Electron Plasma Frequency Ωp Research Articles

Electromagnetic radiation from upper-hybrid wave turbulence in inhomogeneous solar plasmas

Type III solar radio bursts have been commonly observed in the solar wind and coronal plasmas. Electron beams accelerated in the Sun’s atmosphere generate weakly magnetized Langmuir (upper-hybrid) wave turbulence producing in turn electromagnetic emissions at the electron plasma frequency ωp and its harmonic 2ωp, via successive processes involving interactions between the background plasma, the waves and the beam particles. The impact of the random density fluctuations inherent to the background plasma on these processes requires the development of novel approaches and models. Owing to a new theoretical modeling, the radiation efficiency of electromagnetic waves radiated at ωp from a plasma source with random density fluctuations and developed upper-hybrid wave turbulence is calculated analytically and numerically. It is shown that the maximum radiation efficiency at frequency ωp scales as the average level of density fluctuations and as the ratio (c/vT)–2 (where vT is the thermal velocity). These scaling laws are found owing to two different and novel methods of determination of the electromagnetic radiation by turbulent inhomogeneous plasma sources through waves’ transformations on randomly fluctuating density irregularities. These results contribute significantly to the understanding of the processes involved in the generation of Type III solar radio bursts. Their presentation is preceded by a summary of previous studies on the dynamics of beam-driven Langmuir turbulence in inhomogeneous solar plasmas.

Kinematics of electrostatic 3-wave decay of generalized Langmuir waves in magnetized plasmas

The decay of generalised Langmuir waves L into backscattered (generalised) Langmuir waves L and ion acoustic waves S or ion cyclotron waves IC, represented by L→L′+S and L→L′+IC, is a fundamental nonlinear process relevant to beam-plasma instabilities in space and laboratory plasmas and to multiple solar system radio emissions. Both magnetization and arbitrary wavevector directions are included for the generalised Langmuir waves, thereby naturally encompassing both conventional Langmuir waves and upper hybrid waves. A recent 1D analysis for L waves with wavevectors closely parallel to the ambient magnetic field B0 in weakly magnetized plasma (angular electron cyclotron frequency Ωe much less than the angular electron plasma frequency ωp) showed that the electrostatic (ES) decay L→L′+S persists for kL<k0, reversing the old prediction based on the unmagnetized dispersion relation. Here, the kinematics for the processes L→L′+S and L→L′+IC are derived in 2 dimensions for approximately electrostatic waves in arbitrary magnetized plasmas and for all wavevector orientations relative to B0. ES decay processes are shown to exist in both weakly and strongly magnetized plasmas and, under most circumstances, for arbitrary L-wavevector directions, including close to perpendicular to B0, and wavenumbers. For L-wavenumbers kL≳2k0, the decay process is very similar to the standard unmagnetized decay for kL close to parallel with B0, proceeding primarily as a backscatter to kL′≈(kL−k0)kL/kL and a trivial forward-scatter solution with kL≈kL. (Here, k0=2ωpvS/3Ve2, VS is the ion acoustic speed, and Ve is the electron thermal speed.) In addition, the decay persists for kL<k0 to very small kL′≈k*=(ωp/c)(1+fp/fce)−1/2 for arbitrary magnetizations and orientations of kL relative to B0, at least for sufficiently large ion-to-electron temperature ratios Ti/Te. Thus, once magnetization effects are included, the decay is kinematically allowed for essentially all initial wavevectors and can proceed for the very fast beams (with kL<k0) for which modulational instability and not ES decay was previously expected to dominate the nonlinear evolution.

Electron acceleration in a warm magnetized plasma-filled cylindrical waveguide

The effect of plasma-electron collision and their thermal motion is investigated on the externally injected electron in a warm magnetized plasma-filled cylindrical waveguide of cross section of 13.68 cm2. The numerical results are presented for the external electron-energy gain and its trajectory in a nonrelativistic γe=1 and stationary v0=0 warm magnetized plasma-filled waveguide. Results shows that for an electron-cyclotron frequency ωc greater than the electron-plasma frequency ωp, a 100 keV electron acquires a 1.74 MeV energy in a 2.5 cm distance for plasma density n0=1.08×1017/m3, magnetic field B0=0.193 T, microwave frequency f=7.64 GHz, plasma-electron thermal velocity vth=0.2c, and plasma-electron collision frequency ν=4 GHz, which is lower than the 7 MeV electron energy in a cold magnetized plasma-waveguide case. Space-charge effects and other nonlinear effects are assumed to be negligible in this model.

Oscillating two stream instability of a plasma wave in a negative ion containing plasma with hot and cold positive ions

An oscillating two-stream instability (OTSI) is investigated in plasma, which has hot and cold positive ions, negative ions, and the electrons. For this, a long wavelength plasma wave is considered to be driven by two copropagating lasers with frequencies ωL1 and ωL2, such that their difference is almost equal to the electron plasma frequency ωp. In the present mechanism, this plasma beat wave (ωb, kb) is taken to grow in amplitude, so that it becomes susceptible to the OTSI and produces a low frequency electrostatic mode (ω, k), and two shorter wavelength Langmuir wave sidebands (ω1, k1) and (ω2, k2) with ω1 = ω − ωb, ω2 = ω + ωb, k1 = k − kb, and k2 = k + kb in the plasma. The effects of charge number Z, mass, temperature, and density of the ions are studied on the growth rate of the instability, and the amplitudes and phases of the sideband waves generated during the OTSI. It is found that the effects of charge number and mass of the ions are significant on the instability.

