Temperature gradient driven Alfvén instability producing inward energy flux in stellarators

Destabilizing influence of plasma inhomogeneity on Alfvén eigenmodes in stellarators is considered. It is found that the diamagnetic frequency can strongly increase due to the resonance interaction of particles and Alfvén eigenmodes. This occurs when the particle resonance velocity exceeds the thermal velocity, in which case the role of superthermal particles enlarges. Then Alfvén eigenmodes can be destabilized even in the absence of the energetic ion population. It is shown that in the case of the temperature distribution with a large gradient at the periphery, the destabilized mode can channel the energy from the peripheral plasma region to the inner region. A stability analysis employing a model temperature profile of the ions was carried out for the Wendelstein 7-X stellarator. It indicates that the considered mechanism could lead to an Alfvén instability accompanied with the inward energy flux in the first W7-X experiments where long-lasting high-frequency oscillations were observed.     

On the waves and instability in self-gravitating magnetic molecular clouds with ambipolar diffusion Part 2: Cylindrical modal approach and nonlinear effects

The dynamics and evolution of molecular clouds, which are the main sites of active star formation in our Galaxy, are governed by the interaction of the self-gravity, magnetic fields, and ambipolar diffusion, in the form of waves and instability. In our earlier paper (Part 1), we carried out a detailed planar modal analysis. The present paper (Part 2) is an extension of Part 1 in order to include the three-dimensionality and the finite size of the cloud as well as the nonlinear effects. A cylindrical modal approach is developed to take into account the three-dimensionality and the finite size of the cloud as well as the special direction of the mean field B ₀. Dispersion relation and solutions of such cylindrical modes are obtained. It is shown that, in the most unstable direction (∥ B ₀), the growth rate is considerably reduced by the finite lateral size compared with the planar mode of the same wavelength. Nonlinear effects of the magnetic field and magnetic waves are discussed, with particular attention paid to their dependence on the coupling factor σ which is the ratio between the mean collision frequency of a neutral with ions and the gravitational response frequency. It is shown that fast magnetosonic waves are as important as Alfvén waves in the global support of the cloud. In order that the lower limit of the wavelengths in the moderately dissipative range of such waves is small compared with the cloud size, σ should be larger than 5. It is also shown that σ should be larger than 7.3 in order for the density growth of the neutral fluid in a free-fall time to be smaller than 30%. A typical value of σ ≈ 11 in molecular clouds is estimated. This corresponds to an ionization rate ζ = 10^?17 and a metal depletion δ = 0.1. For the clouds with such value of σ, both the density growth and the flux loss are smaller than 20% in a free-fall time. It is shown that a self-adjusting mechanism is able to slow down the global collapse at the early stage of cloud evolution in terms of the interaction between the global collapse and the then existing Alfvén and fast magnetosonic waves, which originate from the inhomogeneous velocity and density distributions in the cloud. Such interaction will not only strengthen these waves, but also create outwards decaying amplitudes of the field perturbation and therefore generate outward net magnetic forces to support the cloud against global collapse. The same mechanism also works for refreshing the outwards propagating Alfvén and fast magnetosonic waves caused by star-forming or core-forming activities, if the total energy supply rate due to these activities is lower than the total dissipation rate of these waves. In this way, a significant portion of the released gravitational energy during the global collapse is tapped and turned into the magnetic waves to slow down the global collapse itself. In terms of such a mechanism, the property that the dissipation rate of Alfvén and fast magnetosonic waves increases with the wave number leads to a simple explanation of the coexistence of the global quasi-stability and the local instability (formation of dense cores) in molecular clouds with cloud mass much larger than the Jeans mass.     

