Longitudinal Plasma Waves Research Articles

Plasma Wave Echo Excited by Two Cyclotron Waves

It is shown that two cyclotron waves excited with a time interval τ between them, in a collisionless plasma, lead to a longitudinal plasma wave echo. The echo appears at the same time as in the case of excitation by two plasma waves.

PARAMETRIC EXCITATION AND QUENCHING OF LONGITUDINAL PLASMA WAVES

General conditions of parametric excitation and parametric quenching of the longitudinal plasma waves involving negative energy wave(s) are derived by expressing the growth rate of these waves in terms of quantities involving only the linear plasma conductivities and the amplitude of density modulation by the pump.

Collisional Absorption and Emission of Longitudinal Waves in a One-Dimensional Plasma

Collisional absorption and emission of longitudinal waves in a one-species, one-dimensional plasma are investigated by numerical experiments. The theory of Birmingham, Dawson, and Kulsrud for longitudinal bremsstrahlung is extended to the one-dimensional case. The results of the numerical experiments are found to be in agreement with the theory. Low-frequency electric field fluctuations for long-wavelength modes are also found and are associated with the random motion of the particles.

Microwave Scattering from Plasma Waves

Experimental studies of the scattering of electromagnetic waves (34 GHz) from longitudinal plasma waves (250-500 MHz) are described. The plasma waves propagate in a 230-cm-long collisionless plasma column, having an electron density on axis of ne0 = 2.7 × 109cm−3 and an electron temperature Te ≈ 13 eV. Scattering was observed both from plasma waves launched by a probe antenna and from waves grown up to a nonlinear saturation out of the white noise background by resonant interaction with an electron beam. The properties of these waves are accurately determined by auxiliary measurement. By using movable antennas we are able to measure the spatial growth and damping coefficients of plasma waves and to measure their absolute amplitudes. The microwave scattering is observed at a frequency displaced from the microwave frequency by the plasma wave frequency, and at an angle related to the Bragg angle. The measured frequency spectrum, angular dependence, and scattering amplitudes are compared with the theory and with rf probe measurements, giving excellent agreement in all cases.

Radio frequency properties of a plane grid capacitor immersed in a hot collision-free plasma

A pair of plane parallel grids is inserted in a hot plasma, and an oscillatory voltage is applied across them. The electric field excited in the plasma, and the complex admittance of the grid/plasma system, are computed for applied frequencies high enough to justify neglect of ion response. The grids are electrically, but not mechanically, coupled to the plasma, which is assumed to be in a spatially uniform collision free Maxwellian equilibrium state. The field is computed as a function of distance from the grid plates over a range of frequencies covering the plasma frequency, and the complex admittance of the system is computed as a function of frequency at various grid separation distances. The real component of the field and the capacitive component of the admittance are subject to three major effects: cold plasma dielectric behaviour, oscillatory Debye sheaths on the grids, and (above the plasma frequency), longitudinal plasma waves. The imaginary field component and the conductive admittance component are produced by spatial Landau damping. In an accompanying paper (Freeston 1968), the computed admittance is compared with laboratory measurements made in a situation approximating well to the idealized problem considered here.

Observation of Plasma Wave Echoes

Experimental observation of a new nonlinear plasma phenomenon, the plasma wave echo, is reported. A recent theory predicts that if a longitudinal electron plasma wave is excited at one position in a collisionless plasma and Landau damps away, and a second wave is excited at another position and also damps away, then a third wave (i.e., the echo) will spontaneously appear at a third position. The existence of various echoes, associated with various orders of the perturbation theory, is demonstrated experimentally. The echoes appear at the predicted position in the plasma. The frequency of the echo wave and the dependence of its amplitude on the amplitude of the initial wave are also in agreement with the theory. Experimental data on the saturation of echo amplitude with increasing initial wave amplitude and increasing distance are given. Data are also presented on another new, but related, phenomenon “the sheath echo.”

