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Notes: Summary Stiff rod-like chain molecules with harmonic bond length potentials and trigonometric bond angle potentials are used to model Langmuir monolayers at high densities. One end of the rod-like molecules is strongly bound to a flat two-dimensional substrate which represents the air-water interface. A ground-state analysis is performed which suggests phase transitions between phases with and without collective uniform tilt. Large-scale off-lattice Monte Carlo simulations over a wide temperature range show in addition to the tilting transition the presence of a strongly constrained melting transition at high temperatures. The latter transition appears to be related to two-dimensional melting of the head group lattice. These findings show that the model contains both, two- and three-dimensional ergodicity breaking solidification transitions. We discuss our findings with respect to experiment.

Notes: This Brief Communication investigates the influence of toroidal effects (due to the coupling of various poloidal harmonics) on the nonlinear saturation of the m=1 island. Bounds are obtained relating the aspect ratio, the shear at the q=1 surface, and the saturated island width. Provided these bounds are satisfied, it is then found that the cylindrical m=1 island theory of Thyagaraja and Haas [Phys. Fluids B 3, 580 (1991)] is valid for toroidal geometry.

Notes: The purpose of this paper is to investigate the possible relationships between transport properties such as thermal diffusivity and resistivity on the one hand, and the magnetic properties such as q profile and toroidal flux change on the other, in tokamaks that exist under macroscopically quasistationary conditions. It is experimentally well established that when the sources are held constant over times long compared with energy and particle confinement times, tokamak discharges can exist in a quasistationary state with or without periodic sawteeth superposed on the basic equilibrium.The principal aim of this study is to provide qualitative physical insight into the nature of such states. For simplicity, single-fluid equations are assumed and the analysis is restricted to a cylinder model. The complete set of conservation equations comprising continuity, pressure balance, Ohm's law, and energy balance are used along with appropriate sources. The conductive energy loss is assumed to occur due to an anomalous thermal diffusivity. Following earlier time-dependent studies of tokamak transport phenomenology due to the authors [Haas and Thyagaraja, Plasma Phys. Controlled Fusion 28, 1093 (1986)], the friction force in the generalized Ohm's law is assumed to be described by an effective resistivity tensor with its principal axes in the poloidal and toroidal directions. The toroidal resistivity is taken to be of order Spitzer while the poloidal component ηθ is assumed to be anomalously large compared with ηz. A range of phenomena involving Ohmic discharges, auxiliary heated discharges, and noninductively driven currents is investigated. Attention is drawn to the joint implications of the conservation laws and the general forms of the constitutive relations for the structure of the profiles and conditions for the existence of equilibria. In particular, it is shown that βp〉1 is achievable in macroscopically steady conditions, only if a sufficiently strong particle source is present in addition to an energy source. It also follows from the analysis that low βp discharges require an anomalous thermal force type term in Ohm's law, in addition to the anomalous poloidal resistivity.Recent experimental results on sawtoothing discharges are used to extend the theoretical considerations from strictly steady discharges to those involving sawteeth. A simple nonlinear dynamical model of sawtoothing is constructed and used to illustrate some of the features of sawtooth oscillations. The paper is intended to complement fuller numerical studies. It may help in understanding transport and large-scale relaxation processes like the sawtooth in tokamaks by providing a set of theoretical relations that can be subjected to a direct experimental test. It is a feature of the results that they are independent of the details of the turbulent dynamics, which are ultimately thought to be responsible both for the form and scaling of the constitutive properties considered.

Notes: Both neoclassical theory and certain turbulence theories of particle transport in tokamaks predict the existence of bootstrap (i.e., pressure-driven) currents. Two new applications of this form of noninductive current are considered in this work. In the first, an earlier model of the nonlinearly saturated m=1 tearing mode is extended to include the stabilizing effect of a bootstrap current inside the island. This is used to explain several observed features of the so-called "snake'' reported in the Joint European Torus (JET) [R. D. Gill, A. W. Edwards, D. Pasini, and A. Weller, Nucl. Fusion 32, 723 (1992)]. The second application involves an alternating current (ac) form of bootstrap current, produced by pressure-gradient fluctuations. It is suggested that a time-dependent (in the plasma frame), radio-frequency (rf) power source can be used to produce localized pressure fluctuations of suitable frequency and amplitude to implement the dynamic stabilization method for suppressing gross modes in tokamaks suggested in a recent paper [A. Thyagaraja, R. D. Hazeltine, and A. Y. Aydemir, Phys. Fluids B 4, 2733 (1992)]. This method works by "detuning'' the resonant layer by rapid current/shear fluctuations. Estimates made for the power source requirements both for small machines such as COMPASS and for larger machines like JET suggest that the method could be practically feasible. This "jitter'' (i.e., dynamic) stabilization method could provide a useful form of active instability control to avoid both gross/disruptive and fine-scale/transportive instabilities, which may set severe operating/safety constraints in the reactor regime. The results are also capable, in principle, of throwing considerable light on the local properties of current generation and diffusion in tokamaks, which may be enhanced by turbulence, as has been suggested recently by several researchers.

