Waves In Nonuniform Plasma Research Articles

Mixed Properties of MHD Waves in Non-uniform Plasmas

This paper investigates the mixed properties of MHD waves in a non-uniform plasma. It starts with a short revision of MHD waves in a uniform plasma of infinite extent. In that case the MHD waves do not have mixed properties. They can be separated in Alfv\'{e}n waves and magneto-sonic waves. The Alfv\'{e}n waves propagate parallel vorticity and are incompressible. In addition they have no parallel displacement component. The magneto-sonic waves are compressible and in general do have a parallel component of displacement but do not propagate parallel vorticity. This clear separation has been the reason why there has been a strong inclination in the literature to use this classification in the study of MHD waves in non-uniform plasmas. The main part of this paper is concerned with MHD waves in a non-uniform plasma. It is shown that the MHD waves in that situation in general propagate both vorticity and compression and hence have mixed properties. Finally, the close connection between resonant absorption and MHD waves with mixed properties is discussed.

An iterative method to include spatial dispersion for waves in nonuniform plasmas using wavelet decomposition

A novel method for solving wave equations with spatial dispersion is presented, suitable for applications to ion cyclotron resonance heating. The method splits the wave operator into a dispersive and a non-dispersive part. The latter can be inverted with e.g. finite element methods. The spatial dispersion is evaluated using a wavelet representation of the dielectric kernel and added by means of iteration. The method has been successfully tested on a low frequency kinetic Alfven wave with second order Larmor radius effects in a nonuniform plasma slab.

Study on the electromagnetic waves propagation characteristics in partially ionized plasma slabs

Propagation characteristics of electromagnetic (EM) waves in partially ionized plasma slabs are studied in this paper. Such features are significant to applications in plasma antennas, blackout of re-entry flying vehicles, wave energy injection to plasmas, and etc. We in this paper developed a theoretical model of EM wave propagation perpendicular to a plasma slab with a one-dimensional density inhomogeneity along propagation direction to investigate essential characteristics of EM wave propagation in nonuniform plasmas. Particularly, the EM wave propagation in sub-wavelength plasma slabs, where the geometric optics approximation fails, is studied and in comparison with thicker slabs where the geometric optics approximation applies. The influences of both plasma and collisional frequencies, as well as the width of the plasma slab, on the EM wave propagation characteristics are discussed. The results can help the further understanding of propagation behaviours of EM waves in nonuniform plasma, and applications of the interactions between EM waves and plasmas.

Excitation of kinetic geodesic acoustic modes by drift waves in nonuniform plasmas

Effects of system nonuniformities and kinetic dispersiveness on the spontaneous excitation of Geodesic Acoustic Mode (GAM) by Drift Wave (DW) turbulence are investigated based on nonlinear gyrokinetic theory. The coupled nonlinear equations describing parametric decay of DW into GAM and DW lower sideband are derived and then solved both analytically and numerically to investigate the effects on the parametric decay process due to system nonuniformities, such as nonuniform diamagnetic frequency, finite radial envelope of DW pump, and kinetic dispersiveness. It is found that the parametric decay process is a convective instability for typical tokamak parameters when finite group velocities of DW and GAM associated with kinetic dispersiveness and finite radial envelope are taken into account. When, however, nonuniformity of diamagnetic frequency is taken into account, the parametric decay process becomes, time asymptotically, a quasi-exponentially growing absolute instability.

Nonlocal, kinetic stimulated Raman scattering in nonuniform plasmas: Averaged variational approach

Excitation of continuously phase-locked (autoresonant) plasma waves in a nonuniform plasma via stimulated Raman backscattering is analyzed with a focus on the kinetic regime (kλD∼1). The dominant nonlinear effect in this regime is that of resonant particles, and the plasma wave excitation is a nonlocal process involving formation and transport of the electron phase space holes. Whitham’s averaged variational principle is applied in studying the coupled plasma, laser pump, and seed waves dynamics. A flat-top electron velocity distribution is used as the simplest model allowing a variational formulation within the water bag theory. The corresponding Lagrangian, averaged over the fast phase variable, yields evolution equations for the slow field variables. The adiabatic multiple water bag extension of the theory for application to autoresonant plasma waves in nonuniform plasmas with more realistic initial distributions is also discussed. Numerical solutions of the system of slow variational equations are compared with Vlasov-Ampere simulations.

