of driver frequencies. The results conclusively show the presence of a thermal resonance and are used to verify the parallel thermal wave dispersion relation based on classical transport theory. A nonlinear transport code is used to verify the analysis procedure. This technique provides an alternative measure of the density normalized thermal conductivity, independent of the electron temperature.

Whistler modes in highly nonuniform magnetic fields. III. Propagation near mirror and cusp fields

The properties of helicon modes in highly nonuniform magnetic fields are studied experimentally. The waves propagate in an essentially unbounded uniform laboratory plasma. Helicons with mode number m = 1 are excited with a magnetic loop with dipole moment across the dc magnetic field. The wave fields are measured with a three-component magnetic probe movable in three orthogonal directions so as to resolve the spatial and temporal wave properties. The ambient magnetic field has the topology of a mirror or a cusp, produced by the superposition of a uniform axial field B0 and the field of a current-carrying loop with the axis along B0. The novel finding is the reflection of whistlers by a strong mirror magnetic field. The reflection arises when the magnetic field changes on a scale length shorter than the whistler wavelength. The simplest explanation for the reflection mechanism is the strong gradient of the refractive index which depends on the density and magnetic field. More detailed observations show that the incident wave splits when the k vector makes an angle larger than 90° with respect to B0 which produces a parallel phase velocity component opposite to that of the incident wave. The reflection coefficient has been estimated to be close to unity. Interference between reflected and incident waves creates nodes in which the whistler mode becomes linearly polarized. When the magnetic field topology is that of a reversed field configuration (FRC), the incident wave is absorbed near the three-dimensional (3D) magnetic null point which prevents wave reflections. However, waves outside the separatrix are not absorbed and continue to propagate around the null point. When waves are excited inside the FRC, their polarization and helicon mode are reversed. Implications of these observations on research in space plasmas and helicon sources are pointed out.

Stability properties of a thin relativistic beam propagation in a magnetized plasma

A self-consistent nonlinear hydrodynamic theory is presented of the propagation of a long and thin relativistic electron beam through a plasma that is relatively strongly magnetized, $|\Omega_e|\sim\omega_{pe}$ and whose density is much bigger than that of the beam. In the regime when the parallel phase velocity in the comoving frame is much smaller than the thermal speed and the beam electrons are thermalized, a stationary solution for the beam is found when the electron motion in the transverse direction is negligibile and the transverse localization comes from the nonlinearity of its 3-D adiabatic expansion. Conversely, when the parallel phase velocity is sufficiently large to prevent the heat convection along the magnetic field, a helicoidally shaped stationary beam is found whose transverse profile is determined from a nonlinear dispersion relation and depends on the transverse size of the beam and its pitch angle.

Geodesic mode instability driven during ion cyclotron heating in tokamaks

The effect of a minor concentration of energetic particles produced by ion cyclotron resonance (ICR) heating on the stability of Geodesic Acoustic Modes (GAM) is studied using fully drift kinetic equation. Assuming the ICR layer position on the high field side of the tokamak magnetic axis, a minority ion distribution is modeled by the energetic ion tail and “triangle”-like pitch angle distribution with the maximum at the trapped-passing ion boundary. The resulting GAM instability is found when the hot ion thermal velocity is larger than the effective parallel GAM phase velocity Rqω and the geodesic frequency has the order of the energetic ion bounce frequency. The standard GAM frequency may be strongly reduced by some small concentration of the energetic ions allowing the mode to be unstable. Respective neoclassical polarization corrections (residual flow) driven by energetic ions are found to be negative and larger than that calculated by Rosenbluth and Hinton [Phys. Rev. Lett. 80, 724 (1998)]. Qualitative comparison of the theory with ICR heating experiments in tokamak is discussed.

