Kinetic theory of almost classical fluids.
Fokker-Planck equation with first order quantum correction extended to mixtures by rearranging terms, noting friction tensor role
Davis, H. T.↗
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Kinetic theory of the sharp leading edge problem in supersonic flow.
Boltzmann equation with BGK model as governing equation for sharp leading edge problem in supersonic flow
Hartley, D. L.↗
Near-surface electron temperature of weakly ionized plasma according to kinetic theory.
Boltzmann equation analysis used to study near surface electron temperature for weakly ionized plasmas, showing nonequilibrium absorption layer governing electron temperature profile
Chung, P. M.↗
Test particle method in kinetic theory of a plasma
Many body correlation and conditional probability functions of plasma shield clouds surrounding test particles
Matsuda, K.↗
Kinetic theory of plasma in a magnetic field
Guiding center equations for charged particle motion and statistical fluctuations of plasma in magnetic field, using Krylov-Bogoliubov transformation
Price, J. C.↗
Kinetic theory of a two-dimensional magnetized plasma.
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.
Vahala, G.↗
Kinetic theory analysis of rarefied gas flow through finite length slots
An analytic study is made of the flow a rarefied monatomic gas through a two dimensional slot. The parameters of the problem are the ratios of downstream to upstream pressures, the Knudsen number at the high pressure end (based on slot half width) and the length to slot half width ratio. A moment method of solution is used by assuming a discontinuous distribution function consisting of four Maxwellians split equally in angular space. Numerical solutions are obtained for the resulting equations. The characteristics of the transition regime are portrayed. The solutions in the free molecule limit are systematically lower than the results obtained in that limit by more accurate numerical methods.
Raghuraman, P.↗
Turbulent Chemically Reacting Flows According to a Kinetic Theory
A review of various methods of calculating turbulent chemically reacting flow such as the Green Function, Navier-Stokes equation, and others is presented. Nonequilibrium degrees of freedom were employed to study the mixing behavior of a multiscale turbulence field. Classical and modern theories are discussed.
Hong, Z. C.↗
A gravitational kinetic theory for planetesimals
An analytical theory is developed for the velocity evolution of nonaccreting planetesimal populations, based on the Boltzmann and Fokker-Planck equations. Adapting Shkarofsky's calculation of plasma viscosities, the rate of increase in random velocities due to gravitational encounters between planetesimals of equal mass is found to be one-third to one-half Safronov's result. Comparison with Wetherill's numerical experiments suggests that the Fokker-Planck equation underestimates the effectiveness of encounters and that Safronov's value is approximately correct. For populations of nonuniform sizes, the Fokker-Planck equation indicates an efficient redistribution of energy from the largest bodies to the smaller ones. By conserving angular momentum, the rate of radial spreading of orbits is also derived.
Stewart, G. R.↗
Two-stream Maxwellian kinetic theory of cloud droplet growth by condensation
A new growth rate formula (NGRF) is developed for the rate of growth of cloud droplets by condensation. The theory used is a modification of the Lees-Shankar theory in which the two-stream Maxwellian distribution function of Lees is used in Maxwell's method of moments to determine the transport of water vapor to and heat away from the droplet. Boundary conditions at the droplet are the usual conditions set in terms of accommodation coefficients, and the solution passes smoothly into diffusion flow in the far region. Comparisons are given between NGRF and the conventional formula showing close agreement (approximately 0.1%) for large radii with significant difference (approximately 5%) for small radii (not greater than 1 micron). Growth times for haze droplets in a Laktionov chamber are computed.
Robinson, N. F.↗
Kinetic theory in astrophysics and cosmology
Results associated with exact solution of the Einstein-Boltzmann and Einstein-Maxwell-Boltzmann equations are presented. The generalization of Ehler's killing vector approach for the distribution function to charged particles is considered.
Ray, J. R.↗
A theory of local and global processes which affect solar wind electrons. I - The origin of typical 1 AU velocity distribution functions - Steady state theory
A kinetic theory for the velocity distribution of solar wind electrons which illustrates the global and local properties of the solar wind expansion is proposed. By means of the Boltzmann equation with the Krook collision operator accounting for Coulomb collisions, it is found that Coulomb collisions determine the population and shape of the electron distribution function in both the thermal and suprathermal energy regimes. For suprathermal electrons, the cumulative effects of Coulomb interactions are shown to take place on the scale of the heliosphere itself, whereas the Coulomb interactions of thermal electrons occur on a local scale near the point of observation (1 AU). The bifurcation of the electron distribution between thermal and suprathermal electrons is localized to the deep solar corona (1 to 10 solar radii).
Scudder, J. D.↗
Matter in general relativity
Two theories of matter in general relativity, the fluid theory and the kinetic theory, were studied. Results include: (1) a discussion of various methods of completing the fluid equations; (2) a method of constructing charged general relativistic solutions in kinetic theory; and (3) a proof and discussion of the incompatibility of perfect fluid solutions in anisotropic cosmologies. Interpretations of NASA gravitational experiments using the above mentioned results were started. Two papers were prepared for publications based on this work.
