Langmuir Oscillations Research Articles

TWO-STREAM NONLINEAR LANGMUIR OSCILLATIONS

Langmuir oscillations of a large amplitude in a cold collisionless plasma are considered in this work. We passed to the conclusion that multiple streams is an inevitable feature of the Langmuir oscillations in the cold collisionless inhomogeneous plasma with resonant point even in the low-signal limit. By extending the equation of the cold plasma oscillations on the multi-stream regimes, we find two-stream modes in the homogeneous plasma, which are stationary solutions of this equation.

Nonlinear Langmuir oscillations in an ultrarelativistic degenerate quantum electron-ion plasma

The investigation of the nonlinear Langmuir associations in an ultrarelativistic, fully degenerate quantum plasma, composed of stationary ions and warm electrons is considered. The quantum hydrodynamic model with the equation of state of electrons is used to derive a nonlinear differential equation that describes the chemical potential of electrons. Then, the Runge Kutta method is used to solve this equation numerically. Hence, the profiles of the chemical potential and electron number density are graphically presented. Numerical results show that the Bohm quantum force produces small scale quantum Langmuir oscillations along with the classical oscillations. These findings are helpful in understanding the features of nonlinear Langmuir waves in various astrophysical plasmas such as planetary interiors and compact objects.

Quantum Level Instability of Transverse Excitation in Electron Flow

In current research, we use the effective Schrödinger-Poisson model to study a new kind of quantum-level instability in an infinite-wall slab electron flow. We use the Madelung fluid representation along with the conventional eigenvalue problem techniques in order to solve the linearized coupled differential equations representing the linear transverse collective excitations in the electron gas of arbitrary degree of degeneracy having a constant perpendicular drift. It is shown that the energy levels of collective electrostatic excitations are doubly quantized due to mutual interactions between single electron oscillations, analogous to the problem of a particle in a box, and collective Langmuir oscillations, which are modulated over single electron quantum state. We also report the transverse excitation instability of plasmon energy level in electron slab flow due to the interplay between the wave-like dispersion and the destabilizing perpendicular electron drift momentum. We further study in detail the parametric dependence of such instability in terms of different aspects of the many-electron system. Such a quantum-level instability may have important applications in characteristic behavior of plasmonic devices and their frequency response. Parametric quantization of drifting electron fluid may also have broad applications in nanoscale quantum device calibration and quantum measurements.

On the Mechanisms of Formation of Density Cavities under Instability of Intense Langmuir Oscillations in a Plasma

The paper considers the instability of intense Langmuir oscillations in nonisothermal (Zakharov's model) and cold (Silin's model) 1D plasma. The main attention is paid to the formation of plasma density caverns in the hydrodynamic and hybrid (electrons are described hydrodynamically, ions are described by model particles) representations. In the hydrodynamic representation, with a small number of spectrum modes, large-scale plasma density caverns are observed, which rapidly deepen. This process is supported by the appearance of small-scale perturbations, and phase synchronization of the Langmuir waves of the instability spectrum is observed. This phase synchronization of the spectrum modes is quite capable of fulfilling the role that was previously proposed to be given exclusively to the effect of extrusion of particles from the cavity by the field. In hybrid models, in the region of consideration, ions are described by model particles, the number of which in the one-dimensional case 104-5*105 (which in the three-dimensional case corresponds to the number of particles 1012-1014). The initial spectrum of perturbations is very wide and rather intense, which leads to an explosive growth of perturbations in the Zakharov model and a rapid development of instability in the Silin model. In this case, in the developed instability regime, the formation of many small-scale plasma density caverns is observed. It is the presence of this small-scale modulation due to the Fermi effect that quickly forms the normal distribution of ions over velocities. In this case, the effect of particle heating due to Landau damping loses its primacy. It is shown that the caverns practically do not change their position; phase changes for the spectral components of the plasma density were not observed. Only individual small-scale caverns demonstrate dynamics similar to the development of caverns in the hydrodynamic representation.

Detecting the meteoroid by measuring the electromagnetic waves excited by the collision between the hypervelocity meteoroid and spacecraft

The electromagnetic pulse excited by the collision between a hypervelocity meteoroid and a spacecraft is studied both numerically and theoretically. It is found that there are two kinds of electromagnetic pulse. The high-frequency electromagnetic pulse may be excited by the sum of all the electric dipoles. Each electron can be considered as an electric dipole. The low-frequency electromagnetic pulse is produced by the Langmuir oscillation of electrons. The energy flux density and the duration time of the excited low-frequency electromagnetic pulse by the meteoroid are also studied in the present paper. It is shown that the energy flux density increases as either the impact speed or the mass of the meteoroid increases. It is also shown that the duration time decreases as both the impact speed and the mass of the meteoroid increase. By measuring the strength and the duration time of the electromagnetic pulse excited by the collision between the hypervelocity meteoroid and spacecraft, we can estimate the speed and the mass of the hypervelocity meteoroid, which will be helpful in space flight and space exploration.

