Nonlinear Plasma Oscillations Research Articles

Van der Pol behavior of relaxation oscillations in a periodically driven thermionic discharge.

The nonlinear dynamics of the frequency entrainment process in periodically driven, self-oscillating thermionic discharges is investigated experimentally. The periodically interrupted frequency entrainment process, known as periodic pulling, is demonstrated to be an essential feature of the transition region between the quasiperiodic state and the entrained state. A detailed comparison of experimental findings with the analytical and numerical study of the driven van der Pol equation x\ifmmode\ddot\else\textasciidieresis\fi{}-\ensuremath{\epsilon}(1-\ensuremath{\beta}${\mathit{x}}^{2}$)${\mathrm{\ensuremath{\omega}}}_{0}$x\ifmmode \dot{}\else \.{}\fi{}+${\mathrm{\ensuremath{\omega}}}_{0}^{2}$x=${\mathrm{\ensuremath{\omega}}}_{0}^{2}$E cos(${\mathrm{\ensuremath{\omega}}}_{\mathit{i}}$t) confirms the relevance of this dynamical model for nonlinear plasma oscillations. A physical explanation is developed based on results from particle-in-cell simulations of periodic pulling in thermionic discharges.

Non-Abelian screening and colour oscillations in a quark gluon plasma

Certain non-perturbative aspects of collective dynamics of quark-gluon plasmas in which quarks and gluons interact self-consistently through strong forces and the associated Yang-Mills field equations have been studied using classical chromohydrodynamic equations. Several novel non-abelian phenomena such as a weakened screening of moving test charges, a new branch of non-linear cold plasma oscillations, collective stopping and transverse flow generation by filamentation instability in colliding nuclei etc have been investigated for the first time.

Wave breaking in cold plasma

Strongly nonlinear plasma oscillations in a cold plasma are investigated in the wave breaking regime using the two-fluid model. The electrons are described in Lagrangian coordinates; the ions are described by the usual Eulerian coordinates. The model is extended to describe the motion after wave breaking has occurred. Numerical solutions are followed up to and beyond wave breaking for both driven and undriven cases. In a driven cold plasma, the plasma waves are excited from fluctuations by the modulational instability, growing to very large amplitudes, which leads to wave breaking. For the undriven cold plasma, large initial perturbations are assumed, which also lead to wave breaking. Multistreams and the generation of fast electrons are observed for both cases after wave breaking.

On stability of strongly nonlinear plasma oscillations

The modulational instability of finite-amplitude, longitudinal, nonlinear plasma oscillations in a cold plasma is discussed. Stable and unstable regimes appear alternatively as the wave nonlinear parameter ε varies. A possible laboratory experiment that may confirm this result is suggested.

Interaction of highly relativistic short laser pulses with plasmas and nonlinear wake-field generation

Generation of nonlinear plasma oscillations by intense short laser pulses is considered. It is shown that longitudinal plasma waves with relativistic amplitudes and phase velocities close to the speed of light c can be excited in the wake of a strong single laser pulse in a cold plasma. The analytical as well as numerical studies of the relativistic wake-field generation by the laser pulses with realistic shapes are carried out. The nonlinear scheme of the laser wake-field accelerator is suggested. It is found that the maximum amplitude of the excited plasma waves is to be expected at the wave phase velocity vp < c and not at vp ≃ c. A second laser pulse sent after the first one is considered and shown that this trailing pulse can both amplify and "absorb" the wake-field created by the first laser pulse. Applications of our results to the proposed Livermore High-Brightness Lasers are discussed.

Relativistic wake-field generation by an intense laser pulse in a plasma

Generation of nonlinear plasma oscillations by an intense laser pulse is considered. It is shown that longitudinal plasma waves with relativistic amplitudes and phase velocities close to the speed of light c can be excited in the wake of a strong single laser pulse in a cold plasma. An analytical and numerical study of the relativistic wake-field generation by laser pulses with realistic shapes is carried out. A nonlinear scheme of the laser wake-field accelerator is suggested.

Langmuir oscillations against a single-ion pulse or cavity background.

Nonlinear plasma oscillations against a background supporting an ion pulse or cavity are considered. We treat two physical cases. The first is that of a cold plasma, the second of a cold-ion--warm-electron plasma. The ion background includes a hyperbolic-secant-squared pulse or cavity but is otherwise uniform. An exact solution is obtained for the cold-plasma case. Infinite electric-field gradients result after some time, followed by a three-valued electric field, a physical impossibility. Thus some modification is called for. When the electrons are assumed to be thermal these infinite gradients can be limited. This will be the case if the ratio of pulse strength to background density is less than ${\ensuremath{\gamma}}^{1/3}$(${\ensuremath{\lambda}}_{\mathit{D}}$/l${)}^{2/3}$, where ${\ensuremath{\lambda}}_{\mathit{D}}$ is the Debye length and l a characteristic width of the pulse. Applications are briefly discussed.

Wavebreaking of longitudinal plasma oscillations

A general treatment for obtaining the maximum amplitude for nonlinear plasma oscillations is given. Both temperature and relativistic effects are included. The maximum or wavebreaking amplitude is derived for cold plasmas and nonrelativistic fluid velocities, cold plasmas and relativistic fluid velocities, warm plasmas and nonrelativistic fluid velocities and, warm plasmas and relativistic fluid velocities. The various derivations which appear in the literature are unified.

Ion density cavities can cause nonlinear plasma oscillations to peak.

In this Letter an exact solution for nonlinear cold-electron plasma oscillations against a periodic ion background is found. The main difference with respect to the known solution corresponding to a uniform ion background is that, after a while, electron density peaks will appear. This phenomenon, which was forseen in general terms by Dawson, has possible practical implications which are indicated briefly. A thermal limitation on the peaks is given.