Dispersion Relations in Relativistic Vlasov Plasmas

The complete solution, for all temperatures and wavenumbers, of the longitudinal and transverse dispersion equations of a relativistic Maxwellian plasma, is presented. It is assumed that the ions are immobile and that there is no zero-order magnetic field. Analytical methods are used for the very small and very large wavenumber cases, and in the intractable intermediate wavenumber regions numerical results are displayed graphically. The existence at all temperatures of very slightly damped longitudinal plasma waves and slightly damped nonoscillatory transverse excitations is established and the damping constants are evaluated. Necessary and sufficient conditions for the existence of slight Landau damping of longitudinal plasma waves in any general isotropic relativistic Vlasov plasma are also derived. Several new dispersion relations for undamped oscillations, which have phase velocity greater than c, are recorded. One of these, which describes transverse oscillations for large wavenumbers, corresponds to the propagation of light waves in the plasma.

Brillouin scattering in plasmas as applied to ionospheric irregularities

Theory of Brillouin scattering in plasmas, i.e., nonlinear interaction of electromagnetic waves with longitudinal (plasma) waves, is developed and applied to the ionospheric irregularities produced by a plasma instability. As a result, characteristic features appearing in VHF radar echoes from the equatorial E region seem to be plausibly explained. Above all, it is found that the main peak echoes and the small image echoes are well interpreted as arising from the phase-matched and mismatched scatterings by unstable ion-acoustic waves, respectively. Furthermore, Dougherty and Farley's interpretation of broad spectra at low frequencies is criticized, and an alternative interpretation is made by introducing another instability, i.e., cross-field instability.

A note on the two-stream instability

Conditions for the instability of longitudinal waves in a single-component two-stream plasma, in which the streams have the same velocity spread, are given in the form of simple relations between the density ratio and the mean velocity difference of the streams.

Interaction between longitudinal and transverse plasma waves

The rate at which energy is fed into the transverse waves due to interaction with longitudinal waves is calculated for the case of an infinite, homogeneous, isotropic, collisionless plasma. The method is based on constructing the Hamiltonian for the system in terms of creation and annihilation operators of second quantization. It turns out from the Hamiltonian that the dominate mechanism is the one in which two longitudinal waves collide to yield one transverse wave. Thus, in general, the energy transfer rate decreases with time. In a special case the results agree with the previous work (Aamodt and Drummond 1964).

Coupling of plasma oscillations to ion sound waves

The interaction between high frequency longitudinal plasma waves and the low frequency ion-sound wave is investigated. The rate of energy transferred to an ion-sound wave has been calculated and compared with the non-linear interaction between longitudinal and transverse waves.

Waves in Collisionless Plasmas. II: Longitudinal Waves

The problem of longitudinal waves in an infinite one-dimensional plasma is treated by expressing the charge density in terms of the exact solution of the collisionless Boltzmann equation and then solving Poisson's equation. For an initially homogeneous plasma the electric field is determined exactly. For an initially inhomogeneous plasma an iterative procedure is developed which in principle determines the electric field for an arbitrary initial inhomogeneity. If the initial inhomogeneity is small with respect to the homogeneous part of the distribution function the problem can be treated by perturbation theory. To each order the field is found to obey a linear integral equation which is readily solved in terms of a Green's function, Γ(z, t), which maps the known nth-order source function into the nth-order field. For t ≠ 0, the Fourier transform of Γ(z, t) is a sum of damped oscillations whose complex frequencies are determined for all 0 < t < ∞ by the plasma-dispersion relation. A general procedure for solving this dispersion relation is developed. For a Maxwellian plasma an infinite number of frequencies are determined for large k in addition to the usual Landau results for small k. A physical interpretation of Landau damping is developed which explains the decrease of E with time in terms of the drifting dispersal of an initially localized inhomogeneity.

