Nonuniform Magnetized Plasma Research Articles

Self-consistent model of electron drift mode turbulence

AbstractThe nonlinear dynamics of magnetic electron drift mode turbulence are outlined and the generation of large-scale magnetic structures in a non-uniform magnetized plasma by turbulent Reynolds stress is demonstrated. The loop-back of large-scale flows on the microturbulence is elucidated and the modulation of the electron drift mode turbulence spectrum in a medium with slowly varying parameters is presented. The wave kinetic equation in the presence of large-scale flows is derived and it can be seen that the small-scale turbulence and the large-scale structures form a self-regulating system. Finally, it is shown by the use of quasilinear theory that the shearing of microturbulence by the flows can be described by a diffusion equation in k-space and the corresponding diffusion coefficients are calculated.

Foundations of nonlinear gyrokinetic theory

Nonlinear gyrokinetic equations play a fundamental role in our understanding of the long-time behavior of strongly magnetized plasmas. The foundations of modern nonlinear gyrokinetic the- ory are based on three important pillars: (1) a gyrokinetic Vlasov equation written in terms of a gyrocenter Hamiltonian with quadratic low-frequency ponderomotive-like terms; (2) a set of gyrokinetic Maxwell (Poisson-Ampere) equations written in terms of the gyrocenter Vlasov dis- tribution that contain low-frequency polarization (Poisson) and magnetization (Ampere) terms derived from the quadratic nonlinearities in the gyrocenter Hamiltonian; and (3) an exact energy conservationlaw for the gyrokineticVlasov-Maxwell equations that includes all the relevant linear and nonlinear coupling terms. The foundations of nonlinear gyrokinetic theory are reviewed with an emphasis on the rigorous applications of Lagrangian and Hamiltonian Lie-transform perturba- tion methods used in the variationalderivationof nonlineargyrokineticVlasov-Maxwell equations. The physical motivations and applications of the nonlinear gyrokinetic equations, which describe the turbulent evolution of low-frequency electromagnetic fluctuations in a nonuniform magnetized plasmas with arbitrary magnetic geometry, are also discussed.

Nonlinear dust acoustic waves in a nonuniform magnetized complex plasma with nonthermal ions and dust charge variation

Propagations of nonlinear dust acoustic (DA) solitary waves and shock waves in a nonuniform magnetized dusty plasma are investigated. The incorporation of the combined effects of nonthermally distributed ions, nonadiabatic dust charge fluctuation, and the inhomogeneity caused by nonuniform equilibrium values of particle density, charging variable, and particle potential on the waves leads to a significant modification to the nature of nonlinear DA solitary waves. The nonlinear wave evolution is governed by a modified Zakhavov-Kusnetsov-Burgers (MZKB) equation, whose coefficients are space dependent. Using a generalized expansion method, new solutions for the MZKB equation are obtained. The form of solutions consists of two parts; one of them is the amplitude factor and the other is a superposition of bell-shaped and kink-type shock waves. New solutions are classified into three categories. A type of the solution is determined depending on the nonthermal parameter. Findings in this investigation should be useful for understanding the ion acceleration mechanisms close to the Moon and also enhancing our knowledge on pickup ions around unmagnetized bodies, such as comets, Mars, and Venus, including medium inhomogeneities with nonadiabatic dust charging processes.

Gyrotropic guiding-center fluid theory for the turbulent heating of magnetospheric ions in downward Birkeland current regions. II

A new fluid theory in the guiding-center and gyrotropic approximation derivable from the ensemble-averaged Vlasov-Maxwell equations that included the effect of wave-particle interactions for weakly turbulent, weakly inhomogeneous, nonuniformly magnetized plasma was recently given by Jasperse, Basu, Lund, and Bouhram [Phys. Plasmas 13, 072903 (2006)]. In that theory, the particles are transported in one spatial dimension (the distance s along the magnetic field) but the turbulence is two-dimensional. In this paper, which is intended as a sequel, the above theory is used for quasisteady conditions to find: (1) a new formula for the perpendicular ion-heating rate per unit volume Ẇi⊥(s), where Ẇi⊥(s) decreases for large s by what we call the “finite ion gyroradius effect”; and (2) a new formula for the perpendicular ion temperature at low altitudes, Ti⊥(s). Parametrized calculations for Ti⊥(s) are also given.

Gyrotropic guiding-center fluid theory for turbulent inhomogeneous magnetized plasma

In this paper, a new fluid theory is given in the guiding-center and gyrotropic approximation which is derivable from the Vlasov-Maxwell equations. The theory includes the effect of wave-particle interactions for the weakly turbulent, weakly inhomogeneous, nonuniformly magnetized plasma, and it is applicable to a variety of space and laboratory plasmas. It is assumed that the turbulence is random and electrostatic, and that the velocity-space Fokker-Planck operator can be used to calculate the correlation functions that describe the wave-particle interactions. Conservation laws are derived that relate the low-order velocity moments of the particle distributions to the turbulence. The theory is based on the work of Hubbard [Proc. R. Soc. London, Ser. A 260, 114 (1961)] and Ichimaru and Rosenbluth [Phys. Fluids 13, 2778 (1970)]. In the work presented here, the idea is proposed that the fluid equations can be solved (1) by using measurements of the turbulence to specify the electric-field fluctuations; and (2) by using measurements of the low-order velocity moments to specify the initial and boundary conditions.

