Nonlinear Plasma Oscillations Research Articles

Terahertz-frequency plasmonic-crystal instability in field-effect transistors with asymmetric gate arrays

We present a theory for plasmonic crystal instability in a semiconductor field-effect transistor with a dual grating gate array, designed with strong asymmetry in the elementary cell of this “crystal”. We demonstrate that, under the action of a dc current bias, the Bloch plasma waves in the plasmonic crystal formed in this transistor develop the Dyakonov–Shur instability. By calculating the energy spectrum and instability increments/decrements—which govern the growth/decay of excitations within the plasmonic crystal—we analyze the dependence of the latter on the electron drift velocity and the extent of the structural asymmetry. In contrast with the corresponding problem for gate arrays with symmetric unit cells, the presence of finite plasma instability increments across the entire Brillouin zone is established. This important difference points to the possibility of exciting sustained, radiating, non-linear electron plasma oscillations in the instability endpoint of the asymmetric array. These structures should be readily implementable in common semiconductor heterostructures, using standard nanofabrication techniques, enabling operation at room temperature. Long-range coherence of the unstable plasma oscillations, generated in the elementary cells of the crystal, should dramatically increase the radiated THz electromagnetic power, making this approach a promising pathway to the generation of THz signals.

Approximate solution to a generalized Van der Pol equation arising in plasma oscillations

Motivated by some published theoretical investigations and based on the two-fluid model, nonlinear plasma oscillations are analyzed and discussed in the framework of the generalized Van der Pol equation. This equation is analyzed and solved using two different analytical approaches. In this first approach, the ansatz method is carried out for deriving an approximation in the form of a trigonometric function. In the second approach, the Krylov–Bogoliubov–Mitropolsky (KBM) technique is applied for obtaining a high-accurate approximation. The obtained approximations are compared with the numerical approximation using the Runge–Kutta (RK) method. Moreover, the distance error between the obtained approximations (using the ansatz method and the KBM technique) and the RK numerical approximation is estimated. In our investigation, both the proposed methods and obtained approximations can help many authors investigate several nonlinear oscillations in different plasma models and fluid mechanics.

Wavebreaking amplitudes in warm, inhomogeneous plasmas revisited

The effect of electron temperature on the space–time evolution of nonlinear plasma oscillations in an inhomogeneous plasma is studied using a one-dimensional particle-in-cell code. It is observed that, for an inhomogeneous plasma, there exists a critical value of electron temperature beyond which the wave does not break. These simulation results, which are in conformity with the purely theoretical arguments presented by Trines [Phys. Rev. E 79, 056406 (2009)], represent the first numerical elucidation of the effect of plasma pressure on wave breaking amplitude. The results presented are of relevance to experiments where moderate to large amplitude plasma waves are excited, e.g., laser–plasma interaction experiments.

A coupled pseudoforce model for quantum plasmon excitations

A coupled nonlinear pseudoforce system is derived from hydrodynamic equations for the nonlinear electron plasma oscillations in an electron-ion plasma with arbitrarily degenerate electron fluid in a background fixed ion potential. The dynamics of the fully nonlinear electron plasma excitations are studied using this generalized coupled pseudoforce model including the damping and driving pseudoforce elements. The fully nonlinear plasma oscillations are shown to be of quite different nature in the extreme classical and quantum limits. In particular, high frequency quantum oscillations due to electron tunneling effect modulates the ordinary large amplitude low frequency periodic Langmuir excitations in the quantum plasma regime. It is shown that such characteristic quantum oscillations appear due to the electron wavefunction overlap which also appear on the quantum shock wave structures. It is found that the stimulation of dense plasmas with the driving frequency matching that of characteristic quantum oscillations leads to the chaotic behavior of the electron fluid. The presented coupled pseudoforce theory can be used to investigate a large number of interesting nonlinear phenomena such as the quantum electron fluid chaos and turbulence, autoresonance phenomenon, quantum harmonic generation, nonlinear resonances, and bistability of quantum electron plasma oscillations.