Resonant absorption with 2D variation of field line eigenfrequencies

Context. Resonant absorption, also known as field line resonance, can be used to describe coupling between fast and Alfven waves in non-uniform plasmas. Since the conditions for resonant absorption occur widely in astrophysics, it is applicable in many different contexts, all of which are united by their common physics. For example, resonant absorption is known to play a major role in the excitation of ultra-low frequency pulsations in the terrestrial magnetosphere and is also a leading explanation for the decay of fast kink oscillations of coronal loops. The occurrence of non-axisymmetric conditions in the magnetosphere, and observational evidence that coronal loops may possess fine transverse structure, highlight a need to consider equilibria that vary in two dimensions across the background magnetic field. Aims. We investigate the properties of resonant absorption when field line eigenfrequencies vary in two dimensions across the background magnetic field. We aim to place the theory on a firm mathematical footing and explore some of its key features. Methods. Using cold, linear, ideal MHD with a straight, uniform background magnetic field, we systematically obtain a complete analytic solution for behaviour at late times. This provides a framework from which the features of resonant absorption may be understood. The time-dependent problem is solved numerically, reproducing key features of the analytic solution. Results. Energy is deposited from a monochromatic fast wave as a phase mixing Alfven wave, in the vicinity of the resonant surface, at which the local field line eigenfrequency matches the frequency of the driver. A generalisation of the one dimensional phase mixing length to higher dimensions is suggested, and shown to successfully estimate the finest lengthscales in time-dependent simulations. The resonant Alfven wave is driven by gradients of the field aligned magnetic field perturbation, which is associated with the fast wave pressure. This leads to amplitude variations of the Alfven wave that can be used to reveal the spatial form of the fast wave.

Hybrid magnetohydrodynamic-kinetic electron closure methods and shear Alfvén waves in nonuniform plasmas

Two hybrid magnetohydrodynamic-kinetic electron models of shear Alfvén waves with different closure schemes involving the assumption of quasineutrality are compared. One method assumes quasineutrality directly while the other allows for a nonzero ∇∙j⃗ that produces a “correcting” electric field. The interpretation of the different closure schemes is discussed and the two methods are shown to yield consistent results for both the cases of a constant and variable density along the field line. In the variable density case the hybrid system with and without a shear Alfvén wave perturbation is also contrasted. In the latter case, static parallel electric fields that increased with the plasma temperature were generated to support the density gradients. When the system was perturbed, a time dependent parallel electric field contribution oscillated around the static field structure needed to support the profile. Landau damping effects were also investigated and the energy invariant for the systems derived.

Evolution and dissipation of imbedded rotational discontinuities and Alfvén waves in nonuniform plasma and the resultant proton heating

We show that nonuniform Alfvén speed gradients across field lines generally arise from the evolution of Alfvén waves. The evolution of a group of nonlinear Alfvén waves with the same sign of parallel wavenumber generate small‐amplitude pressure‐balanced structures (PBSs) which cause the speed variations. This always causes refraction. In most cases, the Alfvén waves also couple to magnetosonic waves and acquire a weak compressional component and can undergo resonant absorption or transfer, wherein wave energy can propagate across field lines. At large amplitudes the waves also generate imbedded rotational discontinuities (RDs). Some of these RDs can be dissipated owing to resonant transfer. This process could partly contribute to the observed decrease of solar wind RDs with increasing distance from the Sun. Resonant transfer also triggers a cascade due to steepening, which leads to sustained proton heating. The cascade produces oblique and large wavenumber waves which travel in different directions and have associated compressions. Protons interact with these by pitch angle scattering. They gain energy from second‐order Fermi acceleration and from Landau and transit time damping. Oblique waves are inferred to be present in the dissipation range of Alfvénic fluctuations at 1 AU. We argue that the process of proton heating should proceed similarly to simulation results. We also propose a role for the wave imbedded RD in coronal heating through its formation in the chromosphere and its likely dissolution in the corona where wave amplitudes are very small.

