Electron Thermal Speed Research Articles

Charge distribution over dust particles in a flowing plasma

This paper presents an analytical model for the physical understanding of the charge distribution on dust particles in meso-thermal flow of plasmas where the flow speed of plasma relative to the dust particle is larger than the ion thermal speed but much less than the thermal speed of electrons. The formulation is based on the master difference equation for population balance and the number and energy balance considerations, allowing the charge to be only an integral multiple (positive or negative) of the electronic charge. The kinetics for (i) dark complex plasmas where accretion of electrons/ionic species are the dominant charging mechanisms and (ii) illuminated complex plasmas where photoemission significantly contributes to dust charging has been developed. The expression for the mean energy associated with the accretion of ionic species over dust gains in meso-thermal flow of complex plasmas has been derived and employed to obtain the charge distribution and other relevant plasma parameters. The high speed of meso-thermal flow of the plasma influences the dust charging towards more positive character and leads to significant reduction in electron and ion densities, even in the presence of photoemission from dust grains.

A resistive instability of lower hybrid-like waves in regions with parallel currents

The resistive instabilities and dispersion of obliquely propagating waves near the lower hybrid (LH) frequency are studied in plasma carrying a current parallel to the magnetic field. Possible applications of these instabilities include magnetic reconnection regions where LH-like waves may accelerate and heat both ions and electrons. A resistive instability is found in one of the four LH-like wave modes for electron drift speeds several times greater than the electron thermal speed for representative parameters. Numerical fully electromagnetic kinetic calculations of the solutions to the linear dispersion equation are compared with more approximate analytic calculations and show good agreement. The analytic results indicate that ion magnetization effects play a critical role in the resistive instability.

Three-dimensional electromagnetic strong turbulence. II. Wave packet collapse and structure of wave packets during strong turbulence

Large-scale simulations of wave packet collapse are performed by numerically solving the three-dimensional (3D) electromagnetic Zakharov equations, focusing on individual wave packet collapses and on wave packets that form in continuously driven strong turbulence. The collapse threshold is shown to decrease as the electron thermal speed νe/c increases and as the temperature ratio Ti/Te of ions to electrons decreases. Energy lost during wave packet collapse and dissipation is shown to depend on νe/c. The dynamics of density perturbations after collapse are studied in 3D electromagnetic strong turbulence for a range of Ti/Te. The structures of the Langmuir, transverse, and total electric field components of wave packets during strong turbulence are investigated over a range of νe/c. For νe/c≲0.17, strong turbulence is approximately electrostatic and wave packets have very similar structure to purely electrostatic wave packets. For νe/c≳0.17, transverse modes become trapped in density wells and contribute significantly to the structure of the total electric field. At all νe/c, the Langmuir energy density contours of wave packets are predominantly oblate (pancake shaped). The transverse energy density contours of wave packets are predominantly prolate (sausage shaped), with the major axis being perpendicular to the major axes of the Langmuir component. This results in the wave packet becoming more nearly spherical as νe/c increases, and in turn generates more spherical density wells during collapse. The results obtained are compared with previous 3D electrostatic results and 2D electromagnetic results.

Three-dimensional electromagnetic strong turbulence. I. Scalings, spectra, and field statistics

The first fully three-dimensional (3D) simulations of large-scale electromagnetic strong turbulence (EMST) are performed by numerically solving the electromagnetic Zakharov equations for electron thermal speeds νe with νe/c≥0.025. The results of these simulations are presented, focusing on scaling behavior, energy density spectra, and field statistics of the Langmuir (longitudinal) and transverse components of the electric fields during steady-state strong turbulence, where multiple wave packets collapse simultaneously and the system is approximately statistically steady in time. It is shown that for νe/c≳0.17 strong turbulence is approximately electrostatic and can be explained using the electrostatic two-component model. For ve/c≳0.17 the power-law behaviors of the scalings, spectra, and field statistics differ from the electrostatic predictions and results because νe/c is sufficiently high to allow transverse modes to become trapped in density wells. The results are compared with those of past 3D electrostatic strong turbulence (ESST) simulations and 2D EMST simulations. For number density perturbations, the scaling behavior, spectra, and field statistics are shown to be only weakly dependent on νe/c, whereas the Langmuir and transverse scalings, spectra, and field statistics are shown to be strongly dependent on νe/c. Three-dimensional EMST is shown to have features in common with 2D EMST, such as a two-component structure and trapping of transverse modes which are dependent on νe/c.