On the inverse problem for Channell collisionless plasma equilibria

Vlasov–Maxwell equilibria are described by the self-consistent solutions of the time-independent Maxwell equations for the real-space dynamics of electromagnetic fields and the Vlasov equation for the phase-space dynamics of particle distribution functions (DFs) in a collisionless plasma. These two systems (macroscopic and microscopic) are coupled via the source terms in Maxwell’s equations, which are sums of velocity-space ‘moment’ integrals of the particle DF. This paper considers a particular subset of solutions of the broad plasma physics problem: ‘the inverse problem for collisionless equilibria’ (IPCE), viz. ‘given information regarding the macroscopic configuration of a collisionless plasma equilibrium, what self-consistent equilibrium DFs exist?’ We introduce the constants of motion approach to IPCE using the assumptions of a ‘modified Maxwellian’ DF, and a strictly neutral and spatially one-dimensional plasma, and this is consistent with ‘Channell’s method’ (Channell, 1976, Exact Vlasov-Maxwell equilibria with sheared magnetic fields. Phys. Fluids, 19, 1541–1545). In such circumstances, IPCE formally reduces to the inversion of Weierstrass transformations (Bilodeau, 1962, The Weierstrass transform and Hermite polynomials. Duke Math. J., 29, 293–308). These are the same transformations that feature in the initial value problem for the heat/diffusion equation. We discuss the various mathematical conditions that a candidate solution of IPCE must satisfy. One method that can be used to invert the Weierstrass transform is expansions in Hermite polynomials. Building on the results of Allanson et al. (2016, From one-dimensional fields to Vlasov equilibria: Theory and application of Hermite polynomials. Journal of Plasma Physics, 82, 905820306, http://doi:10.1017/S0022377816000519), we establish under what circumstances a solution obtained by these means converges and allows velocity moments of all orders. Ever since the seminal work by Bernstein et al. (1957, Exact nonlinear plasma oscillations. Phys. Rev., 108, 546–550) on ‘stationary’ electrostatic plasma waves, the necessary quality of non-negativity has been noted as a feature that any candidate solution of IPCE will not a priori satisfy. We discuss this problem in the context of Channell equilibria, for magnetized plasmas.

A novel numerical scheme for nonlinear electron plasma oscillations

In this work, we suggest an easy-to-code higher-order finite volume semi-discrete scheme to analyze the nonlinear behavior of the electron-plasma oscillations by the direct numerical simulation of electron fluid equations. The present method employs a fourth-order accurate centrally weighted essentially nonoscillatory reconstruction polynomial for estimating the numerical flux at the grid-cell interfaces, and a fourth-order Runge-Kutta method for the time integration. The numerical implementation is validated by reproducing earlier results for both non-dissipative and dissipative cold plasmas. The stability of the present scheme is illustrated by evolving the nonlinear electron plasma oscillations in a cold non-dissipative plasma for hundred plasma periods, which also display a negligible numerical dissipation. Moreover, the fourth-order accuracy of the existing approach is confirmed by evaluating the convergence of errors for nonlinear electron plasma oscillations in a cold non-dissipative plasma.

Influence of Electron Collisions on the Breaking of Plasma Oscillations

The influence of electron collisions on the breaking of plane nonlinear plasma oscillations is analyzed. Numerical calculations by the particle method and analytical consideration in the weakly nonlinear regime show that the breaking time of plasma oscillations increases with increasing electron collision frequency. The threshold value of the electron collision frequency above which no singularity in the electron density arises is found. In this case, the density maximum formed outside the symmetry plane of oscillations, the growth of which in the weakly collisional regime leads to the breaking effect, begins to decrease after some growth because of oscillation damping.

On overturn of two-dimensional nonlinear plasma oscillations

AbstractThe stability problem for spatial structure of plasma oscillations in the process of their dynamics is studied in the paper analytically (by perturbation methods) and numerically. It is shown that if the initial perturbation possesses a local symmetry, then an overturn of oscillations appears simultaneously on a circumference of some nonzero radius. If cross-sections of the initial perturbation of the electron density are ellipses, then a singularity of the electron density appears simultaneously too, but only at two spatial points.The results of calculations performed in the Supercomputing Center ‘Chebyshev’ of Lomonosov Moscow State University using a hybrid parallel code are presented. The results are in a good agreement with analytic calculations and computations with one-dimensional models.

Nonlinear plasma wave in magnetized plasmas

Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic “Four-Ray Star” pattern.

Viscous hydrodynamic model of non-linear plasma oscillations in two-dimensional conduction channels and application to the detection of terahertz signals

In the Dyakonov-Shur detector the plasma resonance in a short channel High Electron Mobility Transistor is used for the resonant tunable detection of terahertz radiation. We derived a viscous hydrodynamic model with temperature dependent transport coefficients for the gated conduction channel. We evaluated the detector response function and obtained the quality factor of the plasma resonance.

Numerical simulation of the breaking effect in nonlinear axially-symmetric plasma oscillations

Numerical simulation of the breaking effect in nonlinear axially-symmetric plasma oscillations

Breaking of nonlinear cylindrical plasma oscillations

Nonlinear axisymmetric cylindrical plasma oscillations are investigated analytically and numerically. It is shown that the breaking of strongly nonlinear oscillations is attributed to a singularity in the electron density and occurs several periods after the onset of an off-axis density maximum. For weakly nonlinear conditions, an analytic dependence of the breaking time of the oscillations on their amplitude is obtained based on the effect of intersection of electron trajectories and is shown to agree with numerical results.

Nonlinear oscillations in a cold dissipative plasma

Recently, it has been shown that when viscosity and resistivity is included in the cold plasma model, nonlinear plasma oscillations exhibit a new nonlinear effect in the form of splitting of density peak [Infeld et al., Phys. Rev. Lett. 102, 145005 (2009)]. Infeld et al. have analytically derived this result for a specific model of viscosity as 4/3νe=ν[n0/ne(x,t)]. In a realistic case however, electron viscosity has a relatively weak dependence on density through Coulomb logarithm. In this work, first Infeld’s result is numerically extended for the more realistic case where electron viscosity is chosen to be independent of density and second an alternative electron dissipative mechanism is studied by substituting viscosity with hyperviscosity. In both cases, results are found to be qualitatively similar to Infeld et al.

