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Notes: A coarse-grained model for surfactant chain molecules at interfaces in the high density regime is studied using an off-lattice Monte Carlo technique. The surfactant molecules are modeled as chains consisting of a small number (e.g., seven) of effective monomers. For the modeling of lipid monolayers, each effective monomer is thought to represent several CH2 groups of the alkane chain, but applications of the model to other polymers end grafted at solid surfaces also should be possible. The head segments are restricted to move in the adsorption plane, but otherwise do not differ from the effective monomers, which all interact with Lennard-Jones potentials. Bond angle and bond length potentials take into account chain connectivity and chain stiffness. The advantage of this crude model is that its phase diagram can be studied in detail. Temperature scans show two phase transitions, a tilting transition at low temperatures between a tilted and an untilted phase, and a melting transition at high temperatures where the lattice of head groups loses its crystalline order. © 1995 American Institute of Physics.

Notes: Tokamaks exhibit several types of relaxation oscillations such as sawteeth, fishbones and Edge Localized Modes (ELMs) under appropriate conditions. Several authors have introduced model nonlinear dynamic systems with a small number of degrees of freedom which can illustrate the generic characteristics of such oscillations. In these models, one focuses on physically "relevant" degrees of freedom, without attempting to simulate all the myriad details of the fundamentally nonlinear tokamak phenomena. Such degrees of freedom often involve the plasma macroscopic quantities such as pressure or density and also some measure of the plasma turbulence, which is thought to control transport. In addition, "coherent" modes may be involved in the dynamics of relaxation, as well as radial electric fields, sheared flows, etc. In the present work, an extension of an earlier sawtooth model (which involved only two degrees of freedom) due to the authors is presented. The dynamical consequences of a pressure-driven "coherent" mode, which interacts with the turbulence in a specific manner, are investigated. Varying only the two parameters related to the coherent mode, the bifurcation properties of the system have been studied. These turn out to be remarkably rich and varied and qualitatively similar to the behavior found experimentally in actual tokamaks. The dynamic model presented involves only continuous nonlinearities and is the simplest known to the authors that can yield features such as sawteeth, "compound sawteeth" with partial crashes, "monster" sawteeth, metastability, intermittency, chaos, periodic and "grassy" ELMing in appropriate regions of parameter space. The results suggest that linear stability analysis of systems, while useful in elucidating instability drives, can be misleading in understanding the dynamics of nonlinear systems over time scales much longer than linear growth times and states far from stable equilibria. © 1999 American Institute of Physics.

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: 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: A general representation of finite-volume-preserving maps induced by solenoidal vector fields in periodic cylinders is derived. An important special case is the area preserving Hamiltonian maps which include the standard mapping. Applications to computational problems in plasma physics are briefly indicated.

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: 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: 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: Using B-dot probes Meyer et al. [J. Appl. Phys. 79, 1298 (1996)] have described a method for calculating the azimuthal current, electric field, plasma permittivity, and electron density in a planar inductively coupled plasma source. They assume the phases associated with the time rate of change of the radial and axial field components to be the same. Furthermore, they restrict their analysis to the situation where the phase is independent of radius. We demonstrate that the phases for the two field directions are different. The subsequent modified forms for the plasma properties considered by Meyer et al. are presented. We also show that their procedure can be extended to cover phases which are an arbitrary function of position, and for completeness, give forms for the generalized plasma properties. © 1997 American Institute of Physics.