Showing papers on "Thermal equilibrium published in 1971"

Temperature Field and Geophysical Effects of a Downgoing Slab

Abstract: The factors affecting the thermal behavior of a lithospheric slab descending into the mantle are so numerous and complicated that only numerical methods can accurately account for them. A series of finite-difference calculations of the temperature field, including the effects of viscous dissipation, adiabatic compression, phase changes and radioactive heat generation are carried out, and the relative effects of different parameters are investigated. An analysis of the stability and convergence of the numerical method indicates that the errors are small and can be reduced to any desired level by varying the grid size and the time steps. At a crustal spreading rate of 8 cm/yr, with all heat sources, the slab reaches thermal equilibrium with the surrounding mantle at a depth of about 650 km. Among observable geophysical quantities, seismic travel times and amplitudes provide the most information about the slab. Surface heat flow is sensitive to subsurface conditions that are at relatively shallow depths, and gravity anomalies are broad and are masked by crustal effects. Three dimensional calculations predict strong bending of seismic rays near slabs, which causes strong focusing and produces shadow zones. Analysis of travel-time data for the Tonga-Fiji region indicates that waves propagating down the slab from shallow events are advanced by about 4 sec. Observations and theoretical travel-time anomalies based on calculated temperature fields are in general agreement.

Generalized thermodynamic potential for Markoff systems in detailed balance and far from thermal equilibrium

Abstract: We analyze the question why there exist systems far from thermal equilibrium, e.g. lasers, whose stationary state may be described by a potential function, which has all the properties of a thermodynamic potential. It is argued, that the physical property, common to thermal equilibrium states and to these more general stationary states is detailed balance.

Kinetic models of the solar wind

Abstract: A new kinetic model of the quiet solar wind is presented and compared with earlier exospheric, semikinetic, and hydrodynamical models. To have equal mean free paths for the protons and electrons at the baropause, the ratio of the proton temperature to the electron temperature is supposed to be Tp(ho)/Te(ho) = 0.645. With the assumption that the trapped electrons are in thermal equilibrium with those emerging from the barosphere, the electric-field distribution is calculated to cancel the electric current and space charge in the exospheric plasma. The bulk velocity, the density, the average electron and proton temperatures, and the energy flux, which are observed at 1 AU for quiet solar-wind conditions, are well represented by such a kinetic model. The average electron temperature is nearly independent of the bulk velocity, whereas a positive correlation between the average proton temperature and the bulk velocity is found. Consequently it is suggested that in the interplanetary medium (r>6RS) no external heating mechanism is needed to explain the observed quiet solar-wind properties. Finally, the electric-field calculations in this kinetic model are found to be in reasonable agreement with the empirical electric-field values deduced from observed coronal-density distribution.

Studies of tunnel MOS diodes II. Thermal equilibrium considerations

Abstract: The oxide thickness δ of a tunnel MOS diode is varied over the range 10 to 45 A. This is done in an effort to establish the restrictions upon δ for which thermal equilibrium in the semiconductor is a valid approximation under the application of bias. Particular attention is paid to the reverse-bias case, and most of the experimental results are for δ>25 A. A transition is observed from the behaviour of the ideal Schottky barrier to that of the thick-film MOS device. The ac conductance and capacitance together with dc current characteristics are studied as continuous functions of bias. From these results, information is obtained which relates the quasi-Fermi levels for (i) majority carriers, (ii) minority carriers and (iii) electrons in the interface states to δ. Thermal equilibrium statistics are found to be applicable to the semiconductor in the presence of a bias voltage when δgreater, similar30 A, which compares with a theoretical prediction of δgreater, similar13 A.

Spin Temperature and Nuclear Magnetic Resonance in Solids

Abstract: M Goldman Oxford: University Press 1970 pp ix + 246 price £4.25 The system of nuclear spins in a solid very often has only weak interaction with the thermal excitations of the lattice of atoms in which they are housed. Nevertheless, they have a relatively strong interaction among themselves and can achieve internal thermal equilibrium among themselves.