Conservation laws and connection formulae for resonant MHD waves

This paper reviews a recent development in the theory of resonant MHD waves in non-uniform plasmas. An asymptotic analysis of the equations for MHD waves in plasmas with high magnetic Reynolds numbers has shown that resonant slow and Alfvén waves obey conservation laws and jump conditions across the dissipative layer. These conservation laws specify the dominant dynamics of the resonant MHD waves. In combination with the jump conditions they enable us to understand the basic physics of resonant MHD waves and also help us with the interpretation of results of large scale numerical simulations in resistive MHD. They also can be used to design an accurate and computationally simple methods for numerical studying resonant MHD waves in non-uniform plasmas.Conservation laws and jump conditions for resonant MHD waves are first discussed in linear MHD for 1-dimensional equilibrium states. Subsequently the generalization of these results to 2-dimensional equilibrium state in linear MHD and to nonlinear MHD is reviewed. The interaction of sound waves with an inhomogeneous plasma is discussed as an application of the theory. Firstly the results of linear theory are used to consider the interaction of sound waves with 1-dimensional magnetic tubes. The phenomenon of total resonant absorption is discussed. Secondly the nonlinear theory of cusp dissipative layers is used to study the interaction of sound waves with 1-dimensional inhomogeneous plasmas in planar geometry. New effects that owe their existence to nonlinearity in the cusp dissipative layer are reviewed.

Hermitian description of interacting inhomogeneous electron beams

Recently developed techniques for finding embedded pairwise mode couplings in high-order systems and calculating the transmission coefficient in linear mode conversion for passive, stable plasmas are extended to the treatment of coupling of positive and negative energy waves in nonuniform plasmas. In particular, the coupling of positive and negative energy waves in costreaming, nonuniform electron beams is treated in detail and the ensuing spatial amplification is determined.

Generation of radiation by upper-hybrid waves in non-uniform plasmas

The decay of an electrostatic upper-hybrid wave into a high-frequency transverse wave and a low-frequency longitudinal wave in an inhomogenous magnetoplasma is considered. The growth rate and threshold of this parametric instability are calculated. The present results should be suited for the understanding of non-thermal radiation arising in non-uniform plasmas such as those found in the terrestrial magnetosphere as well as in the F-region of the ionosphere.

Geometric Optics of Lower Hybrid Waves in Nonuniform Plasmas

The propagation of lower hybrid waves in the presence of strong density and field gradient-produced refractive effects is studied in the geometric optics limit. Attention is focused on the electrostatic wave and the modification of the parallel wavenumber k‖ due to gradients. It is found that in cases where the gradients occur along the direction of the magnetic field the resulting decrease of k‖ gives rise to a cusp or reflection of the ray at the resonance layer. An asymptotic series for the field amplitudes is developed which is valid in the short wavelength limit everywhere except near the cusp point. It is found that the cusp represents a singularity where the geometric optics assumption is invalid; however, the inclusion of thermal effects removes the singularity by linear mode conversion (LMC). The analysis is applied to toroidal geometry and is extended to include distributed sources.

Nonlinear coupling of three waves in non-uniform plasma

This paper considers nonlinear interaction between three monochromatic waves in a hot non-uniform electron plasma. With the aid of coupled mode theory the interaction of three longitudinal waves is studied and a specific case of the interaction of two longitudinal waves and one perpendicular wave is derived for the limiting case of long wavelength. Furthermore, the non-uniformity involves generalization of the theory of the interaction of two transverse waves and one longitudinal wave of a previous contribution.

