Kinetic Theory of Time-Dependent Correlation Functions in a Binary Gas Mixture
The Physics of Fluids, 1972
Time-dependent correlation functions in a binary mixture of gases are studied on the basis of kin... more Time-dependent correlation functions in a binary mixture of gases are studied on the basis of kinetic theory. The problem is formulated as an initial-value solution to the linearized Boltzmann equation for the mixture. The analysis is made tractable by the use of an appropriate kinetic model which is developed for Maxwell molecules (1/r4 repulsive potential). The resulting description yields density correlation functions which are valid for arbitrary ratios of wavelength to mean free path. In particular, the results can be used to discuss deviations from hydrodynamic behavior. With the present theory a detailed analysis of the spectral distribution of laser light scattered by dilute binary gas mixtures is made. Explicit results for xenon-helium mixtures are shown to be in very good agreement with the recent measurements of Clark and Benedek.
Renormalized expressions for the transport coefficients of a normal quantum fluid are derived fro... more Renormalized expressions for the transport coefficients of a normal quantum fluid are derived from a nonlocal kinetic equation. As was shown in the classical case by Forster and Martin and by Resiboie, the expressions for the transport coefficients separate naturally into "kinetic" and "direct" parts. The kinetic terms are proportional to matrix elements of the inverse of the kinetic kernel, and have the same general structure as the "bare" transport coefficients obtained from a local Boltzmann equation. The direct terms are proportional to matrix elements of the kernel itself, and have no counterpart in calculations based on a local kinetic equation, as in the kinetic theory of gases. %'e evaluate the transport coef5cients using the weak- coupling approximation to the kernel derived in a previous paper. Results are given, first, for both Bose and Fermi Auids at arbitrary temperature, and then for the Fermi fluid near T = 0, where complete solutions are obtained. It is found that the direct parts of the shear viscosity and thermal conductivity are of higher order in T than the kinetic parts, and are therefore negligible at very low temperature. The kinetic parts have the same leading temperature dependence as the predictions of the Landau theory, For the bulk viscosity, however, the direct and kinetic contributions begin at the same order (T ) in the temperature.
We study the collision kernels of two linearized equations for a moderately dense gas. These are ... more We study the collision kernels of two linearized equations for a moderately dense gas. These are the low-density Bogoliubov kinetic equation and the equation at the next order in the density (ternary-collision level), in the form given by Green and Cohen. We reduce the collision kernels of these equations to expressions which are nonlocal in space but local in time, and show that each of them breaks up into static and collisional parts, The former parts agree with the mean-field expressions. We compare the collisional parts with the fully dynamical expressions previously found by Mazenko and us, and find complete agreement only at zero wave vector and frequency. For nonzero wave vectors, the desired symmetry in the momentum variables breaks down. We show that this has no effect on the first-order transport coefficients; it would presumably be significant in the kinetic regime. We also find that the speed of sound predicted by the Bogoliubov equation agrees with the thermodynamic result truncated at first order in the density. We write the low-density collision integral of Bogoliubov in the form J, [E(lt)] = -lim i d2L, (12)Z,(12)E(lt)E(2t), OQ (4) Z, (kz;pp')= Z, '"(kp)+Z,"'(kz;pp'), (I= 1, 2), (3) and the I. 's are the usual two-body Liouville opera- tors
Spatial-filter pinholes and knife-edge samples were irradiated in vacuum by 1053-nm, 5-20 ns puls... more Spatial-filter pinholes and knife-edge samples were irradiated in vacuum by 1053-nm, 5-20 ns pulses at intensities to 500 GW/cm*. The knife-edge samples were fabricated of plastic, carbon, ahnuinum, stainless steel, molybdenum, tantalq gold and an absorbing glass. Tie-resolved two-beam interferometry with a 40-ns probe pulse was used to observe phase shifts in the expanding laser-induced plasma For all of these materials, at any time during square-pulse irradiation, the phase shift fell exponentially with distance from the edge of the sample. The expansion was characterized by the propagation velocity V, of the contour for a 2~ phase shift To within experimental error, V, was constant during irradiation at a particular intensity, and it increased linearly with intensity for intensities <300 GW/cn?. For metal samples, V, exhibited an approximate M-O’ dependence where M is the atomic mass. Plasmas of plastic, carbon and absorbing glass produced larger phase shifts, and expanded mor...