Thermally induced flow instabilities in two-phase mixtures in thermal equilibrium

Abstract: Two phase mixtures thermally induced flow oscillations, discussing scaling criteria, phase change numbers and stability boundaries

Fluctuations and stability of stationary non-equilibrium systems in detailed balance

Abstract: A generalized thermodynamic potential for Markoffian systems with detailed balance and far from thermal equilibrium has been derived in a previous paper. It was shown that the principle of detailed balance is equivalent to a set of conditions fulfilled by this potential (“potential conditions”). The properties of this potential allow us to extend the validity of a number of thermodynamic concepts well known for systems in or near thermal equilibrium to stationary states far from thermal equilibrium. The concept of symmetry breaking phase transitions for these systems is introduced in analogy to thermal equilibrium systems by considering the dependence of the stationary probability density of the system on a set of externally controlled parameters {λ}.

Theory of the unmagnetized plasma

Abstract: The Vlasov mathematical model of a plasma, which has come to be thought more useful than any other in describing the dynamical behavior of the majority of plasmas of interest, is first examined. Macroscopic variables and moment equations; linear electrostatics solutions; plasma oscillations, ion acoustic waves, and linear instabilities are treated, as well as external fields, 'test' charges, and nonlinear Vlasov phenomena. Plasmas are statistically described, and attention is given to the kinetic theory of the stable, uniform plasma and the Balescu-Lenard equation; two-time ensemble averages and fluctuation spectra in stable plasmas; the kinetic theory of the unstable plasma; and ensembles of Vlasov plasmas. Some illustrative experiments are described. Four appendixes deal with the electrostatic approximation and transverse waves; solution of the linearized Vlasov equation in a magnetic field; estimates of correlation functions from thermal equilibrium; and equivalence of spatially uniform BBGKY and Klimontovich correlations.

Brillouin-Scattering Analysis of Phonon Interactions in Acoustoelectric Domains in GaAs

Abstract: Acoustoelectrically amplified domains of ultrasonic flux in GaAs were used for analyses of various phonon interactions by Brillouin-scattering techniques. Both the growth of the flux from the thermal equilibrium phonon spectrum and particularly the attenuation (after the amplifying voltage pulse was shut off) were studied as a function of ultrasonic frequency in the broad range from 0.3 to 4.0 GHz at 300 \ifmmode^\circ\else\textdegree\fi{}K. The data were analyzed to give the magnitude and frequency dependence of both the acoustoelectric gain and the lattice attenuation in the weak-flux regime. Comparison with small-signal gain theory in the $\mathrm{ql}\ensuremath{\approx}1$ range, for piezoelectrially active [110] shear waves, gave good agreement. The lattice attenuation was determined not only for the amplified shear waves but also for the piezoelectrically inactive longitudinal waves, which were obtained by mode conversion upon reflection of the amplified shear-wave domain. The frequency dependence of the attenuation, proportional to ${f}^{1.8}$ and ${f}^{1.3}$, respectively, fell well below the expected ${f}^{2}$ behavior. In the strong-flux regime, striking anomalous attention was found, consisting of a too-rapid initial attenuation of low frequencies, and too-slow initial attenuation of higher frequencies. These results are interpreted to represent a dominant trend of up-conversion of intense ultrasonic flux from low to high frequencies by nonlinear frequency-mixing processes. Evidence is summarized favoring such frequency-mixing processes, over possible variation in the frequency dependence of the acoustoelectric gain in strong flux, as a dominant factor in the evolution of the strong-flux spectrum both in growth and attenuation.

Kinetic theory of a two-dimensional magnetized plasma.

Abstract: Several features of the equilibrium and nonequilibrium statistical mechanics of a two-dimensional plasma in a uniform dc magnetic field are investigated. The charges are assumed to interact only through electrostatic potentials. The problem is considered both with and without the guiding-center approximation. With the guiding-center approximation, an appropriate Liouville equation and BBGKY hierarchy predict no approach to thermal equilibrium for the spatially uniform case. For the spatially nonuniform situation, a guiding-center Vlasov equation is discussed and solved in special cases. For the nonequilibrium, nonguiding-center case, a Boltzmann equation, and a Fokker-Planck equation are derived in the appropriate limits. The latter is more tractable than the former, and can be shown to obey conservation laws and an H-theorem, but contains a divergent integral which must be cut off on physical grounds. Several unsolved problems are posed.

