Table of contents

A laboratory experiment concerned with the basic physics of magnetic field line reconnection will be discussed. Stimulated by important processes in space plasmas and anomalous transport in fusion plasmas the work addresses the following topics: Dynamic magnetic fields in a high beta plasma, magnetic turbulence, plasma dynamics and energy transport. First, the formation of magnetic neutral sheets, tearing and island coalescence are shown. Nonstationary magnetic fluctuations are statistically evaluated displaying the correlation tensor ⟨BB⟩ in the ω-k domain for mode identification. Then, the plasma properties are analyzed with particular emphasis on transport processes. Although the classical fluid flow across the separatrix can be observed, the fluctuation processes strongly modify the plasma dynamics. Direct measurements of the fluid force density and ion acceleration indicate the presence of an anomalous scattering process characterized by an effective scattering tensor ν*. Turbulence also enhances the plasma resistivity η* by one to two orders of magnitude. Measurements of the three-dimensional electron distribution function f_e(v_x, v_y, v_z) using a novel energy analyzer exhibit the formation of runaway electrons in the current sheet. Associated microinstabilities are observed. Finally, a macroscopic disruptive instability of the current sheet is observed. Excess magnetic field energy is converted at a double layer into particle kinetic energy and randomized through beam-plasma instabilities. These laboratory results will be compared with related observations in space and fusion plasmas.

Pure electron plasmas are one of the simplest systems on which plasma wave and transport effects can be studied. Two recent experiments on this system are discussed. The loss of electrons due to anomalous transport has been measured over a six order of magnitude variation in containment time. The containment time scales approximately as [magnetic field/plasma length]². The growth of the l = 1 diocotron wave due to resistance between sections of the bounding wall has been observed. The measured growth rates agree with theory.

The theoretical basis for magnetic confinement is examined. Recent progress on confinement of pure electron plasma is magnetic mirrors and simple torodial configurations is described. Non-neutral configurations involving electrons and ions in mirror geometry are investigated. A basic experiment on mirror stability is proposed.

Experimental observations on the interaction of intense electron beams with magnetically confined plasmas, when the beam has a substantial component of the velocity in the direction perpendicular to the magnetic field are summarised. The interaction takes place in two stages; in the first stage the response is essentially magnetic due to return currents induced in the plasma, in the second stage, those currents decay converting energy into plasma heating. Observation of fast magnetic field diffusion point to beam-induced turbulence in the plasma.

The results of the experimental study of the REB–plasma interaction in the two-stream instability regime are presented. The distribution function of plasma electrons has been studied with the use of the laser scattering system, soft X-ray diagnostics and a multifoil analyzer of fast electrons. It is shown that during an effective REB–plasma interaction the distribution function of heated electrons is strongly non-equilibrium. A high-energy part of the distribution function has been registered in the experiments simultaneously by three independent methods. The density of "hot" electrons with a characteristic energy of about 1 keV constitutes several per cent of the total plasma density. The experimental results obtained are discussed in terms of the two-stream instability of the REB in a plasma.

A variety of topics in laser-plasma interaction physics is reviewed. The trend from exploding-pusher experiments to ablative compression studies already evident at the time of the Nagoya Conference in 1980 has gathered momentum. The particular emphasis placed at present on the scaling of interaction phenomena with wavelength, in particular stimulated Raman scattering and two-plasmon decay, filamentation and jet formation together with aspects of absorption and transport phenomena is essential for a proper understanding of laser–plasma interactions.

A broad program of research on the confinement of plasma in nested toroidal magnetic surfaces is being carried out at the Princeton Plasma Physics Laboratory. Tokamak research at PPPL is progressing into the phase of technology development, in preparation for the support of a large-scale reactor-oriented effort. World-wide experimental research has brought the stellarator concept to the point of plasma-physical demonstration; at PPPL, the theoretical study of reactor-compatible stellarator design is yielding promising new results. Initial spheromak formation experiments have been successful. The confinement properties of the spheromak will begin to be studied experimentally during the next year.

In recent years the emphasis in research on the magnetic mirror approach to fusion has been shifted to address what are essentially economically-motivated issues. The introduction of the Tandem Mirror idea solved in principal the problem of low Q (low fusion power gain) of mirror-based fusion systems. In order to optimize the tandem mirror idea from an economic standpoint, some important improvements have been suggested. These improvements include the thermal barrier idea of Baldwin and Logan and the axicell concept of Kesner. These new modifications introduce some special physics considerations. Among these are: (1) The MHD stability properties of high energy electron components in the end cells; (2) The optimization of end-cell magnetic field configurations with the objective of minimizing equilibrium parallel currents; (3) The suppression of microstabilities by use of "sloshing ion" distributions. Following a brief outline of tandem mirror concepts, the above three topics are discussed, with illustrative examples taken from earlier work or from recent design studies.