First-order thermal correction to the quadratic response tensor and rate for second harmonic plasma emission

Three-wave interactions in plasmas are described, in the framework of kinetic theory, by the quadratic response tensor (QRT). The cold-plasma QRT is a common approximation for interactions between three fast waves. Here, the first-order thermal correction (FOTC) to the cold-plasma QRT is derived for interactions between three fast waves in a warm unmagnetized collisionless plasma, whose particles have an arbitrary isotropic distribution function. The FOTC to the cold-plasma QRT is shown to depend on the second moment of the distribution function, the phase speeds of the waves, and the interaction geometry. Previous calculations of the rate for second harmonic plasma emission (via Langmuir-wave coalescence) assume the cold-plasma QRT. The FOTC to the cold-plasma QRT is used here to calculate the FOTC to the second harmonic emission rate, and its importance is assessed in various physical situations. The FOTC significantly increases the rate when the ratio of the Langmuir phase speed to the electron thermal speed is less than about 3.

Development of parallel electric fields at the plasma sheet boundary layer

[1] Many measurements of auroral particles, in particular recent measurements from the FAST satellite, indicate that the auroral electron distribution is often broad in energy and field-aligned in pitch angle. Such electrons are seen in conjunction with strong kinetic Alfven waves with small perpendicular wavelength, and so the aurora produced by these electrons has been termed the “Alfvenic aurora.” The Alfvenic aurora is predominant at the polar cap boundary of the aurora as well as in the auroral arc that brightens during substorm onset. The process of forming parallel electric fields in Alfven waves has been investigated by means of three-dimensional two-fluid simulations. Waves with small perpendicular wavelengths can be produced by phase mixing when perpendicular gradients are present in the plasma. At lower altitudes, Alfven waves can interact with the ionospheric Alfven resonator and phase mix to scales of a few kilometers. At higher altitudes, the electron thermal speed becomes comparable or larger than the Alfven speed, and parallel electric fields due to the Landau resonance can develop. This has been modeled in the fluid code by an approximation to the plasma dispersion function used in kinetic theory. Phase mixing is most effective when there are strong gradients, such as at the plasma sheet boundary layer. Simulations indicate that these processes can produce parallel electric fields on scales of a few kilometers (in the cold plasma case) to a few tens of kilometers (in the warm plasma case), comparable to the scale sizes of auroral arcs.

Possible excitation of solitary electron holes in a laboratory plasma

Plasma response to a fast rising high positive voltage pulse is experimentally studied in a uniform and unmagnetized plasma. The pulse is applied to a metallic disk electrode immersed in a low pressure argon plasma (np∼109 cm−3 and Te∼0.5–2 eV) with the pulse magnitude U0⪢kTe/e, where Te is the electron temperature. Experiments have been carried out for various applied pulse widths τp ranging from less than 3fi−1 to greater than 3fi−1, where fi is the ion plasma frequency. For pulse widths less than 3fi−1, potential disturbances are observed to propagate in two opposite directions from a location different from the actual exciter (metal disk electrode), indicating the presence of a virtual source. For pulse widths equal or greater than 3fi−1, there is no indication of such virtual source. These disturbances propagate with two phase speeds, i.e., vp/ve=1.36±0.11 and 0.4±0.15, where ve is the electron thermal speed. It is also observed that by increasing plasma density, the speed of these disturbances increases, whereas the speed is independent of pulse magnitude. Analysis of these disturbances indicates the excitation of solitary electron holes.

Laboratory Measurements of Electrostatic Solitary Structures Generated by Beam Injection

Electrostatic solitary structures are generated by injection of a suprathermal electron beam parallel to the magnetic field in a laboratory plasma. Electric microprobes with tips smaller than the Debye length (λDe) enabled the measurement of positive potential pulses with half-widths 4 to 25λDe and velocities 1 to 3 times the background electron thermal speed. Nonlinear wave packets of similar velocities and scales are also observed, indicating that the two descend from the same mode which is consistent with the electrostatic whistler mode and result from an instability likely to be driven by field-aligned currents.