Modeling of Powder Absorption in Additive Manufacturing
CLEO: 2014, 2014
We have investigated optical absorption by a powder of metal spheres, via ray-trace calculations.... more We have investigated optical absorption by a powder of metal spheres, via ray-trace calculations. The absorptivity significantly exceeds that for normal incidence, because of multiple scattering. The effect of beam size is also discussed.
For many targets of interest, the thickness is small compared to the conduction length during the... more For many targets of interest, the thickness is small compared to the conduction length during the engagement. In addition, the laser-material interaction region can be treated as flat. We have studied this regime with our 25 kW solid-state laser. We have demonstrated that airflow can reduce by approximately 40% the energy required to break through a thin target. This reduction is caused by the bulging of the softened material and the tearing and removal of the material by aerodynamic forces. We present elastic modeling which explains these results.
Modeling Theory of the Linearized Collision Operator for a Gas Mixture
The Physics of Fluids, 1972
Kinetic models are developed for the linearized Boltzmann collision operator which describes the ... more Kinetic models are developed for the linearized Boltzmann collision operator which describes the collisions between different kinds of molecules. From the known eigentheory of this operator and the method of Gross and Jackson, a sequence of increasingly more accurate model operators is generated. All of the models satisfy the conservation laws, and all except the single-relaxation time model lead to the proper transport coefficients. Explicit expressions are given for some models, including the simplest one compatible with hydrodynamics. In the context of the present development, a unified discussion of the linearized versions of several existing models is given.
Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion
Pinhole plasma effects on parameters of the laser beam passing through the spatial filter in cond... more Pinhole plasma effects on parameters of the laser beam passing through the spatial filter in conditions of interest for large scale ICF laser facilities were investigated. The experiments on pinhole irradiation were conducted at power density range 1010-1011 W/cm2 with approximately 15 ns laser pulses. Al, Fe, and Ta pinholes were used. The diagnostic approach was chosen based on probing the pinhole region with frequency doubled 3-ns-long laser pulse. Ablative-plasma dynamics was studied with shadowgraphy and interferometry. Also measured were the parameters of transmitted probing beam in the near- and far-fields. The rate of pinhole 'closure' is found to decrease with the increase in the atomic number of pinhole material. The rate o pinhole closure ranges from approximately 5*106 cm/s for aluminum pinhole down to approximately 2*106 cm/s for tantalum pinhole in experiments with power density at the pinhole edge of approximately 50 GW/cm2. For aluminum and steel pinholes the...
Advanced Radiographic Capability (ARC) project at the National Ignition Facility (NIF) is designe... more Advanced Radiographic Capability (ARC) project at the National Ignition Facility (NIF) is designed to produce energetic, ultrafast x-rays in the range of 70-100 keV for backlighting NIF targets. The chirped pulse amplification (CPA) laser system will deliver kilo-Joule pulses at an adjustable pulse duration from 1 ps to 50 ps. System complexity requires sophisticated simulation and modeling tools for design, performance prediction, and comprehension of experimental results. We provide a brief overview of ARC, present our main modeling tools, and describe important performance predictions. The laser system (Fig. 1) consists of an all-fiber front end, including chirped-fiber Bragg grating (CFBG) stretchers. The beam after the final fiber amplifier is split into two apertures and spatially shaped. The split beam first seeds a regenerative amplifier and is then amplified in a multi-pass Nd:glass amplifier. Next, the preamplified chirped pulse is split in time into four identical replica...
Neoclassical radial particle and energy fluxes are computed, in the disparate mass limit, for a m... more Neoclassical radial particle and energy fluxes are computed, in the disparate mass limit, for a multicomponent collisional tokamak plasma. Contributions due to charge-exchange friction are included in the fluxes.
