Volume 2, Issue 6, June 1995
Index of content:

Critical neutral density for high‐mode bifurcation in tokamaks
View Description Hide DescriptionThe effects of a neutral population are included in the high‐mode (H‐mode) bifurcation theory [Phys. Rev. Lett. 63, 2369 (1989)]. It is shown that, for a given set of parameters, there exist critical values of neutral density above which H‐mode bifurcation cannot occur. However, if the neutral density is fixed, for a given ion collisionality, this implies the existence of a critical ion temperature below which H‐mode bifurcation cannot occur. These critical values can be tested experimentally.

Analytical results on the breakdown of the convective amplifier model caused by space–time random fluctuations
View Description Hide DescriptionThe space and time behavior of backscatteringinstabilities is computed analytically in the strongly damped regime and in the presence of space–time random fluctuations. The fluctuations are described by a Gaussian process with exponentially decaying correlation function. The breakdown of the strongly damped model of the instability is obtained as a divergence of the average amplitude and intensity of the backscattered light [H. A. Rose and D. F. DuBois, Phys. Rev. Lett. 72, 2883 (1994)]. The length and time it takes for this divergence to occur is analytically computed.

Electron beam pulses produced by helicon‐wave excitation
View Description Hide DescriptionThe 443 nm Ar^{+} line emission intensity in a cylindrical argon magnetoplasma excited by a 13.56 MHz helicon antenna is found to be strongly modulated at the excitation frequency. The peak in optical emission propagates in the axial direction at a velocity corresponding to that of helicon waves launched by the antenna. The spatiotemporal modulation is consistent with pulses of electrons produced by acceleration under the antenna and subsequent entrainment of these electrons over half of a trapping period in the axial electric field of the helicon wave.

Nonlinear dynamical behavior of thermionic low pressure discharges. I. Simulation
View Description Hide DescriptionThe discharge modes of a thermionic low pressure discharge (p<1Pa) are investigated with the one‐dimensional particle‐in‐cell simulation codes PDP1 and XPDP1 [C. K. Birdsall, IEEE Trans. Plasma Sci. 19, 65 (1991)]. The simulation results provide a model approach for stable discharge modes, hysteresis, and for nonlinear relaxation‐oscillations. During this potential‐relaxation instability, nonlinear structures, e.g. electron holes and double layers, are observed. A Pierce–Buneman‐mode is suggested as a trigger mechanism for the onset of the instability. The detailed oscillation process can be subdivided into three distinct phases: expansion phase, double layer phase, and relaxation phase. This allows one to explain the parameter dependencies of the oscillation frequency. For a periodically driven discharge, mode‐locking in a period‐2 state is found and explained by the model. The mode‐locking phenomenon is studied systematically. The results of the simulations are well confirmed by experimental observations presented in Part II of this paper [T. Klinger et al., Phys. Plasmas 2, 1822 (1995)].

Nonlinear dynamical behavior of thermionic low pressure discharges. II. Experimental
View Description Hide DescriptionStrongly nonlinear relaxation oscillations of discharge current and plasma potential are investigated in a magnetized thermionic plasma discharge. The quasi‐one‐dimensional electron motion allows a direct comparison with one‐dimensional models and computer simulations. Two different stable discharge modes can be established, the low‐current space charge limited and the high‐current temperature limited mode. Time resolved probe measurements of the plasma potential distribution demonstrate that the current oscillations result from a strongly nonlinear instability of the potential structure in the weak current discharge mode. This confirms the model based on particle‐in‐cell simulations [F. Greiner et al., Phys. Plasmas2, 1810 (1995)]. The oscillation process consists of three distinct phases. The sequence of events and the observed parameter dependencies of the oscillation frequency is in accordance with the model. The periodically driven system shows the characteristic behavior of nonlinear oscillators: quasiperiodicity, mode‐locking, and period doubling sequences towards chaos. It is possible to link the complex dynamical behavior to the details of the trigger mechanism that are revealed by the simulation.

A self‐consistent quasistatic equilibrium for non‐neutral diamagnetic electron vortices
View Description Hide DescriptionA self‐consistent quasistatic equilibrium for a non‐neutral cylindrical electron vortex has been found using the two‐dimensional relativistic electron fluid equations. While other work on electron vortices considered a regime where the vortex radius is much smaller than the collisionless skin depth λ=c/ω_{ p }, this equilibrium is valid for large‐radius, diamagneticvortices and predicts a maximum radius of 2^{3/2}λ for a highly relativistic electron vortex. The vortex model shows good agreement with observations of diamagnetic electron vortices in two‐dimensional electromagnetic particle‐in‐cell simulations of magnetically insulated transmission lines.