Lower-hybrid (LH) oscillitons evolved from ion-acoustic (IA)/ion-cyclotron (IC) solitary waves: effect of electron inertia

Abstract. Lower-hybrid (LH) oscillitons reveal one aspect of geocomplexities. They have been observed by rockets and satellites in various regions in geospace. They are extraordinary solitary waves the envelop of which has a relatively longer period, while the amplitude is modulated violently by embedded oscillations of much shorter periods. We employ a two-fluid (electron-ion) slab model in a Cartesian geometry to expose the excitation of LH oscillitons. Relying on a set of self-similar equations, we first produce, as a reference, the well-known three shapes (sinusoidal, sawtooth, and spiky or bipolar) of parallel-propagating ion-acoustic (IA) solitary structures in the absence of electron inertia, along with their Fast Fourier Transform (FFT) power spectra. The study is then expanded to illustrate distorted structures of the IA modes by taking into account all the three components of variables. In this case, the ion-cyclotron (IC) mode comes into play. Furthermore, the electron inertia is incorporated in the equations. It is found that the inertia modulates the coupled IA/IC envelops to produce LH oscillitons. The newly excited structures are characterized by a normal low-frequency IC solitary envelop embedded by high-frequency, small-amplitude LH oscillations which are superimposed upon by higher-frequency but smaller-amplitude IA ingredients. The oscillitons are shown to be sensitive to several input parameters (e.g., the Mach number, the electron-ion mass/temperature ratios, and the electron thermal speed). Interestingly, whenever a LH oscilliton is triggered, there occurs a density cavity the depth of which can reach up to 20% of the background density, along with density humps on both sides of the cavity. Unexpectedly, a mode at much lower frequencies is also found beyond the IC band. Future studies are finally highlighted. The appendices give a general dispersion relation and specific ones of linear modes relevant to all the nonlinear modes encountered in the text.

Joule heating and anomalous resistivity in the solar corona

Abstract. Recent radioastronomical observations of Faraday rotation in the solar corona can be interpreted as evidence for coronal currents, with values as large as 2.5×109 Amperes (Spangler, 2007). These estimates of currents are used to develop a model for Joule heating in the corona. It is assumed that the currents are concentrated in thin current sheets, as suggested by theories of two dimensional magnetohydrodynamic turbulence. The Spitzer result for the resistivity is adopted as a lower limit to the true resistivity. The calculated volumetric heating rate is compared with an independent theoretical estimate by Cranmer et al. (2007). This latter estimate accounts for the dynamic and thermodynamic properties of the corona at a heliocentric distance of several solar radii. Our calculated Joule heating rate is less than the Cranmer et al estimate by at least a factor of 3×105. The currents inferred from the observations of Spangler (2007) are not relevant to coronal heating unless the true resistivity is enormously increased relative to the Spitzer value. However, the same model for turbulent current sheets used to calculate the heating rate also gives an electron drift speed which can be comparable to the electron thermal speed, and larger than the ion acoustic speed. It is therefore possible that the coronal current sheets are unstable to current-driven instabilities which produce high levels of waves, enhance the resistivity and thus the heating rate.

Properties of Hall magnetohydrodynamic waves modified by electron inertia and finite Larmor radius effects

The linear wave equation (sixth order in space and time) and the corresponding dispersion relation is derived for Hall magnetohydrodynamic (MHD) waves including electron inertial and finite Larmor radius effects together with several limiting cases for a homogeneous plasma. We contrast these limits with the solution of the full dispersion relation in terms of wave normal (k⊥,k∥) diagrams to clearly illustrate the range of applicability of the individual approximations. We analyze the solutions in terms of all three MHD wave modes (fast, slow, and Alfvén), with particular attention given to how the Alfvén branch (including the cold ideal field line resonance (FLR) [D. J. Southwood, Planet. Space Sci. 22, 483 (1974)]) is modified by the Hall term and electron inertial and finite Larmor radius effects. The inclusion of these terms breaks the degeneracy of the Alfvén branch in the cold plasma limit and displaces the asymptote position for the FLR to a line defined by the electron thermal speed rather than the Alfvén speed. For a driven system, the break in this degeneracy implies that a resonance would form at one field line for small k⊥ and then shift to another as k⊥→∞. However for very large ωk⊥/VA, Hall term effects lead to a coupling to the whistler mode, which would then transport energy away from the resonant layer. The inclusion of the Hall term also significantly effects the characteristics of the slow mode. This analysis reveals an interesting “swapping” of the perpendicular root behavior between the slow and Alfvén branches.