The JET scientific programme is aimed at the achievement of a deuterium-tritium plasma with parameters close to those envisaged for a fusion reactor. The programme is paced and largely determined by the gradual build-up over four years of the additional heating power into the plasma. The present expectation is that it will be possible to reach conditions where the thermonuclear power in alpha particles makes a significant contribution to the energy balance in the core of the JET plasma.

The JET experiment is placed in the context of the European fusion programme and the desiderata and time scales for a large post-JET tritium-burning tokamak (Next European Torus, NET) are deduced.

The physics requirements of a Tokamak Engineering Test Reactor, considered as the step following the generation of large tokamaks presently under construction in developing a fusion reactor, are concisely stated and discussed, using as a starting point the analysis of the INTOR Workshop.

The present state of our understanding of spheromak physics is reviewed by comparing experimental results with MHD equilibrium and stability theory.

A short review of the results of kinetic simulation of collective phenomena in open plasma systems with the variable total energy and number of particles, i.e., the particle and energy fluxes on boundary surfaces and/or their internal sources and channels is given. Three specific problems are considered in different detail for such systems in one-dimensional geometry: the generation and evolution of double layers in a currently unstable plasma: the collisionless relaxation of strongly non-equilibrium electron distributions; the Langmuir collapse and strong electrostatic turbulence in systems with parametric excitation of a plasma by an external pumping wave and with cooling the fast non-Maxwell electrons. In all these cases the non-linearity and a collective character of processes give examples of new dissipative plasma structures that essentially widen our idea about the nature of the plasma turbulence in non-homogeneous open systems.

A new generation of Z-pinches employing high voltage, high current pulsed lines as power sources produce dense hot plasmas with enhanced stability properties. Three methods of Z-pinch formation are currently in use: (1) cylindrical collapse and compression of a pre-ionised gas; (2) laser initiation and Joule heating of a gas embedded pinch, and (3) hollow gas puff and subsequent collapse to the axis. The first method shows no dynamic bounce and no instability over about ten radial Alfvén transit times. The laser initiated Z-pinch shows benign helical structures, whilst the gas puff experiments are known for their high X-ray energy conversion associated with m = 0 instabilities. The first two experimental conditions are relevant for fusion. A calculation of energy balance for satisfying Lawson conditions with axial and radial energy losses and radiation loss shows that a current I of ∼ 10⁶ A and a line density N of 6 × 10¹⁸m^-1 are required. This leads to two coincidences of physical quantities that are very favourable for controlled fusion. The first is that at this line density and under pressure balance the ratio of the ion Larmor radius to pinch radius is of order 1 so that a marked stabilisation of the configuration is expected. The second coincidence is that the current is only just below the Pease–Braginskii limit; this will permit the possibility of radiative collapse to attain the high density (∼ 4 × 10²⁷ m^-3) and small radius (∼ 20 μm) required for a compact (0.1 m long) discharge. The confining self-magnetic field is 10⁴ T, the confinement time ∼ 100 ns, and a matrix of pulsed discharges is envisaged in a moderator and breeding medium which does not have the wall-loading limitations of tokamaks.

The formation, confinement and stability of two types of compact toroids, spheromaks and field reversed configurations (FRC), are reviewed. Spheromaks, which contain both toroidal and poloidal magnetic fields, have been formed with magnetized coaxial plasma guns, by a combination of Z- and θ-pinch techniques and by an electrodeless slow induction technique, and trapped in both prolate and oblate flux conservers. As predicted by theory, the prolate configuration is unstable to the tilt mode, but the oblate configuration with a conducting wall is stable. Configuration lifetimes of up to 0.8 ms are observed. The FRC is a high-beta, highly prolate compact toroid formed with field-reversed theta-pinch techniques and having purely poloidal magnetic field. Theory predicts unstable fluting and internal tilting modes, but they are not observed experimentally. Configurations with high densities ∼ 10¹⁵ cm^-3 and with lifetimes of 50–120 μs are terminated by an n = 2 rotational mode of instability.