On the origin of solar wind. Alfvén waves induced jump of coronal temperature

Absorption of Alfvén waves is considered to be the main mechanism of heating in the solar corona. It is concluded that the sharp increase of the plasma temperature by two orders of magnitude is related to a self-induced opacity with respect to Alfvén waves. The maximal frequency for propagation of Alfvén waves is determined by the strongly temperature dependent kinematic viscosity. In such a way the temperature jump is due to absorption of high frequency Alfvén waves in a narrow layer above the solar surface. It is calculated the power per unit area dissipated in this layer due to damping of Alfvén waves that blows up the plasma and gives birth to the solar wind. A model short wave-length (WKB) evaluation takes into account the 1/f² frequency dependence of the transversal magnetic field and velocity spectral densities. Such spectral densities agree with old magnetometric data taken by Voyager 1 and recent theoretical calculations in the framework of Langevin-Burgers MHD. The presented theory predicts existence of intensive high frequency MHD Alfvén waves in the cold layer beneath the corona. It is briefly discussed how this statement can be checked experimentally. It is demonstrated that the magnitude of the Alfvén waves generating random noise and the solar wind velocity can be expressed only in terms of satellite experimental data. It is advocated that investigation of properties of the solar surface as a random driver by optical methods is an important task for future solar physics.     

Propagation of Alfvén surface waves along the ionospheric plasma slab with the effect of gravity

Ionospheric regions connecting the neutral gas atmosphere have been considered to be an incompressible plasma slab surrounded by incompressible plasma on one side and neutral gas on the other side. The effect of gravity on Alfvén surface waves in the slab geometry is studied. As a special case, the propagation of ASW along the plasma-neutral gas interface is also discussed. The existence of two modes of surface waves has been identified and their characteristic behaviour affected by the gravity has been discussed.     

Excitation of Alfvén vortices in the ionosphere by the magnetospheric convection

We analyze conditions for excitation of ULF waves in the ionospheric Alfvén resonator (IAR), taking into account the altitude-inhomogeneous profile of the magnetospheric convection velocity. This profile is formed as a result of interaction of the convective flow with the neutral atmosphere at altitudes 90–150 km. ULF waves comprise oblique Alfvén waves, trapped into the IAR, and ionospheric drift waves, which are in resonance with them. These waves together form strongly anisotropic, closed current loops, whose scale along the magnetic field greatly exceeds their transverse scale, i.e., l_z ≫ l_⊥, and can be considered Alfvén vortices. Within the framework of the proposed model of the ionosphere, we study the instability threshold and the amplitude growth rate of the Alfvén vortices as functions of different parameters (wave vector k_22A5, angle between the wave vector and the convection velocity, ratio of the Alfvén-wave and Pedersen conductivities, etc.). Some estimates are given in application to the observed small-scale field-aligned currents in the auroral ionosphere. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 376–390, May 2008.     

Collisionless Plasma Expansion in the Presence of a Dipole Magnetic Field

The collisionless interaction of an expanding high–energy plasma cloud with a magnetized background plasma in the presence of a dipole magnetic field is examined in the framework of a 2D3V hybrid (kinetic ions and massless fluid electrons) model. The retardation of the plasma cloud and the dynamics of the perturbed electromagnetic fields and the background plasma are studied for high Alfvén–Mach numbers using the particle–in–cellmethod. It is shown that the plasma cloud expands excluding the ambient magnetic field and the background plasma to form a diamagnetic cavity which is accompanied by the generation of a collisionless shock wave. The energy exchange between the plasma cloud and the background plasma is also studied and qualitative agreement with the analytical model suggested previously is obtained (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scattering of an Alfvén wave by an inhomogeneity in the solar wind density

The interaction between a nonlinear Alfvén wave and intense inhomogeneities in the density of interplanetary plasma is considered in the magnetohydrodynamic (MHD) approximation. The cold-plasma approximation was used to carry out a more correct study of the interaction since the thermal pressure can introduce pronounced changes into the shape of specified inhomogeneities in the plasma density. Results of numerical solution of the well-known MHD equations are presented in the form of three films demonstrating different scenarios of development of the nonlinear dynamics. The films allow us to observe the dynamic evolution of the form of an Alfvén perturbation and the changes in the density inhomogeneities. For small-amplitude Alfvén waves this corresponds to the process of linear transformation by the density inhomogeneities, which does not lend itself to comprehensive analytical study. Numerical simulation reveals the phenomena of reflection from regions of sharp density variation, which are very sensitive to the spatial scales of the interacting objects. The same method is used to investigate the scattering of strong waves. After reversible changes in shape in a high-density region (where oscillations of the shock-wave front are attenuated), a moderate-amplitude Alfvén wave is recovered in a more rarefied medium. A strong scattered Alfvén wave brings about irreversible changes in the shape of the density inhomogeneity. The results obtained illustrate the process of interaction between Alfvén waves and strong density perturbations related to piston or explosive shock waves in the solar wind. State Pedagogikal University, Nizhny Novgorod, Russia; Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 2, pp. 152–163, February, 1998.     