Hydromagnetic waves and instabilities in kappa distribution plasma

Stability properties of hydromagnetic waves (shear and compressional Alfven waves) in spatially homogeneous plasma are investigated when the equilibrium particle velocity distributions in both parallel and perpendicular directions (in reference to the ambient magnetic field) are modeled by kappa distributions. Analysis is presented for the limiting cases |ξα|⪡1 and |ξα|⪢1 for which solutions of the dispersion relations are analytically tractable. Here ξα(α=e,i) is the ratio of the wave phase speed and the electron (ion) thermal speed. Both low and high β (=plasma pressure/magnetic pressure) plasmas are considered. The distinguishing features of the hydromagnetic waves in kappa distribution plasma are (1) both Landau damping and transit-time damping rates are larger than those in Maxwellian plasma because of the enhanced high-energy tail of the kappa distribution and (2) density and temperature perturbations in response to the electromagnetic perturbations are different from those in Maxwellian plasma when |ξα|⪡1. Moreover, frequency of the oscillatory stable modes (e.g., kinetic shear Alfven wave) and excitation condition of the nonoscillatory (zero frequency) unstable modes (e.g., mirror instability) in kappa distribution plasma are also different from those in Maxwellian plasma. Quantitative estimates of the differences depend on the specific choice of the kappa distribution. For simplicity of notations, same spectral indices κ∥ and κ⊥ have been assumed for both electron and ion population. However, the analysis can be easily generalized to allow for different values of the spectral indices for the two charged populations.

Comment on “Role of dispersive Alfvén waves in generating parallel electric fields along the Io-Jupiter fluxtube” by S. T. Jones and Y.-J. Su

Comment on “Role of dispersive Alfvén waves in generating parallel electric fields along the Io-Jupiter fluxtube” by S. T. Jones and Y.-J. Su

Laboratory Observation of Electron Phase-Space Holes during Magnetic Reconnection

We report the observation of large-amplitude, nonlinear electrostatic structures, identified as electron phase-space holes, during magnetic reconnection experiments on the Versatile Toroidal Facility at MIT. The holes are positive electric potential spikes, observed on high-bandwidth ( approximately 2 GHz) Langmuir probes. Investigations with multiple probes establish that the holes travel at or above the electron thermal speed and have a three-dimensional, approximately spherical shape, with a scale size approximately 2 mm. This corresponds to a few electron gyroradii, or many tens of Debye lengths, which is large compared to holes considered in simulations and observed by satellites, whose length scale is typically only a few Debye lengths. Finally, a statistical study over many discharges confirms that the holes appear in conjunction with the large inductive electric fields and the creation of energetic electrons associated with the magnetic energy release.

Electron plasma wave propagation in external-electrode fluorescent lamps

The optical propagation observed along the positive column of external electrode fluorescent lamps is shown to be an electron plasma wave propagating with the electron thermal speed of (kTe∕m)1∕2. When the luminance of the lamp is 10000–20000cd∕m2, the electron plasma temperature and the plasma density in the positive column are determined to be kTe∼1.26–2.12eV and no∼(1.28–1.69)×1017m−3, respectively.

Fundamental emission via wave advection from a collapsing wave packet in electromagnetic strong plasma turbulence

Zakharov simulations of nonlinear wave collapse in continuously driven two-dimensional, electromagnetic strong plasma turbulence with electron thermal speeds v⩾0.01c show that for v≲0.1c, dipole radiation occurs near the plasma frequency, mainly near arrest, but for v≳0.1c, a new mechanism applies in which energy oscillates between trapped Langmuir and transverse modes until collapse is arrested, after which trapped transverse waves are advected into incoherent interpacket turbulence by an expanding annular density well, where they detrap. The multipole structure, Poynting flux, source current, and radiation angular momentum are computed.

Structure of Langmuir and electromagnetic collapsing wave packets in two-dimensional strong plasma turbulence

Nucleating and collapsing wave packets relevant to electromagnetic strong plasma turbulence are studied theoretically in two dimensions. Model collapsing Langmuir and transverse potentials are constructed as superpositions of approximate eigenstates of a spherically symmetric density well. Electrostatic and electromagnetic potentials containing only components with azimuthal quantum numbers m=0, 1, 2 are found to give a good representation of the electric fields of nucleating collapsing wave packets in turbulence simulations. The length scales of these trapped states are related to the electron thermal speed ve and the length scale of the density well. It is shown analytically that the electromagnetic trapped states change with ve and that for ve≲0.17c they are delocalized, in accord with recent simulations. In this case, the Langmuir mode collapses independently, as in electrostatic plasma turbulence. For ve≳0.17c, the Langmuir and transverse modes remain coupled during collapse, with autocorrelation lengths in a constant ratio. An investigation of energy transfer to packets localized in density wells shows that the strongest power transfer to the nucleating state occurs for Langmuir waves. Energy transitions between different trapped and free states for collapsing wave packets are studied, and the transition rate from trapped Langmuir to free plane electromagnetic waves is calculated and related to the emission of electromagnetic waves at the plasma frequency.