Langmuir oscillations breaking in inhomogeneous plasma

The influence of density inhomogeneity on the Langmuir oscillations breaking in plasma in the plane one-dimensional geometry is investigated analytically and numerically. It is shown that the breaking of the Langmuir oscillations in an inhomogeneous plasma occurs as the result of the formation, rapid growth, and approaching to infinity of the maximum of electron density located outside the plane, with respect to which the electrons oscillate. The dependence of the Langmuir oscillations breaking time on the size of the plasma inhomogeneity is investigated, and it is shown that the sharper the density gradient and the greater strength of the initial electric field, the breaking is faster.

Quantitative effects of cyclotron resonance on the coupling of ULF with VLF and langmuir waves

The renewed interest in nonlinear wave–wave coupling phenomena is motivated by the observations of radiation belt storm probes (RBSP) in the Earth's magnetosphere. The recent studies on this subject are mainly limited to the qualitative explanations of RBSP satellites observations. In magnetized plasmas like solar wind, Earth's magnetosphere and many astrophysical environments electrons and ions spiraling along magnetic field lines during cyclotron motion can interfere with the turbulent wave–wave coupling phenomena. This work quantitatively shows that cyclotron resonance plays a complementary role in understanding the turbulent wave–wave coupling in magnetized plasma. It is considered that electrons are in cyclotron resonance with very-low-frequency (VLF) waves, which are coupled with Langmuir oscillations and ultra-low-frequency (ULF) waves. Several illustrative examples are presented. It is found that the resonant electron pitch angles and energy seriously affect the coupling of VLF, ULF, and Langmuir waves. Our findings are important for understanding turbulence in magnetotail region of Earth's magnetosphere.

On Langmuir oscillations breaking driven by ion motion and relativistic effects

The nonlinear evolution of Langmuir oscillations (LOs) is studied in a cold plasma including the ion motion and (weakly) relativistic mass variation of electrons. For the purposes, a simple perturbation technique is used to solve the governing one-dimensional fluid-Maxwell’s equations. The solutions show that the Langmuir mode frequency acquires spatial dependencies due to the finite ion inertia and relativistic effects. As a result, excited LOs mix up in phase and break at arbitrarily low amplitudes. An approximate expression for the phase-mixing time of LOs is then obtained, thus improving some earlier results. Phase-mixing time is found to decrease with the increase of both the electron-to-ion mass ratio parameter and relativistic factor. A comparative analysis between these two effects is also carried out to clarify which effect contributes more to the phase-mixing time. It is revealed that phase-mixing is induced more quickly due to the ion motion than the relativistic effects.

Parametric resonance in the ultracold Rydberg plasma under the influence of an acoustic wave

The article considers weakly ionized ultracold Rydberg plasma under the influence of an acoustic wave of the terahertz range. The effect of an acoustic wave on Langmuir oscillations of Rydberg plasma is described using a hydrodynamic approach. The mechanism of the influence of an acoustic wave on Langmuir oscillations in such plasma, which consists in the scattering of electrons by neutral atoms oscillating in a high-frequency acoustic field, is considered. The unitary Kramers—Henneberger transformation in the Schrцdinger equation is used to calculate the cross section for the scattering of electrons by atoms performing high-frequency oscillations in the field of a terahertz acoustic wave. On this basis, a deep analogy is shown between the problem of scattering of an electron in the field of an external electromagnetic wave by a stationary atom and the problem of scattering of an electron by an atom vibrating in an external acoustic field. Numerical calculations demonstrate the oscillatory character of the cross section for the scattering of an electron by a Rydberg atom vibrating in a high-frequency acoustic field. Within the framework of the chosen hydrodynamic model, in view of the time dependence of the cross section for scattering of electrons by plasma atoms, the change in the electron density in such a system is described by the Mathieu equation, well known in mathematical physics. On the basis of this equation, the fundamental possibility of the appearance of parametric resonance, in the form of the buildup of Langmuir oscillations, in such a system is shown theoretically. The conditions for the appearance of resonance in Rydberg plasma initiated by a high-frequency acoustic wave are indicated.

Effects of finite ion inertia on phase-mixing of Langmuir oscillations in cold electron-positron-ion plasmas

We study the influences of finite ion mass on the phase-mixing process of Langmuir oscillations (LOs) in cold electron-positron-ion (EPI) plasmas. We solve the three fluid-Maxwell's equations in a perturbative way to provide an analytical estimate of phase-mixing time of LOs in such multispecies plasmas. The phase-mixing time is shown to depend on the perturbation amplitude, on the equilibrium ion-to-electron density ratio, and on the electron-to-ion mass ratio. The analytical dependence of phase-mixing time on these parameters is also discussed in various plasma limits.

