Research on the elastic stability of large shells

Tests were conducted to determine the elastic stability of large shell structures. The configuration of the shells and the instrumentation used in the measurements are described. The testing procedures are explained. Results of the stress analysis are plotted in polar graph form to show the areas of strain in micro inches at the outer surface of the skin and the inner lip of the stringer

Neoclassical electron and ion transport in toroidally rotating plasmas

Neoclassical transport processes of electrons and ions are investigated in detail for toroidally rotating axisymmetric plasmas with large flow velocities on the order of the ion thermal speed. The Onsager relations for the flow-dependent neoclassical transport coefficients are derived from the symmetry properties of the drift kinetic equation with the self-adjoint collision operator. The complete neoclassical transport matrix with the Onsager symmetry is obtained for the rotating plasma consisting of electrons and single-species ions in the Pfirsch?Schl?ter and banana regimes. It is found that the inward banana fluxes of particles and toroidal momentum are driven by the parallel electric field, which are phenomena coupled through the Onsager symmetric off-diagonal coefficients to the parallel currents caused by the radial thermodynamic forces conjugate to the inward fluxes, respectively

Nonlinear electromagnetic gyrokinetic equation for plasmas with large mean flows

A new nonlinear electromagnetic gyrokinetic equation is derived for plasmas with large flow velocities on the order of the ion thermal speed. The gyrokinetic equation derived here retains a collision term and is given in the form which is valid for general magnetic geometries including the slab, cylindrical and toroidal configurations. The source term for the anomalous viscosity arising through the Reynolds stress is identified in the gyrokinetic equation. For the toroidally rotating plasma, particle, energy and momentum balance equations as well as the detailed definitions of the anomalous transport fluxes and the anomalous entropy production are shown. The quasilinear anomalous transport matrix connecting the conjugate pairs of the anomalous fluxes and the forces satisfies the Onsager symmetry

Neoclassical and anomalous transport in axisymmetric toroidal plasmas with electrostatic turbulence

Neoclassical and anomalous transport fluxes are determined for axisymmetric toroidal plasmas with weak electrostatic fluctuations. The neoclassical and anomalous fluxes are defined based on the ensemble-averaged kinetic equation with the statistically averaged nonlinear term. The anomalous forces derived from that quasilinear term induce the anomalous particle and heat fluxes. The neoclassical banana-plateau particle and heat fluxes and the bootstrap current are also affected by the fluctuations through the parallel anomalous forces and the modified parallel viscosities. The quasilinear term, the anomalous forces, and the anomalous particle and heat fluxes are evaluated from the fluctuating part of the drift kinetic equation. The averaged drift kinetic equation with the quasilinear term is solved for the plateau regime to derive the parallel viscosities modified by the fluctuations. The entropy production rate due to the anomalous transport processes is formulated and used to identify conjugate pairs of the anomalous fluxes and forces, which are connected by the matrix with the Onsager symmetry

Transport suppression by shear flow generation in multihelicity resistive-g turbulence

Turbulent momentum transport given by the Reynolds stress is considered as a candidate for explaining the production and sustainment of the mean shear flow in the high confinement ``(H)\u27\u27 mode. The fluctuation mechanism for the shear flow generation and transport reduction in the three-dimensional (3-D) multihelicity system is given. The profiles of the Reynolds stress, shear flow, and thermal flux in the 3-D case are compared with those in the two-dimensional (2-D) case. The Beklemishev?Horton theory for the anomalous transport which multiplies the 2-D transport by the density of distinct mode rational surfaces is found to overestimate the observed flux due to the disappearance of a subset of modes on certain rational surfaces. The mixing-length theory, in which the anomalous transport is independent of the density of mode rational surfaces, underestimates the thermal flux

Entropy production and Onsager symmetry in neoclassical transport processes of toroidal plasmas