Plasma Absorption Probe Measurement of Electron Density of Processing Plasmas.

This paper reviews a novel and simple technique for measuring electron density using a plasma absorption probe (PAP). The PAP enables the measurement of local absolute electron density even when the probe surface is soiled with processing plasmas. The technique relies on the absorption of surface waves (SWs) resonantly excited around the probe head at critical frequencies which depend on the electron density. The PAP consists of a small antenna connected to a coaxial cable and is enclosed in a tube of dielectric constant εd inserted in a plasma of electron plasma frequency ωp. A network analyzer feeds a rf signal to the antenna and displays the frequency dependence of the power absorption. A series of resonant absorptions is observed at frequencies slightly above the SW resonance frequency, ωSW = ωp/(1+εd)½, which allows us to determine the electron density. Typical examples of measured PAP data and future challenges are presented.

Large-scale numerical simulations of ion beam instabilities in unmagnetized astrophysical plasmas

Collisionless quasiperpendicular shocks with magnetoacoustic Mach numbers exceeding a certain threshold are known to reflect a fraction of the upstream ion population. These reflected ions drive instabilities which, in a magnetized plasma, can give rise to electron acceleration. In the case of shocks associated with supernova remnants (SNRs), electrons energized in this way may provide a seed population for subsequent acceleration to highly relativistic energies. If the plasma is weakly magnetized, in the sense that the electron cyclotron frequency is much smaller than the electron plasma frequency ωp, a Buneman instability occurs at ωp. The nonlinear evolution of this instability is examined using particle-in-cell simulations, with initial parameters which are representative of SNR shocks. For simplicity, the magnetic field is taken to be strictly zero. It is shown that the instability saturates as a result of electrons being trapped by the wave potential. Subsequent evolution of the waves depends on the temperature of the background protons Ti and the size of the simulation box L. If Ti is comparable to the initial electron temperature Te, and L is equal to one Buneman wavelength λ0, the wave partially collapses into low frequency waves and backscattered waves at around ωp. If, on the other hand, Ti≫Te and L=λ0, two high frequency waves remain in the plasma. One of these waves, excited at a frequency slightly lower than ωp, may be a Bernstein–Greene–Kruskal mode. The other wave, excited at a frequency well above ωp, is driven by the relative streaming of trapped and untrapped electrons. In a simulation with L=4λ0, the Buneman wave collapses on a time scale consistent with the excitation of sideband instabilities. Highly energetic electrons were not observed in any of these simulations, suggesting that the Buneman instability can only produce strong electron acceleration in a magnetized plasma.

Plasma Absorption Probe for Measuring Electron Density in an Environment Soiled with Processing Plasmas

In this paper, we describe a novel and simple technique for measuring electron density using a plasma absorption probe (PAP). PAP enables us to measure the local absolute electron density even when the probe surface is soiled with processing plasmas. The technique relies on the resonant absorption of surface waves (SWs) excited in a “cavity” at the probe head. The PAP consists of a small antenna connected with a coaxial cable and is enclosed in a tube (dielectric constant ε) inserted in a plasma (electron plasma frequency ωp). A network analyzer feeds a rf signal to the antenna and displays the frequency dependence of the power absorption. A series of resonant absorptions are observed at frequencies slightly above the SW resonance frequency, ωSW = ωp/(1+ε)1/2, which allows us to determine the electron density. The measured electron densities are in good agreement with the data obtained by the plasma oscillation method.

Analytic expressions for mode conversion in a plasma with a parabolic density profile: Generalized results

This study provides an analytic solution to the general problem of mode conversion in an unmagnetized plasma. Specifically, an electromagnetic wave of frequency ω propagating through a plasma with a parabolic density profile of scale length Lp is examined. The mode conversion points are located a distance Δ0 from the peak of the profile, where the electron plasma frequency ωp(z) matches the wave frequency ω. The corresponding reflection, transmission, and mode conversion coefficients are expressed analytically in terms of parabolic cylinder functions for all values of Δ0. The method of solution is based on a source approximation technique that is valid when the electromagnetic and electrostatic scale lengths are well separated. For large Δ0, i.e., (cLp/ω)1/2≪Δ0<Lp, the appropriately scaled result [D. E. Hinkel-Lipsker et al., Phys. Fluids B 4, 559 (1992)] for a linear density profile is recovered as the parabolic cylinder functions asymptotically become Airy functions. When Δ0→0, the special case of conversion at the peak of the profile [D. E. Hinkel-Lipsker et al., Phys. Fluids B 4, 1772 (1992)] is obtained.