On some electromagnetic phenomena in the tether magnetoplasma cloud

Summary The tethered satellite system (TSS) will be accompanied by a variety of electromagnetic phenomena. An independent interconnected formation, a ?tethered magnetoplasma cloud? (TMC), moving in space along the orbit of TSS, at an altitude of about 300 km, will be created. This time-dependent cloud will be a very complicated inhomogeneous formation including electromagnetic oscillations and waves of different type. Some of these waves will be observed on the Earth's surface. Rarefiel regions of the magnetoplasma behind, and dense regions in front of the shuttle orbiter (SO) and the subsatellite (SS) will arise. The neutral nitrogen beam ejected by the thruster becomes an ion beam on the day-light part of the orbit. Its energy is much greater than the local thermal energy. Instabilities of different kind as well as diffusion and recombination effects are expected to accompany the interaction of these beams with the surrounding plasma. The electron beams will produce other types of instabilities. By the electrons precessing along the magnetic-field lines, a current (5·10³V, 0.5 A) should be induced in the 20th km length conducting tether. It will be closed at the bottom of the ionosphere. This huge magnetic loop, so-called ?phantom loop? (PL), should accompany the tether system along its orbit. The length of this ?tether electromagnetic tail? (TEMT) is about 200 km, its magnetic moment will be about 10¹³ A·cm². Alfvén waves and nonlinear effects of heating type may be produced by this loop along the magnetic-field lines. ?Strings? of hot plasma may accompany the tether system.     

On the Stability of Ballooning Modes in the Boundary Layers of a Gas Insulated Plasma

In order to fulfill power density requirements in future steady-state fusion reactors the ion density in central parts must be of the order 10²⁰–10²¹–m^?3. In such systems high density neutral gas may surround the hot plasma, whether introduced on purpose or not, provided the neutral gas flux from the plasma is not continuously removed by external means. In gas insulated plasmas large density and pressure gradients will arise close to the boundaries on account of plasma neutral gas interaction effects. In this paper the stability of gravity driven ballooning modes in the boundary region is investigated. In particular, the coupling between plasma and neutral gas investigated in previous stability analysis is reconsidered. Also effects previously neglected for example the Nernst effect is taken into account.     

Plasma-maser interaction of langmuir wave with kinetic Alfvén wave turbulence

A theoretical study is made on the generation mechanism of Langmuir mode wave in the presence of kinetic Alfvén wave turbulence in a magnetized plasma on the basis of plasma-maser interaction. It is shown that a test high frequency Langmuir mode wave is unstable in the presence of low frequency kinetic Alfvén wave turbulence. The growth of the Langmuir wave occurs due to direct and polarization coupling terms. Because of the universal existence of the kinetic Alfvén waves in large scale plasmas, the results have potential importance in space and astrophysical radiation processes.     

Propagation of Alfvén waves in bismuth

The present study reports on experimental investigations about the phase velocity diagrams of Alfvén waves in the anisotropic solid-state plasma of bismuth. Alfvén-wave transmission at 34 GHz and 4.2 K has been observed, using an interference technique of high sensitivity. The experimental results are in good agreement with a theoretical model given by Buchsbaum, which makes only use of the anisotropic mass tensor of bismuth.     