Thermodynamic properties of anisotropic plasmas
View Description Hide DescriptionA novel aspect of the Onsager symmetries in magnetized plasmas is pointed out. If temperature anisotropy exists, the symmetry takes place only for electrostatic waves; for electromagnetic waves, the Onsager reciprocal relations are violated. The entropy production rate is obtained for the quasilinear relaxation. It is pointed out that the entropy production is not the Lyapunov function for the process. The quasi‐H‐theorem for the quasilinear stabilization is discussed by using Renyi’s entropy.

A general critique of inertial‐electrostatic confinement fusion systems
View Description Hide DescriptionThe suitability of various implementations of inertial‐electrostatic confinement (IEC) systems for use as D–T, D–D, D–^{3}He, ^{3}He–^{3}He, p–^{11}B, and p–^{6}Li reactors has been examined, and several fundamental flaws in the concept have been discovered. Bremsstrahlung losses for all of these fuels have been calculated in a general fashion which applies not only to IEC systems but also to most other fusion schemes; these calculations indicate that bremsstrahlung losses will be prohibitively large for ^{3}He–^{3}He, p–^{11}B, and p–^{6}Li reactors and will be a considerable fraction of the fusion power for D–^{3}He and D–D reactors. Further calculations show that it does not appear possible for the dense central region of a reactor‐grade IEC device to maintain significantly non‐Maxwellian ion distributions or to keep two different ion species at significantly different temperatures, in contradiction with earlier claims made about such systems. Since the ions form a Maxwellian distribution with a mean energy not very much smaller than the electrostatic well depth, ions in the energetic tail of the distribution will be lost at rates greatly in excess of the fusion rate. Even by using one of the best electron confinement systems proposed for such devices, a polyhedral cusp magnetic field, and by making exceedingly optimistic assumptions about the performance of that confinement system, the electron losses from the machine prove to be intolerable for all fuels except perhaps DT. In order for IEC systems to be used as fusion reactors, it will be necessary to find methods to circumvent these problems.

Modification of classical Spitzer ion–electron energy transfer rate for large ratios of ion to electron temperatures
View Description Hide DescriptionCorrections to the classical Spitzer heat transfer rate between ions and electrons are calculated for the case when the ion temperature T _{ i } is significantly higher than the electron temperature T _{ e }. It is found that slow electrons are partially depleted by their interactions with the ions, resulting in a decrease in the heat transfer in comparison with the Spitzer rate, which assumes perfectly Maxwellian electrons. The heat transfer steadily decreases from the classical value as T _{ i }/T _{ e } increases; for T _{ i }/T _{ e } values of several hundred, the heat transfer rate drops to around 60%–80% of the Spitzer result. A useful expression for the heat transfer correction factor in the case when all of the ion species are at the temperature T _{ i } is found to be P _{ ie }/(P _{ ie })_{Spitzer} ≊[1+(m _{ e }/m _{ i })(T _{ i }/T _{ e })]^{3/2} exp{−[3.5∑_{ i } (Z ^{2} _{ i } n _{ i }/n _{ e })(m _{ e }/m _{ i }) (T _{ i }/T _{ e })]^{2/3}}. This expression is quite accurate for values of ∑_{ i } (Z ^{2} _{ i } n _{ i }/n _{ e })(m _{ p }/m _{ i })(T _{ i }/T _{ e }) less than about 50 (where m _{ p } is the proton mass), although it underestimates the heat transfer rate for larger values of T _{ i }/T _{ e }, and one must resort to the more accurate but more complex analytical results derived in the paper. In the event that the ion distribution is non‐Maxwellian, T _{ i } in the correction factor should be replaced by 2〈E _{ i }〉/3, where 〈E _{ i }〉 is the mean ion energy.