Influence of diffusion and nonequilibrium populations on noble-gas plasmas in electric arcs

Abstract: Measurements and calculations of temperatures, densities, and field-strength-current characteristics of cascade arcs burning in noble gases under atmospheric pressure are reported. The evaluation of measured arc data assuming Saha equilibrium [complete local thermal equilibrium (LTE)] is not in agreement with the detailed solution of the balance equations. The temperatures of electrons and heavy particles and the density of electrons and neutrals have to be determined from the set of rate equations, from the equation of state, connection with the electron energy balance and the equation of state, the energy balance of the electron gas, and of the total plasma. Solutions of these equations are compared with results following from measured line intensities only solving the rate equations in connection with the electron energy balance and the equation of state. For helium, both methods give results which agree within a few percent. The deviations from Saha equilibrium are caused by diffusion and the overpopulation of ground state atoms. The excited atoms, however, are nearly in equilibrium with free electrons in the range of electron densities reached in our experiment (partial LTE). Measurements of E-I characteristics agree with calculated data, if diffusion is taken into account. A simple criterion for the limit between diffusion-dominated plasma and a plasma in thermal equilibrium is derived.

Equilibrium states for a one dimensional lattice gas

Abstract: The thermodynamic equilibrium state can be defined directly for an infinite system via an equilibrium condition or via the variational principle. Both definitions are used to calculate the equilibrium state for a one dimensional lattice gas with finite range interactions.

Spontaneous Emission in Semiclassical Radiation Theory

Abstract: It has recently been shown by Jaynes and collaborators that semiclassical radiation theory contains a description of spontaneous emission of radiation and of radiative level shifts. The present paper gives a gauge-invariant derivation of the radiant energy production rate, using only Maxwell's equations and the usual definitions of electric current and charge density for a many-particle material system described by Schr\"odinger's equation. A complementary derivation, using the time-dependent Schr\"odinger equation, verifies the instantaneous conservation of energy and probability during the radiation process. The semiclassical rate of spontaneous emission differs from the usual formula (Einstein's $A$ coefficient) because it depends on the occupancy of both initial and final states of the material system. The implications of this with regard to thermal equilibrium and Planck's law are examined. If a new hypothesis is introduced, postulating the decomposition of the equilibrium radiation into incoherent components, each interacting with a specific pair of energy levels of the material system, then Planck's law is shown to hold for the total intensity of radiation. If this hypothesis is not introduced, the equilibrium conditions for different transitions are incompatible, and the semiclassical radiation theory is incapable of describing thermal equilibrium.

Fluctuations in thermodynamic non equilibrium states

Abstract: In a statistical theory an expression is derived for the probability of fluctuations in a thermodynamic non equilibrium state. It is a generalization of the Einstein formula, respectively the formula of Greene and Callen for fluctuations in a thermal equilibrium. The application to steady transport processes is discussed in connection with stability conditions.

Theoretical properties of several metal halide arcs assuming LTE

Abstract: A single-fluid local thermal equilibrium (LTE) model used to predict composition, material functions, and temperature profiles for arc discharges in complex mixtures is reviewed. Results are given for the application of the model to two metal halide discharges used in arc lamps, but predicted arc properties such as central temperature, radiative output, and electrical impedance differ from those observed.

Theory of a cooled spherical electrostatic probe in a continuum gas.

Abstract: The idealized problem of a cooled spherical electrostatic probe in a quiescent continuum slightly ionized chemically frozen gas has been investigated. The electron temperature is described by two limiting models; either the electrons are assumed to be at local thermal equilibrium, or they are assumed frozen at the ambient temperature far from the probe. From numerical solutions of the governing equations, it has been found that with the frozen electron temperature assumption, the probe characteristics for a cold probe are only slightly altered from those of an adiabatic probe. With the electrons at thermal equilibrium, the probe characteristic is only slightly altered when the bias potential is large, but significant changes in the probe characteristic do occur when the bias potential is small, including a significant shift in the floating potential.

Fluctuation-dissipation theorem for a class of stationary open systems

Abstract: A generalized fluctuation-dissipation theorem is proved in the frame of a Liouville-space formalism for stationary open systems in contact with reservoirs, and in general far from thermal equilibrium. It is shown, however, that the wellknown case of thermal equilibrium is included in the result.