Interaction of long magnetoacoustic waves in cosmic plasma with turbulence

The interaction of fast magnetoacoustic (FMA) waves in a plasma with particle concentration n_t∼n_i∼1 cm⁻³ is studied with allowance for Alfvén modes, which simulates turbulence. Equations that describe three-wave interaction of FMAs are derived and a method is indicated for constructing some stationary structures that form in the spatial synchronism of interacting FMA waves. The applicability of the inverse scattering problem method to the problem of the interaction of FMA waves in a turbulent plasma is discussed. Chechen State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, p. 3–9, September, 1997.     

Transformation of alfvén into slow magnetosonic disturbances in the magnetosphere due to reflection from magnetically conjugate ionospheric regions

We perform numerical and analytical studies of MHD phenomena within the framework of a one-dimensional model of the magnetosphere bounded by conjugate reflection surfaces. Specific features of the nonlinear transformation of an Alfvén wave into a slow magnetosonic one upon propagation along the magnetic fieldB ₀ are considered. Effects of reflection of a nonlinear magnetospheric wave from magnetically conjugate ionospheres are analyzed in detail. It is shown that the main effect for the case of a nonlinear Alfvén wave in a low-temperature plasma is the plasma sweeping off the volumes close to the reflecting boundaries. Numerical results which demonstrate the generation dynamics of the slow magnetosonic wave and plasma sweeping upon reflection of a powerful Alfvén wave from the ionosphere are in qualitative agreement with the analytical estimates. In a cold plasma, the effect is so significant that it requires a numerical study even if the initial Alfvén wave is linear. The key role of the ratio between the Alfvén and sound velocities for the value of the density disturbance is revealed. Pedagogical University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 4, pp. 285–295, April, 2000.     

Interaction of shock waves with a jet wake during gas injection into supersonic stream

In the present paper, we report the results of an experimental study of the interaction region of a planar compression shock produced by a wedge in stream with the wake formed behind a cocurrent gas jet (H₂, air, or Ar) injected into the flow. Depending on the gas jet parameters, three modes of interaction could be distinguished: a strong interaction, observed when the flow velocity in the wake was subsonic; a moderate interaction, observed when a subsonic flow region, bounded by a shock of almost conical shape, formed in the vicinity of the compression shock; and a neutral interaction. Three-dimensional non-stationary Euler equations were solved to numerically examine the interaction of an axisymmetric jet with an oblique shock wave. The obtained interaction regimes were found to be in a reasonable agreement with experimental data.     

Chaotic regime of Alfvén Eigenmode wave-particle interaction

The chaotic regime in Alfvén eigenmode wave-particle interaction is identified for the first time in the tokamak plasma of the Joint European Torus. The Alfvén modes are driven by energetic hydrogen minority ions produced by ion cyclotron resonance heating. The experimental signatures of the chaotic regime include spectral broadening, phase flips, and nonperiodic amplitude variations. These phenomena are found to be consistent with a general nonlinear theory of kinetic instabilities near stability threshold developed by Berk, Breizman, and Pekker.     

Alfvén-drift turbulence suppression as triggering mechanism for LH transition

The Alfvén drift turbulence suppression at the plasma edge is suggested as a triggering mechanism for the L to H transition. The stability theory of Alfvén drift-waves shows that with increasing plasma pressure the Alfvén waves get coupled to electron drift waves and as a consequence the unstable long wavelength perturbations (most important for transport) are suppressed. The instability can be characterised by two significant parameters, i.e. the normalised plasma beta, β _n , and the normalised collision frequency, v _n . The resulting turbulent transport coefficient is suppressed when the normalised beta is greater than a critical value, i.e. β _n >1+v _n ^2/3 , which depends on the normalised collision frequency v _n . The transport coefficients change their dependence on plasma parameters at this threshold. Therefore, the possible scenario for the development of the H-mode could be associated with the stabilisation of the electron fluctuation at the plasma edge. The Alfvén drift-wave model predicts the experimental trend of a roughly linear dependence of threshold temperature on magnetic field, with a weak dependence on density at high densities and a strong dependence on density at lower densities.     