Comments on "Longitudinal Waves in a Hot-Nonuniform Plasma" (Correspondence)

Comments on "Longitudinal Waves in a Hot-Nonuniform Plasma" (Correspondence)

Landau Damping and Growth of Electrostatic Modes with Effects of Spatial Variation

For a plasma with finite cross section of the sort which occurs typically in laboratory plasma waves experiments, in a constant magnetic field, the Landau damping (or growth) is obtained by a perturbation procedure in terms of the plasma velocity distribution function and potential and density profiles. The result is applied to the damping associated with the upper and lower branches of the dispersion curve for longitudinal electron plasma waves in the case of a Maxwellian velocity distribution in slab and cylindrical geometries. Application is also made to the growth rates resulting from a low-density electron beam with radially dependent energy superposed on a Maxwellian.

General dispersion relations for linear waves in multicomponent plasmas

The usual linearization technique for the treatment of plane waves propagating through an infinite and homogeneous plasma is applied to the equations of motion, describing a plasma consisting of N different species of particles. The dispersion formula thus obtained is discussed at length for some special positions of the external magnetic field (zero, parallel and perpendicular to the wave vector). It is shown how the number N of components of the plasma has no qualitative influence on the transverse electromagnetic waves. The possible number of longitudinal plasma waves, however, is increased. A comparison between a one-, a two- and a multi-component description of a plasma is made and indicates a preference for a more component theory. Some attention is given to the time-damping of the waves as a result of collisions.

Plasma Thermal Conductivity with Collective Effects

The electron thermal conductivity of a fully ionized Lorentz gas has been studied. The energy transfer among regions of the gas at different local temperatures has been determined by considering the emission and absorption of longitudinal plasma waves. These waves are both collision and Landau damped; the latter type of damping effects the energy transfer only secondarily, since the resulting energy does not go directly into the heating of the gas. The results obtained by assuming infinite Landau damping are expected to agree with typical two-body collision treatments. However a non-vanishing plasma parameter, which results in finite Landau damping, facilitates the introduction of a variety of collective effects. Thus, it is found that, beyond the dependences obtained in conventional two-body collision studies, the thermal conductivity exhibits an additional weak dependence on the plasma parameter.

Relativistic Contribution to Landau Damping

Using the collisionless Boltzmann equation, we study the asymptotic time behavior of longitudinal waves in a one-dimensional plasma of relativistic electrons and stationary ions. The electronic distribution function is assumed to be a perturbed Maxwell-Boltzmann distribution.

Wave Propagation along Warm Plasma Columns

Dispersion relations for waves propagating along homogeneous, isotropic, warm plasma columns surrounded by a dielectric medium are obtained. A steady-state linearized model with temperature introduced through a scalar pressure is analyzed both quasistatically and more rigorously from Maxwell's equations. The results show effects of temperature on the cold plasma surface wave and predict a new series of propagating modes above the plasma frequency related to the Tonks-Dattner scattering resonances near cutoff and to the Bohm-Gross longitudinal plasma waves for large wave numbers. Warm and cold plasmas, large and small columns, and quasistatic and rigorous predictions are contrasted. Regions of the Brillouin diagram corresponding to different bound and radiating wave types are delineated and related to their physical properties.

Ion Waves on Bounded Plasmas

Ion acoustic waves propagating along a cylindrical plasma column are studied theoretically. By neglecting the ion temperature, it has turned out possible to derive a simple boundary condition at the plasma surface. In addition to the infinite number of ion wave modes which degenerate into purely longitudinal waves in an infinite plasma, it is found that there exists a surface mode which is the ion equivalent of the electron surface mode of Gould and Trivelpiece. It is also shown that due to interaction between the ion modes and the Gould and Trivelpiece mode the dispersion curves of the ion waves are strongly modified.

Coupling of Ion-Acoustic to Neutral-Acoustic Waves at a Diffuse Boundary

The coupling of ion-acoustic (longitudinal plasma) waves to neutral-acoustic (sound) waves is treated at a diffuse boundary consisting of a partially ionized plasma of spatially varying composition. Collisions among the electrons, ions, and neutrals are represented by linear velocity terms. The effect of collisions is shown, for low frequencies, to give rise to coupling between an ion—electron (plasma) mode and a neutral (sound) mode. An approximate coupling coefficient is derived, based on an assumed analytic form for the ion—neutral collision frequency.