Thermal instability of a compressible finite Larmor radius, Hall plasma in porous medium
View Description Hide DescriptionThe thermal instability of a compressible plasma in porous medium is considered in the presence of a uniform horizontal magnetic field to include the Hall current and finite Larmor radius effects. The Hall current and finite Larmor radius (FLR), individually, have destabilizing and stabilizing effects, respectively, on the system. In the simultaneous presence of both, there is a competition between the destabilizing role of Hall current and stabilizing role of FLR and each—Hall current and FLR—succeeds in stabilizing a certain wave‐number range. In the absence of magnetic field (and hence absence of Hall current and FLR), the destabilizing effect of medium permeability is depicted but in the presence of magnetic field (and hence presence of Hall current and FLR), the medium permeability may have a stabilizing or destabilizing effect on thermal instability of the plasma. In contrast to the case of vertical magnetic field (and corresponding Hall current and FLR), the oscillatory modes are not allowed for, (c _{ p }β/g)≳1, in the case of horizontal magnetic field (and corresponding Hall current and FLR). The effect of compressibility is found to postpone the onset of thermal instability in plasma.

A paradox involving the second law of thermodynamics
View Description Hide DescriptionA simple paradox is posed that appears to challenge the second law of thermodynamics in a blackbody plasma environment. Laboratory experiments approximating salient aspects of this system fail to resolve the paradox.

Hot‐ion Bernstein wave with finite k _{∥}
View Description Hide DescriptionThe complex roots of the hot plasmadispersion relation in the ion cyclotron range of frequencies have been surveyed. Consistent with current understanding, the cold plasma fast wave appears at low values of perpendicular wave number k _{⊥}, followed by the well‐known Bernstein wave at higher k _{⊥}. At still higher k _{⊥} there can be two previously unappreciated hot plasma waves with relatively little sensitivity to frequency, in contrast to the Bernstein wave which is characterized by large changes in k _{⊥} for small changes in frequency or magnetic field. The latter waves exist only for relatively large k _{∥}, the wave number parallel to the magnetic field. Both waves are strongly absorbed if the electron temperature is near the ion temperature, but not in a hot‐ion, cold‐electron, plasma.

Evolution to turbulence in a capacitor model of resonance absorption
View Description Hide DescriptionThe interaction of a powerful, subpicosecond laser pulse with plasma is modeled within the capacitormodel by means of one‐dimensional electrostatic particle code. The temporal profile of the laser pulse and the growth of the electron energy by several orders of magnitude were taken into account providing adequate temporal and spatial resolution. It is shown that initially, a coherent structure is excited, and growth of plasma waves results in wave breaking and acceleration of electrons followed with decreasing intervals between them, accelerating electrons in both directions. Finally the system evolves to a state of moderate Langmuir turbulence where E ^{2}/(16πnT)≪1 due to the strong heating of plasma electrons and the decrease of excited plasma wave fields.

Turbulent transport across invariant canonical flux surfaces
View Description Hide DescriptionNet transport due to a combination of Coulomb collisions and turbulence effects in a plasma is investigated using a fluid moment description that allows for kinetic and nonlinear effects via closure relations. The model considered allows for ‘‘ideal’’ turbulent fluctuations that distort but preserve the topology of species‐dependent canonical flux surfaces ψ_{♯,s }≡∫d F⋅B _{♯,s }, where B _{♯,s }≡∇ ×[A+(m _{ s }/q _{ s })u _{ s }], in which u _{ s } is the flow velocity of the fluid species. Equations for the net transport relative to these surfaces due to ‘‘nonideal,’’ dissipative processes are found for the total number of particles and total entropy enclosed by a moving canonical flux surface. The corresponding particle transport flux is calculated using a toroidal axisymmetry approximation for the ideal surfaces. The resulting net transport flux includes classical, neoclassical‐like, and anomalous contributions and shows for the first time how these various contributions should be summed to obtain the total particle transport flux.

Nonlinear instability and chaos in plasma wave–wave interactions. I. Introduction
View Description Hide DescriptionConventional linear stability analyses may fail for fluid systems with an indefinite free‐energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave–wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper (submitted to Phys. Plasmas), this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action‐angle form. The normal modes correspond to Doppler‐shifted ion‐acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two‐wave interactions, and to either decay or explosive instability via three‐wave interactions. These instabilities are described for various integrable systems of wavesinteracting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper.

Self‐consistent mean field electrodynamics of turbulent dynamos
View Description Hide DescriptionA turbulent dynamo in a conducting fluid is accompanied by the generation of small‐scale magnetic fields, which are much stronger than the mean dynamo‐generated magnetic field. These small‐scale fields modify the α effect in such a way as to stabilize the dynamo process, α=(α_{0}+β_{0} R⋅/B∇× R)/(1+R ^{2}), where α_{0}, β_{0} are the standard kinematic dynamo parameters, and R is proportional to the mean magnetic fieldB _{0}, R=B _{0}/(4πρV ^{2}/R_{ m })^{1/2}, ρ is the fluid density, V is the characteristic turbulent velocity, and R _{ m } is the magnetic Reynolds number. The derivation of this formula is illustrated using a simple model—the turbulent dynamo for an asymmetrical top.