Ray, J. R.↗
Multi-fidelity kinetic theory-based approach for the prediction of particle attrition: Application to jet cup attrition system
The timescale difference between the “fast” flow dynamics of fluidized bed reactors and the relatively “slow” rate of particle degradation makes the direct computational prediction of attrition challenging. An approach to this challenge is a multi-fidelity strategy where a high fidelity model for the flow dynamics is coupled with a lower fidelity model for the long-time resolution of the bulk attrition of the reactor inventory. We implement this approach using high-fidelity kinetic theory simulations to calculate the flow dynamics which are post-processed to calculate the frequency and intensity of the particle-particle and particle-wall collisions (e.g. collision energy spectra). This is combined with the particle breakage properties to construct the coefficients for a low-fidelity model [e.g. Monazam et al., 2018, Powder Technology 340, p. 528-536]. Simulations are performed of a jet cup attrition system containing Canadian hematite (Monazam et al. 2018). Furthermore, these are first analyzed using the collision energy spectra. Quantitative predictions of the mass loss are made using a low-fidelity model derived from the collision-spectra and a calibrated material breakage coefficient. The results are found to compare favorably with the experimental measurements.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A BBGKY framework for fluid turbulence
A framework is presented for a systematic kinetic theory of turbulence originating from the Liouville equation for the Fourier coefficients of fluid variables. The real and imaginary parts of these Fourier coefficients play the role that particle coordinates (positions and momenta) play in the BBGKY theory. The basic relations of the problem are the incompressible Navier-Stokes equations in two dimensions with zero viscosity, with the probability distributions of Fourier coefficients rather than moments being the basic variables of the theory. A kinetic equation is derived and shown to possess a number of requirements that any reasonable kinetic equation must have: conservation laws, positive-definite spectral densities, and an H-theorem. The major lack in the theory is any reliable information on the relaxation predicted by the complicated linear operator H. Closure of the hierarchy is achieved by the hypothesis that the five-coefficient correlation function is negligible. Problems associated with inclusion of viscosity and external driving forces are discussed.
Montgomery, D.↗
Rarefied gas dynamics; Proceedings of the Eighth International Symposium, Stanford University, Stanford, Calif., July 10-14, 1972
Recent studies in the theory of rarefied gases (kinetic theory, shock structure, molecular forces and interactions, evaporation and condensation, expansions and jets, flow past bodies, gas-solid interactions) are presented along with descriptions of numerous experiments in these areas. Some of the topics covered include: singular limits of solutions of Boltzmann's equations, the Boltzmann and Klimontovich formalisms with reference to turbulent resolution, higher-order kinetic theory for the Lorentz gas, intermolecular potentials from shock structure experiments, cooling of particles in aerosol beams, hypersonic-subsonic transition in spherically symmetric expanding flows, absolute velocity measurements in a rarefied gas flow by an ion time-of-flight technique, the product distribution of gas-solid reactions from absolute rate theory, and relaxation of a gas with internal degrees of freedom. Individual items are announced in this issue.
Karamcheti, K.↗
Transport Properties of Magnetized High-Energy Density Plasma (Final Project Report)
This report summarizes results of project DE-SC0016159 "Transport Properties of Magnetized High-Energy-Density Plasma,'' which ran from 7/15/2016 - 7/14/2021. The primary objectives of the work, as stated in the original proposal, were to develop a theory that describes transport coefficients in magnetized high energy density plasmas and to test the theory with molecular dynamics (MD) simulations. The science challenge is that strong ion coupling, strong magnetization of electrons, and partial degeneracy of electrons, cause the system to be in a regime that is not well described by current theory. The particular processes that were to be investigated include: ion stopping power, diffusion, electron-ion temperature relaxation, thermal conduction and viscosity. All of the primary research objectives were accomplished during the course of this work. In addition, some unexpected results were discovered along the way that led to new and productive research directions. This work resulted in 17 publications in well-respected peer-reviewed journals (primarily Physics of Plasmas and Physical Review E), and 2 more are being prepared for publication. A few of these were selected as Editor's Picks and one was published as a Rapid Communication. Highlights of the research results include: Transport phase space: The first identification of the parameter space that defines fundamental transport regimes in terms of the Coulomb coupling and magnetization parameters. Mean force kinetic theory: Systematic derivation of a kinetic theory for strongly coupled plasmas based on a new expansion parameter of the BBGKY hierarchy. This provided the derivation of a theory that we had previously posed phenomenologically, and also revealed a new term that captures the equation of state properties at all coupling strengths. Transverse friction force: Discovery that the friction force on a test charge in a strongly magnetized plasma includes a component that is perpendicular to the motion of the test charge in the plane defined by the velocity and magnetic field vectors. Gyrofriction force: Discovery that the friction force on a test charge in a plasma that is both strongly magnetized and strongly coupled includes a component of the force in the direction of the Lorentz force. Kinetic theory for warm dense matter: Extension of the mean force kinetic theory to include partial electron degeneracy, so that it applies to warm dense matter.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Second-order spectral line shift comparisons
The second-order spectral line width formulae from the projection operator and kinetic theory methods were recently compared. It was shown that a systematic expansion of the projection operator width expression including initial correlations formally agrees with the second-order kinetic theory result. It is now shown that the second-order dynamic shifts are also formally the same. The static shifts, however, differ due to an ad hoc treatment of electron-electron correlations in the projection operator method. The approximation is necessary in order to screen the radiator-electron interactions. The differences, however, are expected to be small. Finally, the results suggest using the rigorous and more compact second-order width and shift expressions from the kinetic theory method as the starting point for spectral line shape calculations. At line center, however, the projection operator second-order expression for the width and shift simplifies and reduces to the kinetic theory result.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