Dispersion properties and field structures of eigenmodes of nonuniform plasma waveguides in a longitudinal magnetic field

We study the field structure and dispersion properties of a hybrid eigenmode guided by a nonuniform magnetized plasma waveguide. It is shown that the rotational and quasi-potential waves contribute to the formation of such a mode in the whistler frequency range. Depending on the plasma density, the rotational component of the hybrid mode is determined by either waves with complex transverse wave numbers or whistler waves, or by true surface waves. In the presence of an axial nonuniformity of the plasma in a channel, the transverse field structure of the propagating mode changes, which is stipulated by changes in both the values of transverse wave numbers and their dependence on the radial coordinate. It is found that the spectrum of axial wave numbers of eigenmodes of a plasma waveguide undergoes a pronounced condensation when smoothing the waveguide walls. The damping of the hybrid mode of a nonuniform waveguide due to electron collisions is found and it is shown that collisional losses determine the damping of waves trapped in the waveguide in the experiments on ionization self-channeling of whistler waves. We have found the effect of “displacing” the strong field from the inner core to the background outer region of the waveguide with increasing plasma density on its axis and broadening background region.

On the theory of cyclotron absorption at the wing of the absorption line

It is shown that, at the wing of the cyclotron absorption line, the relativistic effects associated with the dependence of the gyrofrequency on the particle energy can play an important role even far from the relativistic cyclotron cutoff region, i.e., even when the resonance lines in velocity space are mainly determined by the nonrelativistic Doppler synchronizm. Simple relationships for the relativistic absorption coefficient and power deposition profile in a nonuniformly magnetized plasma slab, as well as a new condition, which was not discussed earlier, for the applicability of the nonrelativistic approximation, are derived from illustrative physical considerations.

Drift-Alfvén eigenmodes in inhomogeneous plasma

A set of three nonlinear equations describing drift-Alfvén waves in a nonuniform magnetized plasma is derived and discussed both in linear and nonlinear limits. In the case of a cylindric radially bounded plasma with a Gaussian density distribution in the radial direction the linearized equations are solved exactly yielding general solutions for modes with quantized frequencies and with radially dependent amplitudes. The full set of nonlinear equations is also solved yielding particular solutions in the form of rotating radially limited structures. The results should be applicable to the description of electromagnetic perturbations in solar magnetic structures and in astrophysical column-like objects including cosmic tornados.

Two-dimensional convection and interchange motions in fluids and magnetized plasmas

In this contribution some recent investigations of two-dimensional thermal convection relevant to ordinary fluids as well as magnetized plasmas are reviewed. An introductory discussion is given of the physical mechanism for baroclinic vorticity generation and convective motions in stratified fluids, emphasizing its relation to interchange motions of non-uniformly magnetized plasmas. This is followed by a review of the theories for the onset of convection and quasi-linear saturation in driven-dissipative systems. Non-linear numerical simulations which result in stationary convective states reveal the process of laminar scalar gradient expulsion, leading to the formation of temperature plumes and vorticity sheets. These dissipative structures are demonstrated to result in temperature profile consistency and power law transport scaling far from the threshold. The last part of this paper deals with the generation of differential rotation by fluctuating motions through tilting of the convective structures. The role of kinetic energy transfer and shearing due to differential advection is pointed out. Numerical simulations for strongly driven systems reveal turbulent states with a bursty behaviour of the fluctuation level which is associated with relaxation oscillations in the kinetic energy of the azimuthally mean flows. This leads to a state of large-scale intermittency manifested by exponential tails in the single-point probability distribution function of the dependent variables. The global bursting is interpreted in terms of a predator–prey regulation from the point of view of energetics. Finally, a discussion is given of the relevance of these phenomena to a variety of magnetized plasma experiments.

Mechanism and scaling for convection of isolated structures in nonuniformly magnetized plasmas

Large-scale radial advection of isolated structures in nonuniformly magnetized plasmas is investigated. The underlying mechanism considered is due to the nonlinear evolution of interchange motions, without any presumption of plasma sheaths. Theoretical arguments supported by numerical simulations reveal an inertial scaling for the radial velocity of isolated structures in the ideal limit. This velocity increases as the square root of the structure size relative to the length scale of the magnetic field. The magnitude of the radial advection velocity, as well as the dynamical evolution of the structures, compares favorably with recent experimental measurements of radially propagating blob structures in the scrape-off layer of magnetically confined plasmas.

Low-frequency electrostatic dust-modes in a non-uniform magnetized dusty plasma

A self-consistent and general description of obliquely propagating low-frequency electrostatic dust-modes in a non-uniform magnetized dusty plasma system has been presented. A number of different situations, which correspond to different low-frequency electrostatic dust-modes, namely, dust-acoustic mode, dust-drift mode, dust-cyclotron mode, dust-lower-hybrid mode, and other associated modes (such as, accelerated and retarded dust-acoustic modes, accelerated and retarded dust-lower-hybrid modes, etc.), have also been investigated. It has been shown that the effects of obliqueness and inhomogeneities in plasma particle number densities introduce new electrostatic dust modes as well as significantly modify the dispersion properties of the other low-frequency electrostatic dust associated modes. The implications of these results to some space and astrophysical dusty plasma systems, especially to planetary ring-systems and cometary tails, are briefly mentioned.