Chorus Wave Modulation of Langmuir Waves in the Radiation Belts

AbstractUsing high‐resolution waveforms measured by the Van Allen Probes, we report a novel observation in the radiation belts. Namely, we show that multiband, discrete, rising‐tone whistler mode chorus emissions exhibit a one‐to‐one correlation with Langmuir wave bursts. Moreover, the periodic Langmuir wave bursts are generally observed at the phase location where the chorus wave E|| component is oriented opposite to its propagation direction. The electron measurements show a beam in phase space density at the particle velocity that matches the parallel phase velocity of the chorus waves. Based on this evidence, we conclude that the chorus waves accelerate the suprathermal electrons via Landau resonance and generate a localized electron beam in phase space density. Consequently, the Langmuir waves are excited locally and are modulated by the chorus wave phase. This microscale interaction between chorus waves and high‐frequency electrostatic waves provides a new insight into the nonlinear wave‐particle interaction process.

Geodesic mode instability driven by electron and ion fluxes during neutral beam injection in tokamaks

The effect of a minor concentration of energetic particles produced by parallel NB injection on Geodesic Acoustic Modes (GAM) spectrum is analyzed using fully kinetic equation. It is found that the GAM frequency is reduced by the effective mass renormalization due to that new energetic GAM appears with higher frequency. The electron current in combination with NB driven ion flow, modeled by shifted Maxwell distribution, may overcome the ion Landau damping thus resulting in the GAM instability when electron current velocity is larger than the effective parallel GAM phase velocity Rqω. Qualitative agreement of the theory with co/counter NB injection experiments in COMPASS tokamak is demonstrated.

Solitary kinetic Alfvén wave in a bi-ion plasma with superthermal electrons

The dispersion relation and the nonlinear solitary structure of kinetic Alfvén waves (KAWs) have been investigated in bi-ion plasma with superthermal electrons modeled by kappa (κ) distribution. A detailed analysis of the existence condition and the structure of solitary KAW (SKAW) is present. Numerical results indicate there is only the sub-Alfvénic hump type SKAW. For the same parallel phase velocity, the amplitude of SKAW will increase with the increase in the charge number of heavy ion, and with the decrease in the suprathermal index κ and the heavy ion number density. Moreover, the width of SKAW will increase with the decrease in the charge number of heavy ion, and with the increase in the super-thermal index κ and the heavy ion number density. The findings of the present study can be applied to low beta space plasma composed of multi-ion components and suprathermal electrons.

Electromagnetic particle simulation of the effect of toroidicity on linear mode conversion and absorption of lower hybrid waves

Effects of toroidicity on linear mode conversion and absorption of lower hybrid (LH) waves in fusion plasmas have been studied using electromagnetic particle simulation. The simulation confirms that the toroidicity induces an upshift of parallel refractive index when LH waves propagate from the tokamak edge toward the core, which affects the radial position for the mode conversion between slow and fast LH waves. Furthermore, moving LH antenna launch position from low field side toward high field side leads to a larger upshift of the parallel refractive index, which helps the slow LH wave penetration into the tokamak core. The broadening of the poloidal spectrum of the wave-packet due to wave diffraction is also verified in the simulation. Both the upshift and broadening effects of the parallel spectrum of the wave-packet modify the parallel phase velocity and thus the linear absorption of LH waves by electron Landau resonance.

Geodesic mode instability driven by electron and ion fluxes in tokamaks

The effect of the parallel electron current and plasma flux on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current and plasma flow, modeled by shifted Maxwell distributions of electrons and ions, may overcome the ion Landau damping generating the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity of sidebands, Rqω. The instability is driven by the electron current and the parallel ion flux cross term. Possible applications to tokamak experiments are discussed. The existence of the geodesic ion sound mode due to plasma flow is shown.

Magnetic antenna excitation of whistler modes. III. Group and phase velocities of wave packets

The properties of whistler modes excited by single and multiple magnetic loop antennas have been investigated in a large laboratory plasma. A single loop excites a wavepacket, but an array of loops across the ambient magnetic field B0 excites approximate plane whistler modes. The single loop data are measured. The array patterns are obtained by linear superposition of experimental data shifted in space and time, which is valid in a uniform plasma and magnetic field for small amplitude waves. Phasing the array changes the angle of wave propagation. The antennas are excited by an rf tone burst whose propagating envelope and oscillations yield group and phase velocities. A single loop antenna with dipole moment across B0 excites wave packets whose topology resembles m = 1 helicon modes, but without radial boundaries. The phase surfaces are conical with propagation characteristics of Gendrin modes. The cones form near the antenna with comparable parallel and perpendicular phase velocities. A physical model for the wave excitation is given. When a wave burst is applied to a phased antenna array, the wave front propagates both along the array and into the plasma forming a “whistler wing” at the front. These laboratory observations may be relevant for excitation and detection of whistler modes in space plasmas.