A stable relativistic electron beam (REB) ring for plasma confinement was formed by REB injection with the help of image currents in a resistive shell, and then the ring was compressed in major radius by a factor 2.0. The current rise well obeyed the adiabatic scaling law.

The problem of fast magnetic reconnection across an x-type magnetic neutral point is reconsidered. Several different numerical computations of the 2D incompressible MHD equations are presented concerning externally driven as well as spontaneous reconnection. The common result of these computations is that in the limit of small resistivity reconnection occurs in a diffusion layer of finite length, corresponding to the Sweet–Parker reconnection model. A Petschek type process is only obtained by assuming a strongly enhanced resistivity in the diffusion region.

Starting from a model of an interchange-unstable plasma in a shearless magnetic field, the successive bifurcations and the transition to turbulence of the system are studied in various approximations. Numerical calculations using the finite element method and a spectral method with mode truncation yield converging results in certain domains of parameters. In the last part of the paper it is shown that a tearing-unstable plasma in a sheared magnetic field has a formally similar description and therefore should also be investigated in terms of bifurcation theory.

Lower hybrid current-drive experiments have been carried out on the PLT Tokamak. Steady currents up to 175 kA have been maintained for three seconds and 400 kA for 0.3 s by the rf power alone. The principal current carrier appears to be a high energy (∼ 100 keV) electron tail, concentrated in the central 20–40 cm diameter core of the 80 cm PLT discharge. Effective current drive is observed only for _e ⩽ 8 × 10¹² cm^-3. This limitation may be a wave propagation phenomenon and not a fundamental plasma physics effect.

The lower hybrid current drive experiments have been carried out in the WT-2 tokamak. The rf power P_rf is injected near the end of tokamak discharge by the four waveguides array. The plasma can be sustained by the rf driven current only during the rf injection period. The scaling of the rf driven current and the density limit are studied. The scaling of I_rf is obtained as n_e × I_rf/P_rf ≃ 0.15 × 10¹³ kA·cm^-3·kW^-1. The density limit exists and it depends on the energy distribution of electrons in the ohmically heated initial plasmas. The maximum value obtained in the present experiments is 1.4 × 10¹³ cm^-3. The high frequency instability associated with the rf driven current has been studied and found it can be stabilized by the electron cyclotron heating.

This paper contains the analysis of the state of electron cyclotron resonance heating in tokamaks. It presents the results of numerical simulation of ECRH at different conditions and the review of last experiments performed on tokamaks T-10, FT-1, JFT-2 and JSX-B. The opportunities and constraints of ECRH in tokamaks are discussed.

Laboratory observations made on the reversed-field pinch (RFP) show that this magnetic confinement configuration exhibits "metastable" minimum energy properties similar to those predicted by Taylor. The theoretical basis of the RFP is reviewed and compared with recent observations made on the Los Alamos ZT-40 RFP device. Particular emphasis is placed on the observation that the reversed field is regenerated by a dynamo-like mechanism for times large compared to the classical field diffusion time.

Experimental results and theoretical models for the boundary layer of toroidal confinement devices are described. Emphasis is put on the scrape-off layer of poloidal divertor tokamaks which have demonstrated a significant reduction in impurity content as compared to limiter operation. The competition of transport processes parallel and perpendicular to the field lines, determining the profiles of plasma density, temperatures and impurity concentrations, is described. The role of hydrogen recycling in the divertor chamber is underlined, which decides the flow Mach number in the scrape off, the plasma parameters in the target plate vicinity and the regime of energy transport along the field lines.

Limiter and divertor operation in ASDEX are compared and the favourable results of the latter explained by the reduced impurity production of the target plates and their distance from closed field lines, which impurity ions would have to overcome by diffusion against the plasma flow into the divertor chamber.

For an efficient control of the effects of plasma surface interaction improved diagnostics of the plasma edge region is needed. Laser induced fluorescence offers the possibility to measure the density, the velocity distribution and the flux density of neutral and ionized particles with good time and space resolution. In contrast to currently used probes it does not disturb the plasma and is not affected by it. A survey on results obtained with this technique in tokamaks and other magnetic confinement devices is presented. It is shown that fluxes of metal atoms emitted by the wall can be determined with good accuracy. In addition important information on processes of plasma surface interaction can be obtained. From the measured spatial distribution of particle densities the ionization length as well as T_e can be derived and knowledge about the structure of the scrape off layer is gained.

Using laser induced fluorescence on injected beams of suitable chosen metal atoms, n_e and T_e can be determined in the boundary layer even at low n_e.