Nonlinear oscillations in a warm plasma.

Nonlinear electron plasma oscillations in a warm plasma are studied by use of Lagrangean coordinates. Without recourse to amplitude expansion, the electron density is obtained as an explicit function of space and time. In the zero-temperature limit, a restriction on the previously found cold-plasma solutions is found.

Nonlinear plasma dynamics in the plasma wake-field accelerator.

Excitation of nonlinear plasma oscillations by an intense ultrarelativistic electron beam is considered. It is shown, by analytical solutions of the one-dimensional relativistic fluid equations, that under certain conditions on the relative electron beam and plasma densities extremely large longitudinal electric fields can be generated in the beam's wake. This scheme is a nonlinear version of the plasma wakefield accelerator, and is predicted to have advantages over the linear regime.

Nonlinear Plasma Dynanics in the Plasma Wakefield Accelerator

Excitation of nonlinear plasma oscillations by an ultrarelativistic electron beam is considered in this paper. It is shown, by analytical solutions of the fully relativistic nonlinear fluid equations in one dimension, that under certain conditions on the relative densities of the electron beam and the plasma, extremely large longitudinal electric fields can be generated in the wake of the beam. This scheme can be considered as a nonlinear regime of the plasma wakefield accelerator (PWFA), and is seen to have the advantage that the transformer ratio, the ratio of the maximum amplitude of the accelerating field behind the driving beam over the maximum amplitude of the decelerating field inside of the beam, can be made arbitrarily large, dependent only on the length of the driving beam. The effects of beam loading on the efficiency of this scheme are considered, and are shown to be equivalent to those predicted in the linear regime.

Motion of an electron bunch through a plasma

The motion of a tenuous bunch of fast electrons through an isotropic plasma has been studied using a one-dimensional Vlasov code [J. Comp. Phys. 27, 315 (1978)]. Given a fairly large initial perturbation from equilibrium, the moving bunch sheds a train of nonlinear plasma oscillations, which appear to be sustained by a mild instability.

Linear and nonlinear plasma oscillations

Linear and nonlinear plasma oscillations

Aspects of transformation to the space-independent frame for nonlinear wave processes in plasmas. I. Cold plasmas

Transformation of nonlinear plasma equations to a space-independent frame with the help of the Lorentz transformation gives in place of partial differential equations a set of ordinary differential equations in a single independent variable for solution of nonlinear field equations. In this paper, this transformation has been used to yield the nonlinear precessional rotation of electromagnetic waves in plasmas in addition to the nonlinear shift in a wave parameter. Moreover, the Lagrangian and Hamiltonian of motion for a circularly polarised wave have been transformed to the space-independent frame and the equations of Akhiezer and Polovin (1956) for nonlinear plasma oscillations have been rectified by making them relativistically correct.

Some aspects of transformation of the nonlinear plasma equations to the space-independent frame

Abstract Nonlinear field equations for a cold plasma are transformed from the laboratory frame to the space-independent frame for a transverse wave using a special Lorentz transformation. With the help of this transformation a set of partial differential equations can be reduced to a set of ordinary differential equations in a single independent variable. The equations of Akhiezer and Polovin for nonlinear plasma oscillations have been generalized and the results of Arons and Max and others for the wave number shift and the precessional rotation of a strong electromagnetic wave are recovered by analytically finding the nonlinearly developed birefringence effect in a cold, relativistic, collisionless unmagnetized plasma.

Effect of ion dynamics on relativistic nonlinear plasma oscillations

A general dispersion relation is derived for relativistic nonlinear plasma oscillations in a cold electron-ion plasma. Travelling wave solutions for arbitrary wave amplitudes, wave velocities, and plasma stream velocities are obtainable by adjusting a dynamic parameter appropriately. The solution of the problem can be reduced to two equations relative to conservation of energy and momentum of the system. Approximate analytical solutions and exact numerical solutions of the general dispersion relation are presented.

Time behavior of nonlinear plasma oscillations

The time behavior of a single weakly damped electron mode is analyzed. Analytic expressions for the time‐dependent mode damping and frequency shift equivalent to those of O’Neil and to those of Morales and O’Neil are obtained, but in a much simpler form since there are no sums.

Ionic processes in excitable membranes

The dynamical theory of ionized media is applied to the semi-electrolyte component of an excitable cell membrane, and the adjacent electrolytes. The equations of conservation of charge and momentum for the ions, and Poisson's equation for the electrostatic potential, are applied first to investigate the steady states of the membrane, and then transient effects in the membrane. A dispersion equation is derived, and the characteristic modes of relaxation within the membrane are determined. Among these are oscillating modes whose frequencies and amplitudes are of the correct order of magnitude to explain the observed excitation phenomena. A pair of coupled non-linear equations in the ionic potentials, with action potential solutions, is derived from the time-dependent electrodiffusion equations, and calculations are presented which model the behaviour of the excitable membrane during the voltage clamp. It is not necessary to postulate large changes in the ionic permeabilities in the course of the action potential and the voltage clamp to account for the large transient membrane conductances. It is suggested that the sodium hypothesis be replaced by one which attributes the action potential to non-linear plasma oscillations.

Cold plasma wavebreaking in the presence of an electromagnetic driver

Nonlinear electron plasma oscillations driven by an electromagnetic wave are investigated. An improved, self-consistent Lagrangian description of the resonant interaction is derived. The modifications to the simple capacitor plate or uniform electrostatic driver model previously employed are calculated and shown to have a negligible effect on the wavebreaking process for laser intensities I&amp;lt;1017 W cm−2 in the case of Nd lasers.