Analytic expressions for mode conversion in a plasma at the peak of a parabolic density profile

For mode conversion in an unmagnetized plasma with a parabolic density profile of scale length L, analytic expressions, in terms of parabolic cylinder functions, for the energy flux coefficients (reflection, transmission, and mode conversion) and the fields for both the ‘‘direct’’ problem (incident electromagnetic wave converting to a Langmuir wave) and the ‘‘inverse’’ problem (incident Langmuir wave converting to an electromagnetic wave) are derived for the case where the incident wave frequency ω matches the electron plasma frequency ωp at the peak of the density profile. The mode conversion coefficient for the direct problem is equal in magnitude to that of the inverse problem, and the corresponding reflection and transmission coefficients satisfy energy conservation. In contrast to the linear profile problem, the conversion efficiency depends explicitly on the value of the collision frequency (in the cold, collisional limit) or electron temperature (in the warm, collisionless limit), but a transformation of parameters relates the results for these two limits.

Potential bounds and estimation for the multiple water-bag plasma

Bounds are established for the permanent-state radiation-conditioned response to a vibrating charge in the MWB (‘multiple water-bag’) model of a warm Maxwellian plasma. Those bounds vary with the observation position beyond the charge and, along any radial direction, serve as boundary curves of potential bands containing the exact potential curves. They can therefore be employed for potential estimation. The bounds are actually Poisson potentials and are independent of (the degree of accuracy in) the MWB modelling when the charge frequency ω exceeds the electron plasma frequency ωp. In this case each potential band narrows to improve potential estimation as ω/ωp increases, and in fact a relative error in estimation can be uniformly predetermined to as small as one desires for all MWB models, charge distributions and observation points by setting ω beyond an appropriate level above ωp. The bounds are, however, model-dependent if ωp exceeds ω in magnitude, in which case, they are partially Poissonian; moreover, potential estimation based on them improves as ω/ωp decreases, and an error analysis is again performed. In either case, a sharper estimation is obtained by averaging the bounds to get an estimate; thus, for instance, the associated relative error cannot exceed 0·01, 0·02 and 0·05 when ω/ωp = (101)½, (51)½ and (21)½ respectively. Applications are described.

Beat-wave acceleration.

This report reviews the research on a new accelerator concept which uses an intense laser light, that is to say, the plasma beat-wave accelerator. Intense colinear laser beams ωo ko and ω1 k1 shone on a plasma with a frequency seperation equal to the electron plasma frequency ωP can creat a large coherent longitudinal electric field of a few tens GV/m by the laser beat excitation of plasma oscillations. Accompanying favourable and deleterious physical effects using this process for a high energy beatwave accelerator are discussed : dephasing, pump depletion, plasma turbulence effects, plasma fibre effects, surfatron, wakeless triple-soliton, etc.

Perpendicular distribution of electrostatic electron-cyclotron radiation under dense plasma conditions

The electrostatic potential distribution of a point source antenna is studied numerically within the first dispersion branch defined by 1<Ω<2, where Ω is the monochromatic frequency of the source normalized to the electron gyrofrequency. The whole study is performed for the direction of radiation R⊥ perpendicular to the magnetostatic field B0. The least-damped-roots approximation is used which allows the inclusion of two modes, the main mode (m) and the cyclotron harmonic mode (h), the contribution of each being essential for the total potential estimate. It appears that under dense plasma conditions, only the mode h has a low-damped part in its dispersion curves and is primarily responsible for the behavior of the total potential ‖φ‖. The potential then exhibits two different scales in its amplitude modulation as a function of R⊥ and Ω. The small-scale pattern reflects the phase variation of this mode and the large-scale pattern reflects both diffraction and directional effects. A careful diagnosis is necessary since, according to the distance R⊥, a main peak can occur at a frequency which is not the expected usual resonance frequency. Similar results are obtained for various dense plasma conditions provided that the electron plasma frequency Ωp is larger than the higher gyroharmonic of the dispersion branch of concern, i.e., presently Ωp≫2.

Nonlinear High-Frequency Plasma Conductivity

Some numerical results for the high-frequency nonlinear conductivity of a fully ionized plasma are presented. Special attention has been given to the case when the frequency ω of the applied electromagnetic field is close to the electron plasma frequency ωp. Apart from its intrinsic theoretical interest, this frequency range is of relevance to the problem of production and heating of plasmas by laser irradiation.

Plasma Resonance Probe Characteristics in a Magnetic Field

The operation of the plasma resonance probe in the absence of a magnetic field is now well understood, and the resonant frequency can be interpreted to give the electron density in the plasma. In many potential applications of this diagnostic technique to laboratory and space plasmas, a static magnetic field is present. This paper considers the resulting modifications to the resonance. The analysis is based on the simplified model of the probe behavior that has been validated for the zero magnetic field case by the work of Harp and Crawford. It is concluded that the technique can be applied to obtain the electron plasma frequency ωp and the electron density for ωc2≪ωp2; and the electron cyclotron frequency ωc, and hence the local magnetic field when ωc2≫ωp2. An approximate correction formula is derived for the intermediate range ωc2≈ωp2.