Complex (dusty) plasmas: current status, open issues, perspectives

Strong-field effects in laboratory and astrophysical plasmas and high intensity laser and cavity systems are considered, related to quantum electrodynamical (QED) photon-photon scattering. Current state-of-the-art laser facilities are close to reaching energy scales at which laboratory astrophysics will become possible. In such high energy density laboratory astrophysical systems, quantum electrodynamics will play a crucial role in the dynamics of plasmas and indeed the vacuum itself. Developments such as the free-electron laser may also give a means for exploring remote violent events such as supernovae in a laboratory environment. At the same time, superconducting cavities have steadily increased their quality factors, and quantum nondemolition measurements are capable of retrieving information from systems consisting of a few photons. Thus, not only will QED effects such as elastic photon-photon scattering be important in laboratory experiments, it may also be directly measurable in cavity experiments. Here implications of collective interactions between photons and photon-plasma systems are described. An overview of strong field vacuum effects is given, as formulated through the Heisenberg-Euler Lagrangian. Based on the dispersion relation for a single test photon traveling in a slowly varying background electromagnetic field, a set of equations describing the nonlinear propagation of an electromagnetic pulse on a radiation plasma is derived. The stability of the governing equations is discussed, and it is shown using numerical methods that electromagnetic pulses may collapse and split into pulse trains, as well as be trapped in a relativistic electron hole. Effects, such as the generation of novel electromagnetic modes, introduced by QED in pair plasmas is described. Applications to laser-plasma systems and astrophysical environments are also discussed.

Nonlinear collective effects in photon-photon and photon-plasma interactions

The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable whenmore » nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. {copyright} {ital 1998} {ital The American Physical Society}« less

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Hamiltonian description of the ideal fluid

1 The Equations of Gas Dynamics 2 Magnetoplasma Dynamics 3 Waves in Magnetoplasmas 4 Magnetoplasma Stability 5 Transport in Magnetoplasmas 6 Extensions of Theory Bibliography Index

Physics of plasmas

The state of the art in the field of electron cyclotron emission and absorption of fusion plasmas confined by a magnetic field is reviewed. The general theory is described concisely, explicit results being given mainly for plasmas in local thermodynamic equilibrium. Moreover, the practical implications of these effects with respect to cyclotron radiation losses, the use of cyclotron emission as a diagnostic tool, and electron cyclotron heating and current drive are discussed with emphasis on tokamak plasmas.

http://iopscience.iop.org/article/10.1088/0029-5515/23/9/005/pdf

Electron cyclotron emission and absorption in fusion plasmas

Solitary electrostatic structures involving density depletions have been observed in the upper ionosphere by the Freja satellite [Dovner et al., 1994]. If these are interpreted as ion sound solitons, the difficulty arises that the standard Korteweg-de Vries description predicts structures with enhanced rather than depleted density. Here we show that the presence of non-thermal electrons may change the nature of ion sound solitary structures and allow the existence of structures very like those observed.

Electrostatic solitary structures in non‐thermal plasmas

It is found that a dusty plasma with inertial dust fluid and Boltzmann distributed ions admits only negative solitary potentials associated with nonlinear dust‐acoustic waves. The dynamics of small‐amplitude disturbances is governed by the Korteweg–de Vries (KdV) equation, the stationary solution of which assumes the inverted bell‐shaped secant hyperbolic squared profile. The associated dust and ion density perturbations are, on the other hand, positive. The solitary potentials can be identified as nonlinear structures in low‐temperature dusty plasmas such as those in laboratory and astrophysical environments.

Solitary potentials in dusty plasmas

Parallel flows with step function velocity and density profiles can support waves which have negative energy, in the sense that exciting them lowers the total energy of the system. A number of instabilities can occur because of the coexistence of positive and negative energy waves, or because of the damping of negative energy waves; some particular examples are discussed to show how appreciation of this role of negative energy waves allows one to predict the existence of instability before doing any detailed analysis, and to gain insight into the instability mechanism.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112079000495

The role of negative energy waves in some instabilities of parallel flows

The effects of vortex‐like and non‐thermal ion distributions are incorporated in the study of nonlinear dust‐acoustic waves in an unmagnetized dusty plasma. It is found that owing to the departure from the Boltzmann ion distribution to a vortex‐like phase space distribution, the dynamics of small but finite amplitude dust‐acoustic waves is governed by a modified Kortweg–de Vries equation. The latter admits a stationary dust‐acoustic solitary wave solution, which has larger amplitude, smaller width, and higher propagation velocity than that involving adiabatic ions. On the other hand, consideration of a non‐thermal ion distribution provides the possibility of coexistence of large amplitude rarefactive as well as compressive dust‐acoustic solitary waves, whereas these structures appear independently when the wave amplitudes become infinitely small. The present investigation should help us to understand the salient features of the non‐linear dust‐acoustic waves that have been observed in a recent numerical simulation study.

Effects of vortex‐like and non‐thermal ion distributions on non‐linear dust‐acoustic waves

Obliquely propagating ion-acoustic solitons in a magnetized plasma consisting of warm adiabatic ions and nonthermal electrons have been investigated. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation which admits a solitary wave solution for small amplitude limit. The highly nonlinear situation has also been studied by the numerical solution of the full nonlinear system of equations. The presence of nonthermal electrons changes the nature of ion-acoustic solitons. In the small amplitude limit the soliton may change from compressive to rarefactive, while the full nonlinear equations may allow rarefactive and compressive solitary waves to coexist. The effects of external magnetic field, obliqueness and ion temperature on the amplitude and width of the compressive and rarefactive solitons are discussed.

https://iopscience.iop.org/article/10.1088/0031-8949/1996/T63/012/pdf

R. A. Cairns

Papers

Electrostatic solitary structures in non‐thermal plasmas

Solitary potentials in dusty plasmas

The role of negative energy waves in some instabilities of parallel flows

Effects of vortex‐like and non‐thermal ion distributions on non‐linear dust‐acoustic waves

Ion-acoustic solitons in a magnetized plasma with nonthermal electrons