Geodesic mode instability driven by the electron current in tokamak plasmas

• Effect of the electron current and diamagnetic drift on geodesic modes is analyzed. • The effect is treated by kinetic theory using shifted Maxwell electron distribution. • Found instability occurs due to cross term of the electron current with the ion drift. • The threshold electron velocity have to be larger the parallel GAM phase velocity. Effect of the parallel electron current on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current modeled by shifted Maxwell distribution may overcome the phase velocity threshold and ion Landau damping thus resulting in the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity Rqω . The instability occurs due to its cross term of the current with the ion diamagnetic drift. Possible applications to tokamak experiments are discussed.

Lower hybrid instability driven by mono-energy α-particles with finite pitch angle spread in a plasma

A kinetic formalism of lower hybrid wave instability, driven by mono-energy α-particles with finite pitch angle spread, is developed. The instability arises through cyclotron resonance interaction with high cyclotron harmonics of α-particles. The α-particles produced in D-T fusion reactions have huge Larmor radii (∼10 cm) as compared to the wavelength of the lower hybrid wave, whereas their speed is an order of magnitude smaller than the speed of light in vacuum. As a result, large parallel phase velocity lower hybrid waves, suitable for current drive in tokamak, are driven unstable via coupling to high cyclotron harmonics. The growth rate decreases with increase in pitch angle spread of the beam. At typical electron density of ∼1019 m−3, magnetic field ∼4 Tesla and α-particle concentration ∼0.1%, the large parallel phase velocity lower hybrid wave grows on the time scale of 20 ion cyclotron periods. The growth rate decreases with plasma density.

Plasma transport induced by kinetic Alfvén wave turbulence

At the Earth's magnetopause that separates the hot-tenuous magnetospheric plasma from the cold dense solar wind plasma, often seen is a boundary layer where plasmas of both origins coexist. Plasma diffusions of various forms have been considered as the cause of this plasma mixing. Here, we investigate the plasma transport induced by wave-particle interaction in kinetic Alfvén wave (KAW) turbulence, which is one of the candidate processes. We clarify that the physical origin of the KAW-induced cross-field diffusion is the drift motions of those particles that are in Cerenkov resonance with the wave: E×B-like drift that emerges in the presence of non-zero parallel electric field component and grad-B drift due to compressional magnetic fluctuations. We find that KAW turbulence, which has a spectral breakpoint at which an MHD inertial range transits to a dissipation range, causes selective transport for particles whose parallel velocities are specified by the local Alfvén velocity and the parallel phase velocity at the spectral breakpoint. This finding leads us to propose a new data analysis method for identifying whether or not a mixed plasma in the boundary layer is a consequence of KAW-induced transport across the magnetopause. The method refers to the velocity space distribution function data obtained by a spacecraft that performs in situ observations and, in principle, is applicable to currently available dataset such as that provided by the NASA's THEMIS mission.

