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Several recent studies of ELMO Bumpy Torus (EBT) stability show that conflicting results can emerge when different distribution functions for the hot‐electron component are used. In this paper the role of the distribution function is established by examining the stability of various modes with the aid of two models. In the ‘‘slab’’ model where the magnetic field curvature is simulated by a gravitational force it is shown that the stability of the compressional Alfvén wave is insensitive to the distribution function while the interacting interchange mode is sensitive. In the ‘‘local’’ approximation in which the curvature effects enter in a natural way it is seen that the interchange modes are insensitive so long as the anisotropy of the hot electrons is large, while other modes reflect dependence on the distribution function. Finally it...
The macroscopic stability of a model ELMO Bumpy Torus (EBT) plasma taking into account variations of the field curvature along the magnetic field is numerically investigated in the long‐thin limit. When the compression term has a pole in the ring region the background ballooning mode becomes stable for any value of the hot electron beta because of strong line bending which results from the interaction of the hot electron component with the plasma. Axially longer rings give better stability, and the upper bound on the core beta can be improved by increasing the mirror ratio although at the expense of reducing stability of the background ballooning mode.
A two-color pyrometer has been designed, constructed, and used to measure the ignition temperatures of metals and metal alloys. Cylindrical metal and metal alloy specimens were ignited by a focused cw CO2 laser beam in a cool, static, pure oxygen environment. The pyrometer operates in the near-infrared at two narrow spectral regions, with a nominal bandwidth of 10 nm centered at 0.9051 and 1.06 micron, and has a temperature range from 1000 to 4000 K. In the present design the temperature of a spot, about 0.5 mm in diameter, can be recorded with a maximum time resolution of 25 microseconds and with an accuracy of a few percent. Results of CO2 laser ignition of cylindrical specimens of 6061 aluminum alloy and 302 SS in a pure oxygen environment were obtained from the two-color pyrometer and were compared with those obtained from a thermo...
The effect of oxygen pressure on the ignition temperature of cylindrical 302 SS specimens ignited by a focused CW CO2 laser beam in a cool, static, oxygen environment was investigated. The ignition temperature was determined quantitatively from the specimen temperature history obtained from a fast response, near infrared, two-color pyrometer, which recorded the temperature history of a spot approximately 0.5 mm in diameter and located at the center of the cylindrical 302 SS specimen's top surface. Ignition and combustion occurred in three stages. The first stage began with specimen heating and ended with ignition, the second stage corresponded to combustion, and the third stage represented cooling. The physical changes that occurred in the first stage are described.
Experiments were undertaken to study the ignition characteristics of bulk 1018 carbon steel in a pure oxygen environment. Cylindrical 1018 carbon steel specimens 5 mm in diameter and 5 mm high were ignited by a focused CW CO2 laser beam in a cool, static, pure oxygen environment at oxygen pressures ranging from 0.103 to 6.895 MPa. A two-color pyrometer was designed and used to measure the ignition temperatures of the specimens. The temperature history of a spot approximately 0.5 mm in diameter located at the center of the specimen top surface was recorded with a maximum time resolution of 25 microsec, and with an accuracy of a few percent. Ignition temperature of bulk 1018 carbon steel was identified from the temperature history curve with the aid of the light intensity curve. Results show that 1018 carbon steel specimens ignite at tem...
A Hill's Vortex equilibrium model is utilized to calculate the classical transport properties of a plasma confined in a field-reversed magnetic configuration. Consistent with zero dimensional steady state conservation of particles and energy the authors compute the corresponding fluxes at the separatrix using volume-averaged values for the density and conductivity. They find that the confinement times scale directly with the size of the Vortex and conductivity at that point, and inversely with a function of the profile parameter.
In industry sectors where market prices for goods and services are unavailable, it is common to use estimated output and input distance functions to estimate rates of productivity change. It is also possible, but less common, to use estimated distance functions to estimate the normalised support (or efficient) prices of individual inputs and outputs. A problem that arises in the econometric estimation of these functions is that more than one variable in the estimating equation may be endogenous. In such cases, maximum likelihood estimation can lead to biased and inconsistent parameter estimates. To solve the problem, we use linear programming to construct a quantity index. The distance function is then written in the form of a conventional stochastic frontier model where the explanatory variables are unambiguously exogenous. We u...
The theme of this paper is to `solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field $K$. Representations of semi-simple Lie algebras and differential Galois theory are the main tools. The results extend the classical work of G. Fano.
The maximum achievable beta (ratio of plasma pressure to magnetic pressure) value in a bumpy torus such as Elmo (EBT) is determined primarily by the stability of the system to the interchange modes. These modes have as their source of free energy the drifts of the hot electron component that arise from the curvature and gradients of the confining magnetic field. At low (compared to the ion gyro) frequencies the only modes that exist are the core plasma and hot electron interchange, but at frequencies near the ion cyclotron frequency, instabilities arising from coupling of the interchange and compressional Alfven wave also appear. In most, if not all previous treatments of these instabilities, the hot electrons were treated as non-relativistic. In this paper we re-examine these modes using a relativistic formulation for the hot electron...
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