On the waves and instability in self-gravitating magnetic molecular clouds with ambipolar diffusion Part 1: Planar modal approach

It is well established that molecular clouds are the main sites of active star formation in our Galaxy. The interaction of the three major physical agents in molecular clouds, i.e. the self-gravity, magnetic fields, and ambipolar diffusion, in the form of waves and instability, governs the dynamics and evolution of molecular clouds. The present work is a new effort on this subject. This work consists of two parts. In Part 1, we complete the planar modal analysis by removing the restrictions on the direction of the velocity perturbation which were used in previous studies. Thus, the wave number vector k is allowed to take any direction with respect to the mean field B₀. The exact general dispersion relation is found to be a seventh-order equation and can be reduced to a quartic equation as the first approximation about the small parameter x_ρ = ρ_{i, 0}/ρ_n,0, the density ratio between ions and neutrals. The growth rate contour maps in the k plane are obtained for various values of the basic dimensionless parameters Λ and σ, where Λ = V_A,n/C_n is the ratio between the Alfvén speed and the sound speed in the neutrals, and the “coupling factor” σ = v_i/ω_g,n is the ratio between the average collision frequency of a neutral with ions and the self-gravitation response frequency. It is shown that, in all directions, magnetic field only reduces the growth rate but does not change the critical wave length for instability. The reduction of the growth rate depends on not only Λ, the dimensionless measure of the field strength, but also the direction of k as well as the coupling factor σ. The frequencies and the dissipation rates of the Alfvén waves and the fast and slow self-gravitating magnetosonic waves are calculated for all directions of k. The solutions of these waves are also given. Although the planar modal approach is important in understanding the basic mechanism of magnetic waves and instability, it does not take into account the three-dimensionality and the finite size of the cloud and is therefore only suitable to the local analysis. Thus, in order to discuss the global properties, we will develop a cylindrical modal approach in Part 2. There, we will also discuss certain nonlinear effects and show their importance in leading to a self-adjusting mechanism which slows down the global collapse at the early stage of cloud evolution and refreshes the outward propagating Alfvén and fast magnetosonic waves caused by star-forming or core-forming activities. In this way, a significant portion of the released gravitational energy during the global collapse is turned into the magnetic waves to support the cloud against the global collapse itself.     

[Russian Text Ignored].

Using the drift kinetic equation the influence of the ballooning component of the perturbed transit ion pressure on the low-frequency Alfvéen waves in a toroidal plasma is considered. It is shown that this contribution to the plasma pressure leads in a relatively cold plasma (plasma edge) to a stabilization of the Alfvéen modes. Taking into account drift effects the modified Alfvéen wave becomes unstable if the temperature gradient is large enough. All the perturbations are strongly localized around the corresponding rational magnetic surface.     

On the propagation and interaction of ultralow-frequency waves in a waveguide with gyrotropic plasma

The propagation of ultralow-frequency (ULF) electromagnetic waves in a waveguide filled with magnetoactive plasma is consieered on the basis of the monoaxial crystal approximation which is more general than the MHD approximation. The formulas for the phase and group velocities of the ordinary (magnetoacoustic) and extraordinary waves (similar to Alfvén waves in the MHD approximation) are derived. It is shown that analysis outside the scope of the MHD approximation results in a finite (nonzero) velocity of energy propagation of the extraordinary wave (Alfvén wave at the limit) along the waveguide. The possible waveguide mode triplets satisfying the conditions of synchronism are found. Three-wave resonant parametric and nonlinear interaction between waves with such characteristics leads to effective spectral transformation of the ULF radiation. Radiophysical Research Institute, Nizhny Novgorod; State Technical University of Nizhny Novgorod. Translated from lzvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, Nos. 1–2, pp. 111–122, January–February, 1997.     

The interaction of optical phonons with magnetoplasma waves in ionic semiconductors

The interaction of magnetoplasma waves with optical phonons is investigated for propagation both parallel and perpendicular to the external de magnetic field. The low frequency region is considered where helicons and Alfvén waves propagate for uncompensated and compensated materials, respectively. The results are applied to degenerate, ionic semiconductors where the plasma frequency is much larger than the infrared dispersion frequency and the cyclotron frequency. The theory is applied to heavily-doped InSb for the case of helicon-optical phonon interactions.