Entropy production and Onsager symmetry in neoclassical transport processes of magnetically confined plasmas are studied in detail for general toroidal systems, including nonaxisymmetric configurations. It is found that the flux surface average of the entropy production defined from the linearized collision operator and the gyroangle-averaged distribution function coincides with the sum of the inner products of the thermodynamic forces and the conjugate fluxes consisting of the Pfirsch?Schl?ter, banana-plateau, nonaxisymmetric parts of the neoclassical radial fluxes and the parallel current. It is proved from the self-adjointness of the linearized collision operator that the Onsager symmetry is robustly valid for the neoclassical transport equations in the cases of general toroidal plasmas consisting of electrons and multi-species ions with arbitrary collision frequencies. It is shown that the Onsager symmetry holds whether or not the ambipolarity condition is used to reduce the number of the conjugate pairs of the transport fluxes and the thermodynamic forces. The full transport coefficients for the banana-plateau and nonaxisymmetric parts are separately derived, and their symmetry properties are investigated. The nonaxisymmetric transport equations are obtained for arbitrary collision frequencies in the Pfirsch?Schl?ter and plateau regimes, and it is directly confirmed that the total banana-plateau and nonaxisymmetric transport equations satisfy the Onsager symmetry. ?1996 American Institute of Physics

Transport processes and entropy production in toroidally rotating plasmas with electrostatic turbulence

A new gyrokinetic equation is derived for rotating plasmas with large flow velocities on the order of the ion thermal speed. Neoclassical and anomalous transport of particles, energy, and toroidal momentum are systematically formulated from the ensemble-averaged kinetic equation with the gyrokinetic equation. As a conjugate pair of the thermodynamic force and the transport flux, the shear of the toroidal flow, which is caused by the radial electric field shear, and the toroidal viscosity enter both the neoclassical and anomalous entropy production. The interaction between the fluctuations and the sheared toroidal flow is self-consistently described by the gyrokinetic equation containing the flow shear as the thermodynamic force and by the toroidal momentum balance equation including the anomalous viscosity. Effects of the toroidal flow shear on the toroidal ion temperature gradient driven modes are investigated. Linear and quasilinear analyses of the modes show that the toroidal flow shear decreases the growth rates and reduces the anomalous toroidal viscosity

Shear flow generation by Reynolds stress and suppression of resistive g modes

Suppression of resistive g-mode turbulence by background shear flow generated from a small external flow source and amplified by the fluctuation-induced Reynolds stress is demonstrated and analyzed. The model leads to a paradigm for the low-to-high (L?H) confinement mode transition. To demonstrate the L?H transition model, single-helicity nonlinear fluid simulations using the vorticity equation for the electrostatic potential, the pressure fluctuation equation, and the background poloidal flow equation are used in the sheared slab configuration. The relative efficiency of the external flow and the Reynolds stress for producing shear flow depends on the poloidal flow damping parameter nu, which is given by neoclassical theory. For large nu, the external flow is a dominant contribution to the total background poloidal shear flow and its strength predicted by the neoclassical theory is not enough to suppress the turbulence significantly. In contrast, for small nu, it is shown that the fluctuations drive a Reynolds stress that becomes large and suddenly, at some critical point in time, shear flow much larger than the external flow is generated and leads to an abrupt, order unity reduction of the turbulent transport just like that of the L?H transition in tokamak experiments. It is also found that, even in the case of no external flow, the shear flow generation due to the Reynolds stress occurs through the nonlinear interaction of the resistive g modes and reduces the transport. To supplement the numerical solutions, the Landau equation for the mode amplitude of the resistive g mode is derived, taking into account the fluctuation-induced shear flow and the opposite action of the Reynolds stress in the resistive g turbulence compared with the classical shear flow Kelvin?Helmholtz (KH) driven turbulence is analyzed

On the elastic stability of shells

A synopsis of a series of investigations into the instability of axially compressed cylindrical shells is given. The objective of the research, which was made with models, was to devise a technique of nondestructive evaluation. The results show that, with models at any rate, success was achieved. Probing methods which can be used to determine the locations of weakness and the pertinent instability load levels were devised. The research on large scale shells was undertaken to determine the critical loads under as uniform a circumferential distribution of axial compressive force as possible. It is clear from the results presented that this objective was met