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11765017, 11865014, 11847304, and 11764039), the Scientific Research Project of Gansu Higher Education, China (Grant No. 2019B-034), and the Science and Technology Project of Guizhou Province, China (Grant No. Qiankehe- LH-[2017]7008).

By one-dimensional particle-in-cell (PIC) simulations, the propagation and stability of relativistic electromagnetic (EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas. The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 1023 m−3 and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases (decreases) with the increase of the carrier wave frequency (vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude. This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.

On the criteria of the Langmuir oscillations breaking in a plasma

The influence of the initial distribution of the plasma electron density on the temporal dynamics of nonlinear Langmuir oscillations in plane one-dimensional geometry has been analytically and numerically studied. It is shown that if the concentration of electrons at the initial time in a certain region is less than or equal to half the background value, then the density singularity or breaking always occurs during the first half-period of oscillations in the plane of symmetry with respect to which the electrons oscillate. If the electron concentration at the initial time exceeds half the equilibrium value, then the density singularity appears outside the plane of symmetry due to the relativistic dependence of the oscillation frequency on the amplitude. In this case, the breaking time of oscillations is inversely proportional to the initial value of the electron density perturbations and the square of the electric field at the initial time.

Single-cycle THz signal accompanying laser wake in photoionized plasmas

Photoionization of an ambient gas by a weakly relativistic, femtosecond laser pulse leaves behind the pulse a flat-top plasma column. The uniform-density core of the column is surrounded by a micron-thin shell, within which the density of plasma species falls down to zero. As the laser pulse ponderomotive force drives the wave of charge separation (the laser wake), electron fluid velocity oscillates along this boundary layer. Coupling velocity oscillations to the transverse density gradient forms an azimuthally polarized rotational current confined within the boundary layer. At each radial offset, this current oscillates with a local (THz-scale) Langmuir frequency, transforming the cylindrical electrostatic plasma wave into a radially evanescent Fourier component of an electromagnetic signal. Summing up these Fourier components yields the time-domain THz signal which is (a) non-local (i.e. not phase-locked to the Langmuir oscillation at any given location), (b) contains the entire frequency band from zero to the Langmuir frequency of the density plateau, and (c) is detectable at a distance orders of magnitude larger than the plasma column radius. A few millimeters away from the column, rapid evanescence of the higher-frequency components transforms the signal into a radially polarized, single-cycle picosecond pulse with a kV m−1-scale electric field. Detecting this pulse with existing (e.g. electro-optical) techniques may bring information on the efficiency of laser coupling to the plasma, the amplitude of wake fields, and the structure of the column boundary.

Reply to "Comment on 'Langmuir oscillations in a nonextensive electron-positron plasma'".

In their Comment, Rehman and Ahmad have noted that the damping rate of Langmuir oscillations in a q-nonextensive electron-positron plasma is always negative and so resulting only in Landau damped oscillations and no unstable modes. As a Reply, I would like to resolve the origin of the misleading result in Phys. Rev. E 87, 053112 (2013)10.1103/PhysRevE.87.053112, which had arisen from a misprint in numerical programming of one of the equations there. Furthermore, I would like to point out that this picture is not solely connected to the problem of Langmuir oscillations in an electron-positron plasma, but this is in fact a reemphasizing of the stability of q distribution as a decreasing function with velocity. In this Reply, the corrected and modified pattern of the Landau damping rate of Langmuir oscillations in an electron-positron plasma is given in the superextensive region q<1 (the subsection involved an inappropriate result) and the modified results are confirmed. Hereby, it is confirmed that all analytical solutions of Phys. Rev. E 87, 053112 (2013)10.1103/PhysRevE.87.053112 are true and the misleading result there arose from a misprint in numerical programming of one of the equations.

Comment on "Langmuir oscillations in a nonextensive electron-positron plasma".

Saberian and Esfandyari-Kalejahi [Phys. Rev. E 87, 053112 (2013)10.1103/PhysRevE.87.053112] have discussed Langmuir oscillations in a q-nonextensive electron-positron plasma. However, some of the results obtained and the conclusions drawn in this paper are not appropriate. In Fig.3 of the above mentioned paper, the authors have claimed that for certain values of nonextensivity parameter q the imaginary part of the frequency becomes positive, resulting in unstable oscillations. In this Comment we shall discuss the fact that the Landau damping rate of Langmuir oscillations in a q-nonextensive electron-positron plasma is negative and results in damped oscillations. We hope that this Comment will be helpful in providing a better picture of Langmuir oscillations in nonextensive electron-positron plasma.