Dust-lower-hybrid drift instabilities with dust charge fluctuations in an inhomogeneous dusty magnetoplasma.

Effects of a uniform magnetic field, the plasma inhomogeneity, and dust charge fluctuations on low-frequency dust-lower-hybrid drift waves have been investigated. Charging currents of electrons and ions to a spherical dust grain in a nonuniform magnetized dusty plasma have been calculated to study the charge fluctuation induced damping or growth of low-frequency drift waves. It is found that for strongly magnetized electrons and ions, the charge fluctuation damping is reduced significantly from that of an unmagnetized plasma. For sufficiently hot electrons, the drift wave exhibits instability in the absence of dust charge fluctuation damping.

Relativistic quasilinear diffusion in axisymmetric magnetic geometry for arbitrary-frequency electromagnetic fluctuations

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with arbitrary-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the elements of a relativistic quasilinear diffusion tensor are calculated explicitly for magnetically trapped particle distributions in axisymmetric magnetic geometry in terms of gyro-drift-bounce wave-particle resonances. The resonances can destroy any one of the three invariants of the unperturbed guiding-center Hamiltonian dynamics.

Streaming ion instability in nonuniform magnetized plasmas and nonlinear structures

A linear and nonlinear analysis is presented of coupled ion-acoustic and drift waves in a plasma consisting of electrons and ions that is penetrated by a mono-energetic stream of ions of another kind. All the plasma species (electrons and two ion fluids) are allowed to have density gradients in the direction perpendicular to the external magnetic field lines. In the linear domain the standard streaming instability of the acoustic modes and their interaction with drift modes is demonstrated. The threshold values of the stream velocity and the parallel wave number are calculated and discussed. In the nonlinear limit stationary coherent solutions are found which can represent the saturated state of the linearly unstable modes.

Magnetic-curvature-driven interchange modes in dusty plasmas

The magnetic-curvature-driven interchange mode instability of a weakly inhomogeneous dusty plasma is rigorously investigated. It is shown that the electric drift convection of the equilibrium dust charge density is a stabilizing factor for long wavelength interchange modes. In a fully nonlinear regime, the finite amplitude interchange modes may self-organize in the form of a dipolar vortex. The present results should be useful in the understanding of the properties of the interchange mode turbulence in nonuniform magnetized plasmas containing charged dust particles.

Collective motions in non-uniformly magnetized plasmas

While the reduced particle and fluid descriptions of magnetized plasma dynamicsare based on the same set of approximations they apparently give differingresults for the collective motions in non-uniform magnetic fields. Here it isshown that these two pictures give identical results when the diamagneticeffects due to charged particle gyration are taken into account. The subtlekinematical effects of the latter are revealed through many illustrations. Finally,this insight is used to explain the physical mechanism behind the idealinterchange instability. All these topics are intimately connected and have sofar not been given an adequate presentation in introductory textbooks.

Skin Size Vortices in Streaming Plasmas

Response of nonuniform magnetized plasma to strongly nonlinear electromagnetic perturbations driven by nonuniform flows is studied. Various types of coherent structures with spatial scales of the order of the electron skin depth are found carried by the flow or propagating through the plasma, with spatial scales measured in tens of kilometers for the magnetotail region.

Relativistic bounce-averaged quasilinear diffusion equation for low-frequency electromagnetic fluctuations

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with low-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the relativistic quasilinear diffusion coefficients are calculated explicitly for magnetically-trapped particle distributions in axisymmetric magnetic geometry in terms of drift-bounce resonant contributions associated with low-frequency fluctuations which conserve the first adiabatic invariant.

Linear and nonlinear electrostatic modes in a nonuniform magnetized electron plasma

Linear and nonlinear low-frequency modes in a magnetized electron plasma are studied, taking into account a proper description of the equilibrium plasma state that is inhomogeneous. Assuming a homogeneous magnetic field and sheared plasma flows, flute-like perturbations are studied in the presence of density and potential gradients. Linear analysis reveals the presence of a streaming instability and depicts conditions for global linear spiral mode. In the nonlinear domain, a tripolar vortex, which is driven and carried by the flow, is found. Also investigated are the consequences of a magnetic shear as well as nonuniformities along the magnetic field lines, which are shown to be responsible for the possible annulment of the magnetic shear effects. Streaming along the lines of the sheared magnetic field is also studied. A variety of nonlinear structures (viz. global multipolar vortices, local vortex chains, and tripolar vortices) is shown to be the consequence of the simultaneous action of the parallel and perpendicular flows.

Role of quasineutrality in drift waves

The ambiguity in using the quasineutrality approximation to describe the low-frequency plasma perturbations in nonuniform magnetized plasmas is pointed out.