A Compact Line Replaceable Unit Laser Driver for Laser Inertial Fusion Energy
Conference on Lasers and Electro-Optics 2012, 2012
ABSTRACT The laser system has predicted performance of 8100-J at 16-Hz with 18% wallplug efficien... more ABSTRACT The laser system has predicted performance of 8100-J at 16-Hz with 18% wallplug efficiency. This laser also has broad industrial applications including materials processing, and Chirped-Pulse-Amplification pump/amplifier sources which in turn can produce secondary radiation sources.
Model of pulse extraction from a copper laser amplifier
A computational model of pulse propagation through a copper laser amplifier has been developed. T... more A computational model of pulse propagation through a copper laser amplifier has been developed. The model contains a system of 1-D (in the axial direction), time-dependent equations for the laser intensity and amplified spontaneous emission (ASE), coupled to rate equations for the atomic levels. Detailed calculations are presented for a high-power amplifier at Lawrence Livermore National Laboratory. The extracted power agrees with experiment near saturation. At lower input power the calculation overestimates experiment, probably because of increased ASE effects. 6 refs., 6 figs.
Kinetic Theory of a Dense Gas: Triple-Collision Memory Function
Physical Review A, 1973
We study the phase-space density-correlation function S(r-->t p-->p-->') for a dens... more We study the phase-space density-correlation function S(r-->t p-->p-->') for a dense classical gas with repulsive interaction using the language of memory functions. We derive the kinetic equation for S which is valid at all wavelengths and frequencies but limited to second order in the density (triple collisions). This model equation is, on the one hand, an extension of the earlier work of Mazenko to the next order in density and, on the other hand, an extension to arbitrary wavelengths and frequencies of some suggested generalizations of the linearized Boltzmann equation. The memory function for this kinetic equation is shown to be compatible with symmetry properties, sum rules, and the conservation laws. As an illustration of the hydrodynamics, we calculate the shear viscosity and show that the term linear in density agrees with an earlier calculation by Kawasaki and Oppenheim. We also give the analogous kinetic equation for the single-particle correlation function.
Kinetic Theory of Time-Dependent Correlation Functions in a Binary Gas Mixture
The Physics of Fluids, 1972
Time-dependent correlation functions in a binary mixture of gases are studied on the basis of kin... more Time-dependent correlation functions in a binary mixture of gases are studied on the basis of kinetic theory. The problem is formulated as an initial-value solution to the linearized Boltzmann equation for the mixture. The analysis is made tractable by the use of an appropriate kinetic model which is developed for Maxwell molecules (1/r4 repulsive potential). The resulting description yields density correlation functions which are valid for arbitrary ratios of wavelength to mean free path. In particular, the results can be used to discuss deviations from hydrodynamic behavior. With the present theory a detailed analysis of the spectral distribution of laser light scattered by dilute binary gas mixtures is made. Explicit results for xenon-helium mixtures are shown to be in very good agreement with the recent measurements of Clark and Benedek.
Renormalized expressions for the transport coefficients of a normal quantum fluid are derived fro... more Renormalized expressions for the transport coefficients of a normal quantum fluid are derived from a nonlocal kinetic equation. As was shown in the classical case by Forster and Martin and by Resiboie, the expressions for the transport coefficients separate naturally into "kinetic" and "direct" parts. The kinetic terms are proportional to matrix elements of the inverse of the kinetic kernel, and have the same general structure as the "bare" transport coefficients obtained from a local Boltzmann equation. The direct terms are proportional to matrix elements of the kernel itself, and have no counterpart in calculations based on a local kinetic equation, as in the kinetic theory of gases. %'e evaluate the transport coef5cients using the weak- coupling approximation to the kernel derived in a previous paper. Results are given, first, for both Bose and Fermi Auids at arbitrary temperature, and then for the Fermi fluid near T = 0, where complete solutions are obtained. It is found that the direct parts of the shear viscosity and thermal conductivity are of higher order in T than the kinetic parts, and are therefore negligible at very low temperature. The kinetic parts have the same leading temperature dependence as the predictions of the Landau theory, For the bulk viscosity, however, the direct and kinetic contributions begin at the same order (T ) in the temperature.