Collisional regimes of radiation‐driven Langmuir turbulence
View Description Hide DescriptionNumerical solutions of the Zakharov equations for a plasma driven above the electron plasma frequency by a long‐wavelength radiation pump can be applied to both ionospheric modification experiments and laboratory laser‐plasma interactions. A key difference between these two environments is the much larger collisional damping of Langmuir waves near the critical density in laser plasmas. Zakharov equation simulations in one and two dimensions reveal a significant change in the character of the saturated turbulence state of the electromagnetic ion‐acoustic decay instability for pump strengths near threshold as the collisional damping is increased to values appropriate to certain (low‐intensity) laboratory laser‐plasma experiments [Phys. Fluids B 3, 1983 (1991)]. The linear‐instability is then characterized by the coupling of the up‐ and downshifted Langmuir decay modes. A new turbulence regime differing from existing models of both weak and strong turbulence is found, which is characterized by a sequence of narrow peaks in the Langmuir frequency spectrum and a nonlinearly broadened wave‐vector spectrum centered near the linearly most unstable modes. Results in this regime may be relevant to second harmonic emission experiments [Phys. Fluids B 3, 1983 (1991)].

Excitation of Alfvén cyclotron instability by charged fusion products in tokamaks
View Description Hide DescriptionThe spectrum of ion cyclotron emission (ICE) observed in tokamak experiments shows narrow peaks at multiples of the edge cyclotron frequency of background ions. A possible mechanism of ICE based on the fast Alfvén Cyclotron Instability (ACI) resonantly excited by high energy charged products (α‐particles or protons) is presented here. Two‐dimensional eigenmode analysis of ACI mode structure and eigenfrequency are obtained in the large tokamak aspect ratio limit. The ACI is excited via wave‐particle resonances in phase space by tapping the fast ion velocity space free energy. The instability growth rates are computed perturbatively from the perturbed fast particle distribution function, which is obtained by integrating the high frequency gyrokinetic equation along the particle orbit. Numerical examples of ACI growth rates are presented for TokamakFusion Test Reactor (TFTR) [World Survey of Activities in Controlled Fusion Research [Nuclear Fusion special supplement 1991] (International Atomic Energy Agency, Vienna, 1991)] supershot plasmas. The fast ion distribution function is assumed to be singular in pitch angle near the plasma edge. The results are employed to understand the ICE in Deuterium‐Deuterium (DD) and Deuterium‐Tritium (DT) tokamak experiments.

Effect of E×B drift on divertor plasma flows
View Description Hide DescriptionDue to the influence of a sheared E×B drift affecting the inertia term in the plasma momentum equation a strong variation of the plasma pressure along the magnetic field lines can appear similar to experimental observations of the ‘‘detached divertor’’ regimes. The typical radial scale length of plasma parameter variation, such that the E×B drift becomes important, is of the order of the poloidal ion gyroradius.

Two‐dimensional magnetohydrodynamic simulation of a flowing plasma interacting with an externally imposed magnetic field
View Description Hide DescriptionThe problem of plasma flow relative to a modulated magnetic field has been the subject of several studies. One motivation for studying this problem is the possibility of using a deliberately imposed surface of magnetic islands as a means of velocity profile control. This subject is also of importance for the study of stability against ideal and resistive magnetohydrodynamic(MHD) modes and the topic of locked modes. A two‐dimensional (2‐D) MHD simulation code is used to examine the behavior of a plasma flowing, in steady state, past a modulated magnetic field in ‘‘slab geometry.’’ It is shown that at ‘‘low’’ velocities the stress is dominated by the Maxwell and the viscosity terms and that forces are exchanged between the plasma and the magnetic field in a narrow boundary surrounding the island. It is found that the island is suppressed when the viscous force at the separatrix exceeds the maximum force that can be supported by an island. For ‘‘high’’ velocities (velocities beyond the critical velocity for island suppression), the stress is dominated by the Maxwell and the Reynolds terms, and the exchange of forces is taking place in a narrow region around the point where the plasma flow velocity matches the Alfvén speed.