A mechanism for heating electrons in the magnetopause current layer and adjacent regions

Abstract. Taking advantage of the string-of-pearls configuration of the five THEMIS spacecraft during the early phase of their mission, we analyze observations taken simultaneously in the magnetosheath, the magnetopause current layer and the magnetosphere. We find that electron heating coincides with ultra low frequency waves. It seems unlikely that electrons are heated by these waves because the electron thermal velocity is much larger than the Alfvén velocity (Va). In the short transverse scale (k⊥ρi >> 1) regime, however, short scale Alfvén waves (SSAWs) have parallel phase velocities much larger than Va and are shown to interact, via Landau damping, with electrons thereby heating them. The origin of these waves is also addressed. THEMIS data give evidence for sharp spatial gradients in the magnetopause current layer where the highest amplitude waves have a large component δB perpendicular to the magnetopause and k azimuthal. We suggest that SSAWs are drift waves generated by temperature gradients in a high beta, large Ti/Te magnetopause current layer. Therefore these waves are called SSDAWs, where D stands for drift. SSDAWs have large k⊥ and therefore a large Doppler shift that can exceed their frequencies in the plasma frame. Because they have a small but finite parallel electric field and a magnetic component perpendicular to the magnetopause, they could play a key role at reconnecting magnetic field lines. The growth rate depends strongly on the scale of the gradients; it becomes very large when the scale of the electron temperature gradient gets below 400 km. Therefore SSDAW's are expected to limit the sharpness of the gradients, which might explain why Berchem and Russell (1982) found that the average magnetopause current sheet thickness to be ~400–1000 km (~500 km in the near equatorial region).

Excitation of ion Bernstein and ion cyclotron waves by a gyrating ion beam in a plasma column

AbstractGyrating ion beams, produced by quick ionization of neutral beams, employed for plasma heating, are susceptible to ion Bernstein and ion cyclotron instabilities. The Bernstein wave, having large parallel phase velocity, is excited via cyclotron interaction whereas the ion cyclotron wave with lower parallel phase velocity could be driven by Cerenkov interaction as well. The maximally growing modes have transverse wave number of the order of inverse ion Larmor radius. The nonlocal effects cause reduction in the growth rate.

Radial electric field generated by resonant trapped electron pinch with radio frequency injection in a tokamak plasma

Radial electric fields in tokamaks can be generated by charge accumulation due to a resonant trapped electron pinch effect. The radial field can then drive a toroidal flow. This resonant pinch effect was evaluated for the current-drive scheme that diffused electrons in the direction parallel to the toroidal field. It was found that, for typical tokamak parameters, to generate a radial electric field on the order of 100 kV/m, an rf power density on the order of kW/m3 is required. This power, absorbed by trapped electrons, is a small fraction of rf power density for current drive which is absorbed by passing electrons. However, according to the Landau resonant mechanism, the fraction of the momentum to trapped electrons decays exponentially with the square of the parallel phase velocity of the wave; therefore, the power absorbed at lower resonant velocities is the key. On the other hand, the redistribution of the current profile, due to rf current, decreases the local poloidal field and may reduce the particle transport significantly. It can relax the requirement of momentum deposited to trapped electrons, and, at the same time, contribute to explain the strongly correlation between the rotation and the driven current observed in experiments.

Low Frequency Magnetic Fluctuations during Magnetic Reconnection in Laboratory Experiment

Large amplitude magnetic fluctuation with ion cyclotron range frequency was observed inside the current sheet region during magnetic reconnection in the plasma merging experiment for the first time. The fluctuation exhibited parallel phase velocity close to the drift velocity in the current sheet and parallel wavelength comparable with the ion gyroradius, suggesting that the reconnection rate enhancement is influenced by the drift kink instability of the current sheet.

Using multispectral optical observations to identify the acceleration mechanism responsible for flickering aurora

We present an analysis of flickering (2–10 Hz) auroras observed with a state‐of‐the‐art multispectral imaging system, Auroral Structure and Kinetics, located in Tromsø, Norway. Short (1–2 s) periods of flickering aurora have been identified in which the frequency of the brightness oscillations decreases or increases smoothly over time. To the authors' knowledge this is the first detailed analysis of such “chirps” in flickering aurora or field‐aligned bursts. We have found that the electron precipitation energy is strongly anticorrelated with the flickering frequency during all identified chirps. This result is consistent with the theory that flickering aurora is caused by the resonance interaction between electromagnetic ion cyclotron waves and precipitating electrons and that the wave parallel phase velocity is the primary factor determining the electron acceleration produced by this mechanism. Other current theories known to the authors cannot completely explain our observations.