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DOE OSTI2010

Dirac equation for the harmonic scalar and vector potentials and linear plus coulomb-like tensor potential; the SUSY approach

The problem of analytical solutions of the 3-dimensional Dirac equation is usually studied via techniques such as The Nikiforov-Uvarov (NU) method. Here, we see that one of the most attractive potentials can be brought into a well-known form of Schroedinger-like problem possessing known solutions via the methodology of supersymmetry (SUSY). Next, using the idea of shape invariance, we calculate exact solutions of Dirac equation for quadratic scalar and vector potentials in the presence of a tensor potential that depends on the radial component either linearly or inversely. The tensor potential itself, besides its applications, removes degeneracy, too.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Nonlinear theory for a terahertz gyrotron with a special cross-section interaction cavity

The fully numerical nonlinear theory for a gyrotron with a special cross-section interaction cavity has been developed in this paper. In this theory, the analytical solution to different modes in the special cross-section interaction cavity is replaced by the numerical solution based on electromagnetic simulation results. A 0.4 THz third harmonic gyrotron with an azimuthally corrugated interaction cavity has been investigated by using this theory and simulation results show that this approach has a significant advantage of developing high harmonic terahertz gyrotrons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Theoretical analysis of sound transmission loss through graphene sheets

We examine the potential of using graphene sheets (GSs) as sound insulating materials that can be used for nano-devices because of their small size, super electronic, and mechanical properties. In this study, a theoretical analysis is proposed to predict the sound transmission loss through multi-layered GSs, which are formed by stacks of GS and bound together by van der Waals (vdW) forces between individual layers. The result shows that the resonant frequencies of the sound transmission loss occur in the multi-layered GSs and the values are very high. Based on the present analytical solution, we predict the acoustic insulation property for various layers of sheets under both normal incident wave and acoustic field of random incidence source. The scheme could be useful in vibration absorption application of nano devices and materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Self-consistent initial conditions for primordial black hole formation

For an arbitrarily strong, spherically symmetric super-horizon curvature perturbation, we present analytic solutions of the Einstein equations in terms of the asymptotic expansion over the ratio of the Hubble radius to the length-scale of the curvature perturbation to set initial conditions for numerical computations of primordial black hole formation. To obtain this solution we develop a recursive method of quasi-linearization which reduces the problem to a system of coupled ordinary differential equations for the Nth order terms in the asymptotic expansion with sources consisting of a non-linear combination of the lower order terms.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method

Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation has been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

Electrodynamics of a planar photodiode discharge for an obliquely incident initiating laser pulse

An approximate analytic solution of Maxwell's equations is obtained inside a photodiode. Analysis of this solution shows that the earlier discovered significant decrease in the radiation field characteristics over an anode is caused by a considerable increase in the amplitude of a wave generated inside the photodiode, which for angles of incidence {theta} {yields} {pi}/2 achieves a value comparable to the initial electric field strength applied to the photodiode. In this case, the electromagnetic energy flux density inside the photodiode exceeds tens times or more the electromagnetic energy flux density over the anode. The results of numerical calculations confirm the analytic results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

A study of solid wall models for weakly compressible SPH

This paper is concerned with a comparison of two methods of treating solid wall boundaries in the weakly compressible (SPH) method. They have been chosen because of their wide use in simulations. These methods are the boundary force particles of Monaghan and Kajtar [24] and the use of layers of fixed boundary particles. The latter was first introduced by Morris et al. [26] but has since been improved by Adami et al. [1] whose algorithm involves interpolating the pressure and velocity from the actual fluid to the boundary particles. For each method, we study the effect of the density diffusive terms proposed by Molteni and Colagrossi [19] and modified by Antuono et al. [3]. We test the methods by a series of simulations commencing with the time-dependent spin-down of fluid within a cylinder and the behaviour of fluid in a box subjected to constant acceleration at an angle to the walls of the box, and concluding with a dam break over a triangular obstacle. In the first two cases the results from the two methods can be compared to analytical solutions while, in the latter case, they can be compared with experiments and other methods. These results show that the method of Adami et al. together with density diffusion is in very satisfactory agreement with the experimental results and is, overall, the best of the methods discussed here.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Ecosystem carbon storage capacity as affected by disturbance regimes: A general theoretical model

Disturbances have been recognized as a key factor shaping terrestrial ecosystem states and dynamics. A general model that quantitatively describes the relationship between carbon storage and disturbance regime is critical for better understanding large scale terrestrial ecosystem carbon dynamics. We developed a model (REGIME) to quantify ecosystem carbon storage capacities (E[x]) under varying disturbance regimes with an analytical solution E[x] = U {center_dot} {tau}{sub E} {center_dot} {lambda}{lambda} + s {tau} 1, where U is ecosystem carbon influx, {tau}{sub E} is ecosystem carbon residence time, and {tau}{sub 1} is the residence time of the carbon pool affected by disturbances (biomass pool in this study). The disturbance regime is characterized by the mean disturbance interval ({lambda}) and the mean disturbance severity (s). It is a Michaelis-Menten-type equation illustrating the saturation of carbon content with mean disturbance interval. This model analytically integrates the deterministic ecosystem carbon processes with stochastic disturbance events to reveal a general pattern of terrestrial carbon dynamics at large scales. The model allows us to get a sense of the sensitivity of ecosystems to future environmental changes just by a few calculations. According to the REGIME model, for example, approximately 1.8 Pg C will be lost in the high-latitude regions of North America (>45{sup o} N) if fire disturbance intensity increases around 5.7 time the current intensity to the end of the twenty-first century, which will require around 12% increases in net primary productivity (NPP) to maintain stable carbon stocks. If the residence time decreased 10% at the same time additional 12.5% increases in NPP are required to keep current C stocks. The REGIME model also lays the foundation for analytically modeling the interactions between deterministic biogeochemical processes and stochastic disturbance events.