Present limits of the method with respect to type and density of species to be detected and future prospects are discussed.

Density fluctuation observation can be obtained by scattering of electromagnetic radiation. New developments and applications are presented. By heterodyne detection the scattered signal is shown to be the time variation of a space Fourier transform of the density. The antenna beam, that especially defines the sensitivity, is experimentally investigated. The time variation is used in two occurrences, to check quantum efficiency uniformity on detectors area, and in an air turbulence where the interspectrum is obtained between two scattering devices looking at different regions. Calibration formulas are given for quantitative measurement of density fluctuation spectrum. Observations are also reported on a tokamak plasma, on the drift wave spectrum, and on a new second order group of oscillations that were observed during ion cyclotron radio-frequency heating. The analysis shows this new group is a forced oscillation by beating of the drift waves with the high-frequency heating wave, and its amplitude provides a measurement of the HF wave electric field.

The generation of hydrogen and deuterium negative ions and beams is reviewed, with particular emphasis on volume production in plasmas, which has recently been found to be a useful element of possible high-power negative-ion-based neutral beam systems. The experimental evidence for volume production is based on the measurement of high density (5 × 10¹⁰ cm⁻³) and high fractions (10–35%) of H⁻ and D⁻ ions in plasmas, using the photodetachment method, and on measurements or ro-vibrational populations using coherent anti-Stokes Raman scattering (CARS). These measurements are discussed in terms of a theoretical model relying on the assumption that the dominant negative ion production process is the recently discovered dissociative electron attachment to highly vibrationally excited molecules.

Photodetachment, CARS and extraction experiments performed in different magnetic multipole configurations are described; they indicate that the magnetic multipole may be a useful device for this application.

Implosion processes of 1.053 μm laser irradiated (1) thin solid density Be coated plastic microballoon and (2) thick low Z foam coated glass micro-balloon have been diagnosed by an X-ray flash radiography method to investigate implosion symmetry of the pellet shell.

Asymmetric implosion of Be coated pellet is found to be due to a strong inhibition of lateral energy transport by self-generated magnetic field. In the foam coated pellet significant improvement of the symmetry has been achieved.

Implosion process has been investigated by using blue, green, red and far infrared lasers. Various types of target are compared to improve the implosion properties. "Cannon ball" target is proposed and tested to show the high efficiency in implosion.

We present the results of a study, using Thomson scattering, of parametrically driven ion and electron plasma waves in a CO₂ laser–plasma interaction. The experiments were conducted in a pre-formed plasma at a density near the quarter critical density of the CO₂. Waves produced by two plasmon decay as well as the Raman and Brillouin scattering instabilities are observed.

We report on experimental and theoretical studies of stimulated Brillouin and Raman scattering occurring simultaneously in moderate density, long scale length plasma irradiated by a moderate intensity CO₂ laser beam. Saturated Brillouin (20%) and Raman (0.7%) backscatter are observed, the former as a convective and the latter as an absolute instability. Importantly, it is found both experimentally and theoretically that the presence of ion fluctuations associated with the Brillouin process can profoundly affect the Raman instability.

Hydrodynamic stability theory has focussed on a few simple test cases to obtain the sharpest possible confrontations between theory and experiment. Six of these are briefly reviewed: plane Poiseuille and Couette flow, pipe flow, rotating Couette flow, thermally-driven Bénard convection, and the Blasius laminary boundary layer. Linear perturbation theory seems inadequate in the first three cases, and satisfactory in the last three. Insufficient information, experimental or theoretical, exists in magnetohydrodynamics to make any comparably decisive tests.

We give the systematic theory of the derivation of the generalized set of Zakharov equations for a collisionless isotropic plasma taking into account the nonlinear Landau damping and relativistic effect. The conditions of deriving the nonlinear Schrödinger equation from the generalized system are shown. The new branch for modulational instability is found. It is shown that the wave-wave-particle interaction leads to the braking of the soliton.

Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering.

We discuss the generalized Zakharov equations derived by Ovenden and Statham and given reasons for being sceptical about using the fluid approximation as is done in the derivation of these equations - except perhaps for those situations which involve weakly magnetized Langmuir plasmas and we also compare them with equations suggested by other authors to describe strong turbulence in a magnetized plasma.

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Turbulence and solitary vortex structures of electrostatic drift waves are presented using a simple model equation based on two-dimensional cold ions and Boltzmann electrons.