Extracting the differential inverse inelastic mean free path and differential surface excitation probability of Tungsten from X-ray photoelectron spectra and electron energy loss spectra

Precise knowledge of the differential inverse inelastic mean free path (DIIMFP) and differential surface excitation probability (DSEP) of Tungsten is essential for many fields of material science. In this paper, a fitting algorithm is applied for extracting DIIMFP and DSEP from X-ray photoelectron spectra and electron energy loss spectra. The algorithm uses the partial intensity approach as a forward model, in which a spectrum is given as a weighted sum of cross-convolved DIIMFPs and DSEPs. The weights are obtained as solutions of the Riccati and Lyapunov equations derived from the invariant imbedding principle. The inversion algorithm utilizes the parametrization of DIIMFPs and DSEPs on the base of a classical Lorentz oscillator. Unknown parameters of the model are found by using the fitting procedure, which minimizes the residual between measured spectra and forward simulations. It is found that the surface layer of Tungsten contains several sublayers with corresponding Langmuir resonances. The thicknesses of these sublayers are proportional to the periods of corresponding Langmuir oscillations, as predicted by the theory of R.H. Ritchie.

Parametric decay of current‐driven Langmuir waves in plateau plasmas: Relevance to solar wind and foreshock events

AbstractLangmuir amplitude modulation in association with type III radio bursts is a well‐known phenomenon since the beginning of space observations. It is commonly attributed to the superposition of beam‐excited Langmuir waves and their backscattered counterparts as a result of parametric decay. The dilemma, however, is the discrepancy between fast beam relaxation and long‐lasting Langmuir wave activity. Instead of starting with an unstable electron beam, our focus in this paper is on the nonlinear response of Langmuir oscillations that are driven after beam stabilization by the still persisting current of the (stable) two‐electron plasma. The velocity distribution function of the second population forms a plateau (index h) with a point at which associated with weak damping over a more or less extended wave number range k. As shown by particle‐in‐cell simulations, this so‐called plateau plasma drives primarily Langmuir oscillations at the plasma frequency (ωe) with k = 0 over long times without remarkable change of the distribution function. These Langmuir oscillations act as a pump wave for parametric decay by which an electron‐acoustic wave slightly below ωe and a counterstreaming ion‐acoustic wave are generated. Both high‐frequency waves have nearly the same amplitude, which is given by the product of plateau density and velocity. Beating of these two wave types leads to pronounced Langmuir amplitude modulation, in reasonable agreement with solar wind and terrestrial foreshock observations made by the Wind spacecraft.

Langmuir wave in a dusty plasma with nonextensive electrons

The effect of the dust charge perturbation on Langmuir waves in a dusty plasma with nonextensive electrons and Maxwellian ions is investigated within the fluid theory framework, where the sink term of electrons in the continuity equation is considered. The dispersion of Langmuir waves shows that the dust charge relaxation introduces an additional source of dissipation in Langmuir waves. The damping rate of Langmuir oscillation caused by the dust charge fluctuations is bigger than the one with Maxwellian electrons when the nonextensively distributed electrons have a suprathermal tail. On the contrary, the excess of low energy electrons for nonextensively distributed electrons can lower the damping rate of Langmuir oscillation. These differences are mainly due to the modification of the unperturbed electron attachment frequency by the nonextensively distributed electrons. Our results may be of wide relevance to space and interstellar plasmas.

Langmuir oscillations in a nonthermal nonextensive electron-positron plasma

The high-frequency Langmuir-type oscillations in a pure pair plasma are studied using Vlasov-Poisson's equations in the presence of hybrid nonthermal nonextensive distributed species. The characteristics of the Langmuir oscillations, Landau damping, and growing unstable modes in a nonthermal nonextensive electron-positron (EP) plasma are remarkably modified. It is found that the phase velocity of the Langmuir waves increases by decreasing (increasing) the value of nonextensive (nonthermal) parameter, q (α). In particular, depending on the degree of nonthermality and nonextensivity, both damping and growing oscillations are predicted in the proposed EP plasma. It is seen that the Langmuir waves suffer from Landau damping in two different q regions. Furthermore, the mechanism that leads to unstable modes is established in the context of the nonthermal nonextensive formalism, yet the damping mechanism is the same developed by Landau. The present study is useful in the regions where such mixed distributions in space or laboratory plasmas exist.

The effect of zero Langmuir oscillations of an electromagnetic field on the transverse dielectric permittivity of a degenerate electron–ion plasma

It is shown theoretically that the electromagnetic background of longitudinal zero oscillations of a temperature-degenerate electron–ion plasma in a thermodynamic equilibrium state resonantly distorts the wave functions of its electrons. This gives rise to a characteristic quantum frequency that nonanalytically depends on Planck’s constant ℏ. Vacuum phenomena in plasma attributed to zero oscillations turn out to be anomalously large. Quantum corrections to the transverse dielectric permittivity of a degenerate electron–ion plasma, which are nonanalytic with respect to ℏ and are attributed to the zero-point oscillations of the plasma, are determined.