09 BIOMASS FUELS↗

DOE OSTI2011

Stationary light pulse in solids with long-lived spin coherence

We present a detailed analysis of stationary light pulses (SLP's) for the case of inhomogeneous broadening in both optical and spin transitions, which is normally found in solid materials with long-lived spin coherence. By solving the Langevin equations of motion for the density matrix elements under the integral over the entire range of the inhomogeneous broadenings, the necessary conditions for creating the SLP in a solid are obtained. Then the decay and diffusion processes that the SLP undergoes are analyzed. The characteristics of such processes are studied based on the analytic solution of the SLP with a slowly varying envelope. The dependence of SLP lifetime on inhomogeneous broadenings of spin and optical transitions, which can be regarded as the laser linewidth in the repump scheme, has been discussed.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2014

Directivity patterns and pulse profiles of ultrasound emitted by laser action on interface between transparent and opaque solids: Analytical theory

The analytical theory for the directivity patterns of ultrasounds emitted from laser-irradiated interface between two isotropic solids is developed. It is valid for arbitrary combinations of transparent and opaque materials. The directivity patterns are derived both in two-dimensional and in three-dimensional geometries, by accounting for the specific features of the sound generation by the photo-induced mechanical stresses distributed in the volume, essential in the laser ultrasonics. In particular, the theory accounts for the contribution to the emitted propagating acoustic fields from the converted by the interface evanescent photo-generated compression-dilatation waves. The precise analytical solutions for the profiles of longitudinal and shear acoustic pulses emitted in different directions are proposed. The developed theory can be applied for dimensional scaling, optimization, and interpretation of the high-pressure laser ultrasonics experiments in diamond anvil cell.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2010

Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory

The nonperturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields E-vector(x-vector,t). Based on the Dirac-Heisenberg-Wigner formalism, we derive a system of partial differential equations of infinite order for the 16 irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field E(t)=E{sub 0} and the Sauter-type electric field E(t)=E{sub 0}sech{sup 2}(t/{tau}). These analytic solutions translate into corresponding expressions within the Dirac-Heisenberg-Wigner formalism and allow to discuss the effect of higher derivatives. We observe that spatial field variations typically exert a strong influence on the components of the Wigner function for large momenta or for late times.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2010

Some approaches to investigation of the influence of variable energy release on heat transfer and temperature fields of fuel elements of nuclear reactors

Different methods for estimating the effect of energy release reduction in the second half of the active core on the temperature field of fuel elements are considered: analytical solution of the problem, recalculation of the temperature field obtained at constant energy release for variable energy release, and so on. An enhanced role of this effect for peripheral fuel elements of fuel assemblies of fast reactors is noted.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Closure of the single fluid magnetohydrodynamic equations in presence of electron cyclotron current drive

In the presence of electron cyclotron current drive (ECCD), the Ohm's law of single fluid magnetohydrodynamics is modified as E + v × B = η(J – J{sub EC}). This paper presents a new closure relation for the EC driven current density appearing in this modified Ohm's law. The new relation faithfully represents the nonlocal character of the EC driven current and its main origin in the Fisch-Boozer effect. The closure relation is validated on both an analytical solution of an approximated Fokker-Planck equation as well as on full bounce-averaged, quasi-linear Fokker-Planck code simulations of ECCD inside rotating magnetic islands. The new model contains the model put forward by Giruzzi et al. [Nucl. Fusion 39, 107 (1999)] in one of its limits.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Effective of the q-deformed pseudoscalar magnetic field on the charge carriers in graphene

In this paper, we have obtained exact analytical solutions of the time-independent Dirac-Weyl equation for the charge carriers with q-deformed pseudoscalar magnetic barrier (PMB) in graphene by using the ansatz method. We have also found a solution that describes the left propagating wave function to calculation of the reflection and transmission coefficients using the Riemann’s equation. This allows us to conclude about the Dirac-Weyl equation with PMB and to understand quantum behavior of the Dirac fermions. Finally, some of the numerical results are shown, too.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Transversely diode-pumped alkali metal vapour laser

We have studied theoretically the operation of a transversely diode-pumped alkali metal vapour laser. For the case of high-intensity laser radiation, we have obtained an analytical solution to a complex system of differential equations describing the laser. This solution allows one to exhaustively determine all the energy characteristics of the laser and to find optimal parameters of the working medium and pump radiation (temperature, buffer gas pressure, and intensity and width of the pump spectrum). (lasers)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Radial acceleration of ions during adiabatic expansion of a multicomponent cylindrical plasma

The methods of modern group analysis allow an analytic solution of the Cauchy problem to be constructed for the system of kinetic equations for a fully ionised electron – ion plasma, describing the acceleration of ions during the adiabatic expansion of a cylindrical plasma. Time and spatial dependences of the distribution functions of particles are obtained and their integral characteristics, such as density, average velocity, temperature, and energy spectrum, are found. The formation of the energy spectrum of accelerated ions, asymptotically repeating the spatial distribution of their density, and the cooling of electrons in the process of ion acceleration are analytically described. Particular attention is paid to the investigation of the influence of the heavy ionic component on the dynamics of the light component. The features of ion acceleration in the case of a two-temperature electron distribution function that describes the presence of hot and cold electron components are studied, which corresponds to the typical conditions of the experiment on plasma heating by intense laser radiation. (paper)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2010

Analytic theory of curvature effects for wave problems with general boundary conditions

A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found, the perturbative solution is shown to yield the same result. The present technique allows the generalization of earlier results to arbitrary boundary conditions. The power of the method is illustrated using examples based on Maxwell's and Schroedinger's equations for applications in photonics and nanoelectronics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