The effects of resonant particles on the propagation of Langmuir solitons are studied. The main effects are found to be a deceleration of the solitons, and for high-amplitude solitons, emission of ion-sound tails. Results from perturbation theory are compared with numerical solutions of the model equations.

The effects of plasma turbulence on the generation of radiation in a system of a free-electron-laser and a molecular and plasma medium is investigated by means of a kinetic description. The results are that low frequency waves become damped due to the presence of turbulence, whereas for sufficiently high frequencies (ω > ω_peγ, the plasma frequency times the relativistic factor) the turbulence, also in the presence of a molecular medium (ω > ω_r, the molecular resonance frequency), may lead to amplification of the radiation.

The evolution of a steep wavefront propagating perpendicular to an externally applied homogeneous magnetic field is considered. The propagation is accompanied by the excitation of low-frequency waves. When the nonlinear interaction is taken into account we observe the evolution of a modulational instability trailing the wavefront.

Approximate analytical solutions are obtained for the set of coupled nonlinear partial differential equations which govern the evolution of a steep wavefront propagating perpendicular to an externally applied homogeneous magnetic field. Several of the features noted in a numerical solution of these equations by Pécseli and Thomsen are predicted by these approximate solutions.

The formation of small scale striations observed in ionospheric heating experiments is explained in terms of electrostatic waves propagating across the magnetic field, generated by linear conversion on the local density gradient and trapped in the density depletions. Enhancement of the process is due to ohmic overheating of the depletions, resulting in decreased density there. The process is centered at the upper hybrid level. Further growth is predicted when the initial density depressions exceed a threshold which is calculated. Such a nonlinear threshold is shown to be associated with a certain hysteresis phenomenon which has been observed in experiments.

Microscopic analysis on the basis of the improved hypernetted chain equations shows that the plasma fluid may form a metastable glassy state in the supercooled domain over a wide range of the plasma parameter. Transition time from the metastable state to the crystalline state is estimated to be sufficiently large so that the possibility of the glassy state has an astrophysical relevance.

A new theory of cosmic ray spectra if presented which predicts the energy spectra for cosmic ions and electrons ∼ 1/^γ, up to the highest possible in the spectra with the value of γ = 3 very close to that observed ( is the particle energy). The theory shows that the He³ cosmic ions are preferentially created as copared to He⁴ cosmic ions in coincidence with observations. The theory shows that the abundance of heavy ions in cosmic rays with Z > 20 should be two orders of magnitude larger than the abundance of these elements in usual matter with agreement to observations. The theory gives the subcosmic ray ( ≪ mc²) spectra ∼ 1/ ( is the kinetic energy) and gives also the increase of the abundances or nonrelativistic but superthermal He³ ions as compared to He⁴ ions, which could be used to explain the increase in the abundances of He³ in active solar regions.

There is not any ad hoc assumptions in the theory, it is based on the well established resonant wave particle interactions in turbulent plasmas and especially the radiative effects in these interactions (this interaction is called here radiative resonant wave particle interaction).

The nonlinear evolution of Langmuir waves excited by the beam-plasma instability is studied experimentally. The emission of electromagnetic waves at the second harmonic of the plasma frequency and the formation of a density depression have been observed. These phenomena are consistent with the predictions of the strong Langmuir turbulence theory.

It is demonstrated that steady-state cyclotron radiation of extraordinary electronic waves (whistlers) may be unstable in a plasma trap with magnetic mirrors. The periodic self-modulation of cyclotron instability takes place for a certain (sufficiently small) power of a particle source and a certain angular dependence of its parameters. This modulation is due to the change in the distribution function anisotropy. The change in anisotropy has an effect similar to that of an optic nonlinear filter. The characteristics of spike-like periodic cyclotron instability regime are found.

Different methods of plasma stabilization in axisymmetric mirrors are described. Some stabilizing mechanisms of MHD and kinetic nature are discussed for rather long systems.

Experiments have been performed in a steady-state linear machine with a low temperature, low density plasma in the collisionality regime of the dissipative trapped ion instability. This instability was seen and identified through the observed dependence of wave amplitude on trapped fraction, axial and radial structure, and collisionality and through the scaling of the real frequency with trapped fraction.

Possible change of ignition condition by plasma turbulence is discussed.

On the basis of present day knowledge of plasma physics and available technologies it is shown that experiments having the purpose to test the thermonuclear burn conditions of plasmas with fusion reactions that do not produce neutrons can be undertaken.