Langmuir Turbulence In Plasma Research Articles

On profiles of hydrogenic spectral lines under stochastic electric fields of plasma turbulence: Applications to diagnostics of the Langmuir turbulence

Studies of the effects of various oscillatory electric fields on hydrogenic spectral lines have a long history. Over the years various effects of a monochromatic linearly-polarized electric field were analyzed and applied to spectroscopic diagnostics of laboratory and astrophysical plasmas.Then in 1996 a paper was published where the author analyzed how profiles of hydrogen spectral lines are affected by a multi-mode non-monochromatic linearly-polarized electric field E(t). Specifically it concerned the situation where the power spectrum of the field E(t) has the Lorentzian form. In the present paper we obtained a general analytical result for the shape of hydrogenic (i.e., hydrogen and hydrogenlike) spectral lines under the same kind of the field E(t), but whose power spectrum has the Gaussian form. We consider this kind of electric field to be caused by the Langmuir turbulence in plasmas. We show that if the power spectrum of the field is Gaussian, then for the relatively small value of the average Langmuir field, the profile of each Stark component is Lorentzian, while for the relatively large value of the average Langmuir field, the profile of each Stark component is Gaussian. We analyze theoretical profiles of the hydrogenic Ly-beta line under the Langmuir field of either one of the above two kinds of the power spectrum. On the basis of this analysis, we propose a new diagnostic method allowing for the first time not only to measure experimentally the average field of the Langmuir turbulence in dense plasmas, but also to find out the information on the power spectrum of the Langmuir turbulence. This diagnostic method is not limited to using the Ly-beta line: it would work while using other intense hydrogenic spectral lines that do not have the central Stark components, such as, e.g., Ly-delta, Balmer-beta, and Balmer-delta.

Bell-polynomial approach and N-soliton solution for the extended Lotka–Volterra equation in plasmas

Symbolically investigated in this paper is the extended Lotka–Volterra (ELV) equation, which can govern the kinetics of the discrete peaks of the weak Langmuir turbulence in plasmas without the linear damping and random noise. Binary Bell polynomials are applied to the bilinearization of the discrete system. Bilinear Bäcklund transformation of the ELV equation is constructed. N-soliton solution in terms of the extended Casorati determinant is also presented and verified. Propagation and interaction behaviors of the Langmuir turbulence are analyzed. It is demonstrated that the number of the interacting Langmuir waves can influence the soliton velocity and amplitude as well as the collision phase shift. Graphic illustrations of the solitonic collisions show that the repulsion effects and nonlinear interactions are also associated with the number of the interacting Langmuir waves.

Orbital Instability of Standing Waves for the Klein-Gordon-Zakharov System

Abstract This paper deals with the instability of the ground state solitary wave solution to the Klein-Gordon-Zakharov system in three space dimensions with c ≥ 1, which is a model to describe the Langmuir turbulence in plasma. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational calculus and scaling argument. Then by defining invariant sets and applying some priori estimates, we prove the orbital instability of the ground state in the following sense: in each neighborhood of it, there exists a solution whose energy diverges in finite or infinite time.

Excitation of strong Langmuir turbulence in plasmas near critical density: Application to HF heating of the ionosphere

Results are presented for an extensive study of strong Langmuir turbulence (SLT) in plasmas excited near the critical density by intense coherent radiation beams. The nominal parameters for HF heating experiments imply that the ionospheric plasma is in such a state. A large body of experimental data exists, particularly from incoherent scatter radar (ISR) measurements of HF‐enhanced fluctuation levels. Long‐time simulations of Zakharov's model of SLT and related theoretical arguments have led to new conclusions and insights: (1) linear parametric instabilities may play a role only during the first few milliseconds after heater turn‐on in a quiescent ionosphere, but there is also the possibility of “direct nucleation” of cavitons in preexisting density fluctuations; (2) both possibilities lead to Langmuir collapse; (3) the turbulence is sustained by nucleation of trapped electric fields in burnt‐out density cavities from previous collapses; (4) the nucleation‐collapse‐burnout scenario explains several features of the observed ISR plasma line power spectra in early‐time, low‐duty cycle experiments and predicts new features; (5) ISR spectra obtained at early times in low‐duty cycle heating experiments are consistent with the spectra of uncorrelated caviton events; (6) these spectra contain a “free mode” peak which is due to the radiation of free Langmuir waves by collapsing cavitons; this peak has recently been observed; (7) sharp spectral peaks observed in strong spectra in longer‐time, high‐duty cycle or CW heating can arise in the SLT model from spatio‐temporal caviton correlations, provided overdense domains exist and a Bragg resonance condition is satisfied; (8) correlation models can explain all the sharp features including the decay line, the cascade, the narrow oscillating two‐stream instability line, and the anti‐Stokes line; these models do not involve parametric instabilities; (9) the characteristic structure of the ISR spectrum is maintained over a much wider range of angles relative to the geomagnetic field than is the case for weak turbulence predictions; (10) the altitude dependence of the plasma line is consistent with observation without postulating large‐scale density modifications; and (11) the nonlinear absorption rate of heater energy is much larger than collisional absorption, the absorbed energy going mainly into suprathermal electrons.

Solitons in Laser Physics

We survey some of the applications of soliton theory in laser physics. We briefly treat the theory of optical self-focussing and optical filamentation in neutral dielectrics and plasmas where the governing equation is the non-linear Schrödinger equation or one of its generalisations. We establish the connection of this theory with 1-dimensional Langmuir turbulence in plasmas. We treat the theory of optical self-induced transparency (SIT) at greater length and develop the Maxwell-Bloch (MB), reduced Maxwell-Bloch (RMB), SIT and sine-Gordon (s-G) equations to describe it. An optical three-wave interaction is related to the s-G equation; and reference is made to recent work on solitons in stimulated Raman scattering.The RMB equations are solved by a Zakharov-Shabat-AKNS inverse scattering scheme. The inhomogeneously broadened RMB equations have the unusual feature that ln a is not a constant of the motion. However, the sharp line RMB equations have two infinite sets of conserved densities, and the system constitutes one more example of a completely integrable infinite dimensional Hamiltonian system. In terms of scattering data the Hamiltonian of the RMB equations separates into soliton, breather and `background', that is `radiation', contributions. The sine-Gordon equation and its separable Hamiltonian are found as a special case of the RMB equations and its Hamiltonian. Averaged Lagrangian techniques are independently used to relate the c-number MB, RMB and SIT equations and to analyse the slowly varying phase and envelope approximations by which the SIT equations are derived from the MB or RMB equations. The connection of this Lagrangian theory with the Hamiltonian theory is not established.The Hamiltonian formalism in terms of the scattering data is used to quantise the RMB and s-G equations. The RMB, like the s-G, has the discrete energy level spectrum associated with a quantised breather; but only in the s-G limit is the quantised system easy to interpret. The quantised s-G is used to model a `coarse grained' operator theory of strictly resonant sharp line optical pulse propagation. The validity of such a description is examined.The physics of the c-number RMB equations is also discussed and particularly the relation of the c-number breather solutions to the 2π-pulse solutions of the SIT equations. The c-number RMB breather solutions provide a more general theory of SIT valid (within the 2-level atom model) at all electromagnetic field intensities and restricted only by the low density condition which permits the neglect of back scattering.Finally we look at four problems in resonant non-linear optics from a physical point of view. These are degenerate SIT and singular perturbation theory for it; the collision of oppositely directed resonant optical pulses; the theory of super-radiance; and the theory of optical self-focussing in resonant SIT.