Notes: In this paper the necessary and sufficient conditions required for the existence of a nonlinearly saturated m=1 tearing mode in tokamaks with q0〈1 are considered in cylindrical tokamak ordering using the asymptotic techniques developed by one of the authors in an earlier paper [Phys. Fluids 24, 1716 (1981)]. The outer equations for the helical perturbation amplitude ψ1(r) are solved exactly, in closed form for an arbitrary mean profile ψ0(r) in leading order. This is shown to result in a "no disturbance'' theorem: the m=1 perturbation must be confined to within the radius ri such that q(ri)=1. The bifurcation relation for the nondimensional perturbation amplitude is then constructed by solving the nonlinear inner critical layer equations using an ordered iterative technique. For monotonically increasing q profiles, the equation has a solution if and only if the toroidal current density of the unperturbed equilibrium has a maximum within ri and the parameter d log q(r)/[d log η(r)] [where η(r) is the resistivity profile consistent with the q profile of the unperturbed equilibrium] is sufficiently small at ri. The considerations are extended to nonmonotonic profiles as well. When the conditions are met, a nonlinearly saturated m=1 tearing mode is shown to exist with a novel island structure, quite different from those obtained from the usual Δ' analysis, which is shown to be inappropriate to the present problem. The relevance of the results of the present theory to sawtooth phenomena reported in JET [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. 1, p. 377] and other tokamaks is briefly discussed. The solution constitutes an analytically solved test case for numerical simulation codes to leading orders in a/R and the shear parameter d log q/d log η.

Notes: Thomson scattering is proposed for the direct measurement of magnetic field fluctuations in a tokamak. The analysis is based on the electron fluid equations. The ordering λ(very-much-less-than)λturb(very-much-less-than)a, where λ and λturb are the incident and turbulence wavelengths, respectively, and a is the torus minor radius, is suggested by spectral information from observations on the TEXT tokamak, as well as general theoretical arguments. With this ordering, temperature effects are unimportant and an expression is derived for probe radiation-induced plasma polarization that depends upon density and magnetic fluctuations only. By choosing the incident probe beam to have its plane of polarization parallel to the local mean magnetic field B0, and observing the scattered power in the plane of polarization perpendicular to B0, it is shown that contributions from density fluctuations are automatically excluded. Faraday rotation is shown to have negligible influence on the scattered signal, which is accordingly determined by magnetic field fluctuations alone.

Notes: The "hydrodynamic model'' developed by Haas, Holmes, and Lea has been extended to include all elastic collision processes between the species. The properties of the electron momentum equations are investigated in detail; the solution of these equations revealing a critical point along the source axis at which the electron drift velocity reverses direction.

Notes: Thomson scattering is proposed for the direct measurement of magnetic field fluctuations in a tokamak. The analysis is based on the electron fluid equations. The ordering λ(very-much-less-than)λturb(very-much-less-than)a, where λ and λturb are the incident and turbulence wavelengths, respectively, and a is the torus minor radius, is suggested by spectral information from observations on the TEXT tokamak, as well as general theoretical arguments. With this ordering, temperature effects are unimportant and an expression is derived for probe radiation-induced plasma polarization that depends upon density and magnetic fluctuations only. By choosing the incident probe beam to have its plane of polarization parallel to the local mean magnetic field B0, and observing the scattered power in the plane of polarization perpendicular to B0, it is shown that contributions from density fluctuations are automatically excluded. Faraday rotation is shown to have negligible influence on the scattered signal, which is accordingly determined by magnetic field fluctuations alone.

Notes: Abstract Excitation functions for12C+12C elastic and inelastic scattering to 2+ level have been measured over the energy range 30–60 MeV (cm) by 250 keV steps using the kinematical coincidence method. The intermediate structure resonances disappear aboveE cm=35 MeV while the broad and irregular structure becomes a general feature of the interaction at higher energies.