Predicted Arc Properties in Sulfur Hexafluoride

Abstract: Calculations of spectral absorptivities of sulfur hexafluoride for continuum radiation ranging from the far ir to 300 A have been made as a function of temperature and pressure. These values are used together with theoretical values of thermal and electrical conductivity to derive temperature profiles of arcs in sulfur hexafluoride, taking into account effects due to self‐absorption of radiation, but assuming local thermal equilibrium. The temperature profile for a 100‐A arc is in good agreement with the experimental measurements of Motschmann. The sensitivity of the derived temperature profile to the input material functions is examined. It is predicted that radiation losses at the arc center are dominated by radiation of wavelengths in the region of 1000 A. Using the theoretical material functions, an estimate is made of central arc temperatures and electric field strengths for currents of up to 60 000 A and arc radii of up to 2 cm for gas pressures of 1 and 8 atm.

Transient temperature distributions in cylindrical arc columns following abrupt current changes

Abstract: Using the shock wave technique, radial distributions of gas temperature have been measured in cylindrical, wall stabilized, arc columns under both steady state and transient conditions. The arc atmosphere was air and the current range 0?5-100 A. The transient measurements included the case of free recovery following sudden current interruption. The temperature profiles have been used in conjunction with published electrical conductivity data to determine electrical conductance values and these show good agreement with direct electrical measurements and theory. This result confirms that the arc plasma is in approximate thermal equilibrium so that the column behaviour may be described solely in terms of thermal processes. The importance of natural radial flow under transient conditions has been estimated by calculating flow velocity profiles from the measured temperature distributions and published gas density data. The results are in good agreement with theory, and show the increasing importance of the radial flow at higher currents.

A model for grain dispersion and magnetic anisotropy in sedimentary rocks

Abstract: This paper is concerned with deriving the susceptibility ellipsoids for aggregates of small anisotropic magnetic grains dispersed thinly in a nonmagnetic matrix, given the individual grain susceptibilities. The statistical orientation of the magnetic grains is assumed to be represented by a Boltzmann distribution of their individual magnetic moments in thermal equilibrium with the earth‘s ambient magnetic field. This argument is similar to that used to describe a classical paramagnetic gas, in which it is assumed that magnetic grain interactions are negligible. Once the equilibrium distribution is reached, the aggregate is assumed to be cemented, and the anisotropy of the aggregate is calculated from the susceptibility parallel to and perpendicular to the preferred direction. Two types of grains are considered, grains with prolate and oblate susceptibility ellipsoids. The aggregate susceptibility is found to be prolate with both types of grains. The conclusion reached is that this should always be so unless factors other than thermodynamic equilibrium in the earth’s field affect individual magnetic grains during the accumulation and lithification of a sedimentary rock.

Cooling power of underground environments

Abstract: The problem of heat stress underground in the gold mines is approached on the basis of the heat transfer between the human body and the underground environment. Experimental measurements of radiant and convective heat transfer and a theoretical calculation of maximum evaporative heat transfer enable the maximum cooling power of an environment to be calculated in terms of the dry-bulb and wet-bulb temperature, the mean radiant temperature, the wind speed and the barometric pressure. For most underground applications the cooling power can be expressed as a function of wet-bulb temperature and wind speed only. The relative importance of wind speed and wet-bulb temperature can be assessed: in working places where wind speed is Iow additional cooling of workmen can be achieved better by increased wind speed than by decreased wet-bulb temperature. The wet kata reading proves to be of limited value as an index of heat stress because environments with equal wet kat a do not necessarily have the same cooling power. Finally, thermal equilibrium with the environment is possible when cooling power equals or exceeds the rate of met

Temperature Dependence of the Positron-Annihilation Angular Correlation in Metals

Abstract: The thermal smearing of the positron-annihilation\char22{}angular-correlation curves is studied. In the case where the medium is a homogeneous interacting electron gas in thermal equilibrium, the analysis applied by Stewart and co-workers to the thermal smearing is shown to correctly give the effective mass. In conjunction with previous calculations of the effective mass, our results indicate that the observed thermal smearing cannot be explained as mainly caused by electron-gas effects. It is shown how the model can be modified to take into account the positron-phonon interaction. This reduces the discrepancy between theory and experiment, but not sufficiently to account fully for the experimental data. It is argued that new experiments are needed before one can decide whether it is necessary to consider new mechanisms in order to explain the effect. A convenient formalism is presented, which allows one to calculate all positron quantities at moderate nonzero temperatures within a given approximation scheme. The "ladder" approximation is used to illustrate the argument and to estimate correction terms.