Fluid Turbulence in Quantum Plasmas

Nonlinear fluid simulations are developed by us to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a very dense Fermi (quantum) plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations (EPO) is determined critically by a ratio of the energy density of the EPOs and the electron kinetic energy density of quantum plasmas. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory.

Phase mixing due to ion motion and relativistic effects in nonlinear plasma oscillations

Nonlinear electron plasma oscillations in a cold-plasma have been studied numerically using one-dimensional (1D) Vlasov–Poisson equations. It is shown that both ion motion and the relativistic effect of electron motion can lead to phase mixing phenomena even if a plasma oscillation is at a moderate amplitude. When its amplitude is relatively small, the phase mixing is mainly caused by the ion motion. When its amplitude is large, the relativistic effect of electrons is dominant. The nonlinear process caused by the relativistic effect depends significantly upon the phase velocity of the plasma oscillation, while that caused by the ion motion depends weakly upon its phase velocity.

Nonlocal electrodynamics of fluxons and nonlinear plasma oscillations in a distributed Josephson junction with electrodes of arbitrary thickness

We considered a distributed Josephson junction formed by superconducting plates of arbitrary thickness in the case of high critical current density when Josephson penetration depth ${\ensuremath{\lambda}}_{j}$ is less than London length ${\ensuremath{\lambda}}_{L}$. A nonlocal equation describing electrodynamics of such a junction in nondissipative approximation is derived. The soliton-like excitations of kink type (fluxons) and of breather type are studied. It is shown that the role of nonlocality is crucial for the dynamical properties of these entities: if the nonlocality is strong enough, fluxons can lose their mobility. Interactions between fluxons in the nonlocal model are studied. It is shown that for some interval of fluxon velocities and for some parameters of the junction the interactions are of solitonic type. Also the interaction may result in the emergence of a robust and long-living oscillating state of breather type. These states are studied separately using the approximation of the solution profile by one temporal Fourier harmonic.

Effects of electron depletion on nonlinear dusty plasma oscillations

A kinetic analysis of the excitation of dust BGK (Bernstein–Greene–Kruskal) modes in a noncollisional dusty plasma is presented. It is found that in the case where all the electrons are attached to the dust particles, consequent modifications in the electrostatic potential structure can significantly influence the existence and properties of the nonlinear BGK modes. The derivation goes parallel to that done in standard kinetic analysis.

Nonlinear response of two-dimensional electron plasmas in the conduction channels of field effect transistor structures

The response of an electron gas in a quasitwo-dimensional conduction channel depends on a characteristic frequency ω0, defined as the ratio of the plasma wave velocity to the channel length. For a short-gate high electron mobility transistor ω0 can be in the terahertz range. We have used a self-consistent hydrodynamic model of the confined electron plasma to show that significant nonlinear effects are present in its response to harmonic signals at microwave frequencies much lower than ω0. We obtain the oscillatory time dependence of the terminal currents and study the interior dynamics of the electron plasma. We find that in certain device parameter ranges the essential nonlinearity in the microwave response may lead to nonlinear hydrodynamic effects, such as shock wave propagation in the conduction channel. When the boundary conditions at the source and drain terminals are asymmetric, the nonlinear plasma oscillations result in a nonzero dc component of the terminal current, which could be measured by using standard microwave circuits.

Phase Mixing of Nonlinear Plasma Oscillations in an Arbitrary Mass Ratio Cold Plasma

Nonlinear plasma oscillations in an arbitrary mass ratio cold plasma have been studied using 1D particle-in-cell simulation. In contrast to earlier work for infinitely massive ion plasmas it has been found that the oscillations phase mix away at any amplitude and that the rate at which phase mixing occurs depends on the mass ratio ( $\ensuremath{\Delta}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}m}_{\ensuremath{-}}/{m}_{+}$) and the amplitude. A perturbation theoretic calculation carried up to third order predicts that the normalized phase mixing time ${\ensuremath{\omega}}_{p\ensuremath{-}}{t}_{\mathrm{mix}}$ depends on the amplitude $A$ and the mass ratio $\ensuremath{\Delta}$ as $\ensuremath{\sim}[({A}^{2}/24)(\ensuremath{\Delta}/\sqrt{1+\ensuremath{\Delta}}){]}^{\ensuremath{-}1/3}$. We have confirmed this scaling in our simulations. These cold plasma results may have direct relevance to recent experiments on superintense laser beam plasma interactions with applications to particle acceleration, fast ignitor concept, etc.

Frequency Increase and Damping of Nonlinear Electron Plasma Oscillations in Cylindrical Symmetry

Radial electron plasma oscillations excited by a laser wake field are measured by frequency domain interferometry. In the nonlinear regime we observe two important effects: (i) an increase of the oscillation frequency and (ii) the damping of the oscillation in a few plasma periods. Simulations show that this last effect is related to the presence of a steep radial density gradient near the focus edge. {copyright} {ital 1997} {ital The American Physical Society}