Kinetic Alfvén waves and electron physics. I. Generation from ion-ion streaming

Short-wavelength kinetic Alfvén waves (KAWs) that propagate at large angles with respect to the magnetic field and interact with both electrons and ions have broad application to laboratory and space plasmas. Using linear Vlasov theory and particle-in-cell (PIC) simulations, the generation of KAWs by ion-ion streaming along the magnetic field at relatively low (2.5× the Alfvén speed) and low plasma beta (ratio of plasma thermal pressure to magnetic pressure ⩽0.1) are investigated. The instability has been examined previously using linear theory and a hybrid simulation method in which the ions are treated kinetically and the electrons as an adiabatic fluid. In this work it is found that when the electron Landau resonance factor or equivalently the ratio of the Alfvén speed to the electron thermal speed is large enough, the interaction of KAWs with the electrons produces strong parallel electron heating. The electron parallel heating in turn increases both the wave growth rates and the range of unstable modes of the instability, leading to enhanced saturated wave levels, increased perpendicular ion heating and larger spatial fluctuations in the drift speeds of the ions that appear as greater reductions of relative ion streaming in localized regions, compared to results from hybrid simulations. The interaction of KAWs with the electrons shifts from the bulk to the tail of the parallel velocity distribution at larger values of the resonant factor, corresponding to situations at lower electron beta or more obliquely propagating waves. Ion-to-electron mass ratio effects are considered together with the scaling to electron beta and the resonant factor in order to apply the results to systems of interest. In particular, KAWs and electron kinetics are discussed in the context of oblique slow shock formation and structure [Yin et al., Phys. Plasmas 14, 062105 (2007)].

Large parallel electric fields, currents, and density cavities in dispersive Alfvén waves above the aurora

Large parallel electric fields (E∥ > 10 mV/m) are sometimes observed with intense filamentary field‐aligned currents (J∥ > 10 μA/m2 mapped to 100‐km altitude) on transverse scales where kxc/ωpe ≈ 1 above the auroral oval. The ratio of the transverse electric (Ex) and magnetic field (By) variations is approximately the local Alfvén speed and increases with decreasing transverse scale in a manner consistent with inertial Alfvén wave dispersion. These fields are typically observed in association with density cavities. Statistically, it is shown that the depth of the cavities observed over the altitude range from 350 to 4175 km by the Fast Auroral Snapshot (FAST) satellite typically lies between 30 and 50% of the background plasma with 90% depletions being observed for 1% of the recorded events. The wave currents embedded within these cavities exceed 100 μA/m2 for 2% of the ensemble and are typically found over transverse widths of ∼2πλe. Using a fluid description of the plasma, we show statistically that electron pressure gradients provide a probable means for balancing the large E∥ found in these structures with a likely but unknown contribution from anomalous resistivity. Furthermore, we find that the ratio of the average drift speed of the bulk electron plasma (vd) to the electron thermal speed (ve) inside these structures is vd/ve ≥ 0.1 and that in at least 2% of cases veh05d/ve ≥ 1.0. On the basis of recent simulation results and the Bohm criterion for double layer formation, these statistics indicate that the large E∥ sometimes observed in density cavities may occur in double layers driven by the Alfvén wave current.

Extraordinary electromagnetic waves in a warm dense magnetoplasma

Abstract The linear dispersion relation for elliptically polarized electromagnetic waves in a dense fermionic quantum magnetoplasma is derived, taking into account the quantum forces associated with the quantum Bohm potential and the magnetization energy of the electrons due to the 1/2-electron spin effect. It is found that the quantum forces modify the wave dispersion at scales that depend upon λ q = ℏ / 2 m V F and λ B = ℏ / 2 m ω c , where ℏ is the Planck constant divided by 2π, m is the electron mass, V F is the Fermi electron thermal speed, and ω c is the electron gyrofrequency.