Thermal equilibrium in argon induction discharges

Abstract: The equilibrium state of induction discharge plasmas in argon has been examined for a wide range of pressures (7?6 to 760 Torr) and with electron densities ranging from 3?1014 to 8?1015 cm?3. Grossly non-thermal conditions are obtained when the electron density falls below 1015 cm?3. For higher densities the approach to LTE (local thermal equilibrium) depends on the strength of the local heating fields and temperature gradients. The conventionally used LTE criteria are found to give only order of magnitude predictions of the onset of experimental departures from LTE. Kinetic non-equilibrium arising from the heating fields is shown to be strongly affected by diffusion mixing of hot electrons over distances comparable with the plasma size. Even at atmospheric pressure diffusion-mixing distances in non-uniform fields are of the order of 2 mm. Strong temperature gradients are also found to be important but only indirectly, and the observed departures from LTE are not adequately explained by the conventional criterion (d/T) (dT/dr)<<1. Instead ambipolar diffusion coupled with recombination appears to be a major factor. An LTE criterion based on this mechanism has been developed and fits the experimental results quite closely. Recombination data needed to verify the ambipolar diffusion model have been obtained in a discharge with gas flow, and a virtually constant recombination time of 370 microseconds has been measured in the decaying plasma for conditions ranging from Ne=2?1015 and Te=9000 K to 3?1014 cm?3 and 5500 K.

Calorimeter for high power lasers

Abstract: A calorimeter of the ballistic thermopile type particularly useful for measuring energy in high power pulsed laser beams utilizes a glass filter as the absorbing medium. Since the thermal conductivity of glass is ordinarily poor, a highly thermally conductive material such as a copper disc is bonded directly to the rear surface of the glass. By providing this copper backing to the glass, the absorbing medium comes to thermal equilibrium considerably faster than would be the case in the absence of any backing. The volume of the absorbing medium is relatively small in relation to the usable aperture and the sensitivity is accordingly greatly increased in addition to the feature of a shortened time to arrive at thermal equilibrium.

Two-phase two- and one- component critical flows with the variable slip model

Abstract: From international symposium on two-phase systems; Haifa, Israel (29 Aug 1971). See CONF-710836-. For describing two-phase one-component annular flows with thermodynamic equilibrium in constant cross-section pipes, a system of four differential equations must be solved by a stepby-step procedure. It is shown that this system must include one continuity equation, two momentum equations, and one energy equation. The critical flow condition is given by the vanishing condition of a fourth-order determinant. At given pressure and quality, this condition can be presented as a relation between critical mass-velocity and slip- ratio. An entropy balance equation is deduced from the other balance equations by means of the second principle of thermodynamics and it is shown that it can be used to derive the same critical flow condition. This variable slip model exhibits the increase of critical flow-rates with decreasing slip ratios occurring experimentally when decreasing the L/D parameter. The hypothesis of thermal equilibrium may be avoided in order to include jet flows which occur in short pipes. This requires an additional heat-balance equation. The critical flow conditions are also determined for two-component flows with separated phases with or without thermal equilibrium. (auth)

Measurement of the Photoionization Cross Section in the Resonance Continuum of C i Using a Wall-Stabilized Arc*

Abstract: A wall-stabilized high-current (100 A) arc was operated in argon at a pressure of 1 atm. Different gases (CO2, O2) could be added to the plasma. Temperature, electron, ion, and atom densities have been determined by spectroscopic observations in the visible and in the vacuum-ultraviolet (vuv) regions of the spectrum, assuming local thermal equilibrium. These values, together with the absolute emission intensities in the vuv region between 980 and 1250 A, allowed the calculation of the photoionization cross section of carbon. This experimental value compared well with previously published theoretical calculations: it was 19×10−18 cm2 at threshold.