Propagation of shock waves in nonuniform plasma

Results of numerical simulation of the propagation of one-dimensional magnetohydrodynamic shock waves in a nonuniform plasma containing a magnetic field are discussed. Possible uses for the production of high velocities and temperatures and astrophysical applications are considered. The essential effect of the magnetic field is shown; acceleration of a shock wave is intensified in a medium with decreasing density.

Ion-cyclotron waves in nonuniform plasmas and parametric instabilities

A general formalism for studying waves propagating in a plasma with density and magnetic field gradients in slab geometry is discussed. Specializing to electrostatic ion-cyclotron waves propagating perpendicular to the gradients, it is shown that a density profile can lead to local or nonlocal structure around points where N′ (x)/N (x) has a local maximum while inhomogeneous magnetic fields provide the wave with the profile of an Airy function. Application of the formalism to parametric instabilities driven by magnetosonic waves and with kyρi≫1 is discussed. In particular, it is concluded that density and magnetic field gradients should not be critical in the development of the cyclotron decay instability in the FM-1 (floating multipole-1), ATC (adiabatic toroidal compressor), and PLT (Princeton large torus) devices of Princeton.

The Propagation of Compressional Alfven Waves in Nonuniform Plasmas

A theoretical treatment is presented for the propagation of Alfven waves in a plasma. It includes the effects of resistivity, ion-neutral collisions, the ion cyclotron frequency and radial nonuniformities in ion density, neutral particle density and temperature. The theory is applied to plasmas with conducting and nonconducting walls and the results are compared with those of experiments conducted in the afterglow of a shock-produced plasma. Nonuniformity in the ion density is found to have a marked effect on the dispersion relation and wave field profiles, while non uniformities in the total particle density and temperature are less important. Excellent agreement is obtained between theory and experiment and this allows unambiguous and accurate determinations to be made of the average total particle density, which is found to be - 50 % of the initial filling density, and of the cross section for momentum transfer between protons and hydrogen atoms.

Non-linear waves in a non-uniform plasma

The work of Butler & Gribben (1968) on a general formulation ofthe problem of non-linear waves in non-uniform plasmas is extended. The particular case treated in Butler & Gribben, § 6, is discussed again (the distribution functions fs and electrostatic potential depend only on one space co-ordinate, that in the direction of propagation of the wave, the wave is slowly varying only with respect to this co-ordinate and time, the magnetic field vanishes and relativistic effects are negligible). Conditions necessary to avoid secular terms in the solutions of the Vlasov and Poisson equations are rederived, but without resorting to assumed series expansions in e, the perturbation parameter describing the non-uniformity, for the dependent variables, and using a different notation which simplifies and retains the symmetry of the equations. The corresponding general boundary condition, to be satisfied by fs innergy space at the boundary of the trapped particle region, is also derived.Particular attention is devoted to the Vlasov equation, and the derived general result is used to obtain the appropriate necessary condition from this equation, correct to O(ε). This shows that, unlike the leading-order theory, at the next stage an extra length scale appears in the equations, which would be needed if e.g. the theory were to be used to discuss shock waves. It is argued that this result, taken with the mixing process described in Butler & Gribben (which supplies a mechanism for the formation of shocks), appears to place the theory at least on as satisfactory a level as the Navier-Stokes theory for the discussion of shock wave structures.Another aspect of the analysis is the comparison with the Whitham (1965a) averaging method for treating the propagation of non-linear waves in other fields. Similar features are pointed out, and it seems likely that the averaging method is equivalent to the leading-order theory. It is thought that the present approach might prove to be useful in other wave problems.

Coupling of Waves in Nonuniform Plasma

This paper studies mutual coupling of transverse and longitudinal high-frequency waves of both electron and ion fluid motions of perturbation in slowly varying nonmagnetized equilibrium plasma. Besides, the particular problem of coupling of ion acoustic and electromagnetic waves is considered in detail. The power of electromagnetic radiation generated by an ion acoustic wave and also in reverse from the latter to the former have been evaluated.