We study the collision kernels of two linearized equations for a moderately dense gas. These are ... more We study the collision kernels of two linearized equations for a moderately dense gas. These are the low-density Bogoliubov kinetic equation and the equation at the next order in the density (ternary-collision level), in the form given by Green and Cohen. We reduce the collision kernels of these equations to expressions which are nonlocal in space but local in time, and show that each of them breaks up into static and collisional parts, The former parts agree with the mean-field expressions. We compare the collisional parts with the fully dynamical expressions previously found by Mazenko and us, and find complete agreement only at zero wave vector and frequency. For nonzero wave vectors, the desired symmetry in the momentum variables breaks down. We show that this has no effect on the first-order transport coefficients; it would presumably be significant in the kinetic regime. We also find that the speed of sound predicted by the Bogoliubov equation agrees with the thermodynamic result truncated at first order in the density. We write the low-density collision integral of Bogoliubov in the form J, [E(lt)] = -lim i d2L, (12)Z,(12)E(lt)E(2t), OQ (4) Z, (kz;pp')= Z, '"(kp)+Z,"'(kz;pp'), (I= 1, 2), (3) and the I. 's are the usual two-body Liouville opera- tors
Spatial-filter pinholes and knife-edge samples were irradiated in vacuum by 1053-nm, 5-20 ns puls... more Spatial-filter pinholes and knife-edge samples were irradiated in vacuum by 1053-nm, 5-20 ns pulses at intensities to 500 GW/cm*. The knife-edge samples were fabricated of plastic, carbon, ahnuinum, stainless steel, molybdenum, tantalq gold and an absorbing glass. Tie-resolved two-beam interferometry with a 40-ns probe pulse was used to observe phase shifts in the expanding laser-induced plasma For all of these materials, at any time during square-pulse irradiation, the phase shift fell exponentially with distance from the edge of the sample. The expansion was characterized by the propagation velocity V, of the contour for a 2~ phase shift To within experimental error, V, was constant during irradiation at a particular intensity, and it increased linearly with intensity for intensities <300 GW/cn?. For metal samples, V, exhibited an approximate M-O’ dependence where M is the atomic mass. Plasmas of plastic, carbon and absorbing glass produced larger phase shifts, and expanded mor...
Modeling of Powder Absorption in Additive Manufacturing
CLEO: 2014, 2014
We have investigated optical absorption by a powder of metal spheres, via ray-trace calculations.... more We have investigated optical absorption by a powder of metal spheres, via ray-trace calculations. The absorptivity significantly exceeds that for normal incidence, because of multiple scattering. The effect of beam size is also discussed.
For many targets of interest, the thickness is small compared to the conduction length during the... more For many targets of interest, the thickness is small compared to the conduction length during the engagement. In addition, the laser-material interaction region can be treated as flat. We have studied this regime with our 25 kW solid-state laser. We have demonstrated that airflow can reduce by approximately 40% the energy required to break through a thin target. This reduction is caused by the bulging of the softened material and the tearing and removal of the material by aerodynamic forces. We present elastic modeling which explains these results.
Modeling Theory of the Linearized Collision Operator for a Gas Mixture
The Physics of Fluids, 1972
Kinetic models are developed for the linearized Boltzmann collision operator which describes the ... more Kinetic models are developed for the linearized Boltzmann collision operator which describes the collisions between different kinds of molecules. From the known eigentheory of this operator and the method of Gross and Jackson, a sequence of increasingly more accurate model operators is generated. All of the models satisfy the conservation laws, and all except the single-relaxation time model lead to the proper transport coefficients. Explicit expressions are given for some models, including the simplest one compatible with hydrodynamics. In the context of the present development, a unified discussion of the linearized versions of several existing models is given.
Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion
Pinhole plasma effects on parameters of the laser beam passing through the spatial filter in cond... more Pinhole plasma effects on parameters of the laser beam passing through the spatial filter in conditions of interest for large scale ICF laser facilities were investigated. The experiments on pinhole irradiation were conducted at power density range 1010-1011 W/cm2 with approximately 15 ns laser pulses. Al, Fe, and Ta pinholes were used. The diagnostic approach was chosen based on probing the pinhole region with frequency doubled 3-ns-long laser pulse. Ablative-plasma dynamics was studied with shadowgraphy and interferometry. Also measured were the parameters of transmitted probing beam in the near- and far-fields. The rate of pinhole 'closure' is found to decrease with the increase in the atomic number of pinhole material. The rate o pinhole closure ranges from approximately 5*106 cm/s for aluminum pinhole down to approximately 2*106 cm/s for tantalum pinhole in experiments with power density at the pinhole edge of approximately 50 GW/cm2. For aluminum and steel pinholes the...
Advanced Radiographic Capability (ARC) project at the National Ignition Facility (NIF) is designe... more Advanced Radiographic Capability (ARC) project at the National Ignition Facility (NIF) is designed to produce energetic, ultrafast x-rays in the range of 70-100 keV for backlighting NIF targets. The chirped pulse amplification (CPA) laser system will deliver kilo-Joule pulses at an adjustable pulse duration from 1 ps to 50 ps. System complexity requires sophisticated simulation and modeling tools for design, performance prediction, and comprehension of experimental results. We provide a brief overview of ARC, present our main modeling tools, and describe important performance predictions. The laser system (Fig. 1) consists of an all-fiber front end, including chirped-fiber Bragg grating (CFBG) stretchers. The beam after the final fiber amplifier is split into two apertures and spatially shaped. The split beam first seeds a regenerative amplifier and is then amplified in a multi-pass Nd:glass amplifier. Next, the preamplified chirped pulse is split in time into four identical replica...
Neoclassical radial particle and energy fluxes are computed, in the disparate mass limit, for a m... more Neoclassical radial particle and energy fluxes are computed, in the disparate mass limit, for a multicomponent collisional tokamak plasma. Contributions due to charge-exchange friction are included in the fluxes.
A Compact Line Replaceable Unit Laser Driver for Laser Inertial Fusion Energy
Conference on Lasers and Electro-Optics 2012, 2012
ABSTRACT The laser system has predicted performance of 8100-J at 16-Hz with 18% wallplug efficien... more ABSTRACT The laser system has predicted performance of 8100-J at 16-Hz with 18% wallplug efficiency. This laser also has broad industrial applications including materials processing, and Chirped-Pulse-Amplification pump/amplifier sources which in turn can produce secondary radiation sources.
Model of pulse extraction from a copper laser amplifier
A computational model of pulse propagation through a copper laser amplifier has been developed. T... more A computational model of pulse propagation through a copper laser amplifier has been developed. The model contains a system of 1-D (in the axial direction), time-dependent equations for the laser intensity and amplified spontaneous emission (ASE), coupled to rate equations for the atomic levels. Detailed calculations are presented for a high-power amplifier at Lawrence Livermore National Laboratory. The extracted power agrees with experiment near saturation. At lower input power the calculation overestimates experiment, probably because of increased ASE effects. 6 refs., 6 figs.
Kinetic Theory of a Dense Gas: Triple-Collision Memory Function
Physical Review A, 1973
We study the phase-space density-correlation function S(r-->t p-->p-->') for a dens... more We study the phase-space density-correlation function S(r-->t p-->p-->') for a dense classical gas with repulsive interaction using the language of memory functions. We derive the kinetic equation for S which is valid at all wavelengths and frequencies but limited to second order in the density (triple collisions). This model equation is, on the one hand, an extension of the earlier work of Mazenko to the next order in density and, on the other hand, an extension to arbitrary wavelengths and frequencies of some suggested generalizations of the linearized Boltzmann equation. The memory function for this kinetic equation is shown to be compatible with symmetry properties, sum rules, and the conservation laws. As an illustration of the hydrodynamics, we calculate the shear viscosity and show that the term linear in density agrees with an earlier calculation by Kawasaki and Oppenheim. We also give the analogous kinetic equation for the single-particle correlation function.
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Papers by Charles Boley