Losses and nonlinear steady-state particle distribution functions for fully ionized tokamak-plasmas in the collisional transport regimes

Fully ionized L-mode tokamak plasmas in the fully collisional (Pfirsch-Schlüter) and in the low-collisional (banana) nonlinear transport regimes are analyzed. We derive the expressions for particles and heat losses together with the steady-state particle distribution functions in the several collisional transport regimes. The validity of the nonlinear closure equations, previously derived, has been indirectly tested by checking that the obtained particle distribution functions are indeed solutions of the nonlinear, steady-state, Vlasov-Landau gyro-kinetic equations. A quite encouraging result is the fact that, for L-mode tokamak plasmas a dissymmetry appears between the ion and electron transport coefficients: the latter submits to a nonlinear correction, which makes the radial electron coefficients much larger than the former. In particular we show that when the L-mode JET plasma is out of the linear region, the Pfirsch-Schlüter electron transport coefficients are corrected by an amplification factor, which may reach values of order 10². Such a correction is absent for ions. On the contrary, in the banana regime, the ion transport coefficients are increased by a factor 2 and the nonlinear corrections for electrons are negligible. These results are in line with experiments.     

A deterministic method study of the impact of the Pauli principle in double-gate MOSFETs

The Pauli principle is included in a multisubband deterministic solver for two-dimensional devices without approximations.The nonlinear Boltzmann equations are treated properly without compromising on accuracy,convergence,or CPU time.The simulation results indicate the significant impact of the Pauli principle on the transport properties of the quasi-2D electron gas,especially for the on state.     

Electronic Green's functions in a T-shaped multi-quantum dot system

We developed a set of equations to calculate the electronic Green's functions in a T-shaped multi-quantum dot system using the equation of motion method. We model the system using a generalized Anderson Hamiltonian which accounts for finite intradot on-site Coulomb interaction in all component dots as well as for the interdot electron tunneling between adjacent quantum dots. Our results are obtained within and beyond the Hartree–Fock approximation and provide a path to evaluate all the electronic correlations in the multi-quantum dot system in the Coulomb blockade regime. Both approximations provide information on the physical effects related to the finite intradot on-site Coulomb interaction. As a particular example for our generalized results, we considered the simplest T-shaped system consisting of two dots and proved that our approximation introduces important corrections in the detector and side dots Green's functions, and implicitly in the evaluation of the system's transport properties. The multi-quantum dot T-shaped setup may be of interest for the practical realization of qubit states in quantum dot systems.     

Transport theory for quantum crystals

A correlation function approach is developed to treat non-equilibrium phenomena of quantum crystals at low frequency and long wavelength within the renormalized harmonic approximation (RHA). The derivation of the transport equations is carried out by studying the hierarchy of equations of motion for the retarded Green's functions of a pure, nonprimitive, nonionic, anharmonic lattice. Using a factorization technique to take into account the most important terms due to the particle fluctuations and the leading contributions to the hydrodynamic singularities of the phonon self-energy, we find a differential equation for the displacement field and a generalized transport equation for the phonon gas. The microscopic RHA expressions for the local temperature, the local heat density and the energy current are derived; the quasiparticle parameters (elastic constants, generalized Grüneisen parameters, quasiparticle interaction) entering the equations of motion are shown to be consistent with the RHA. In the hydrodynamic regime the general equations are reduced to two coupled differential equations for the lattice deformations and for the local temperature. Then only the displacement-displacement, the displacement-energy density and the energy density-energy density correlation functions show macroscopic fluctuations; for these functions thermodynamical sum-rules are derived.     

Hydrodynamics and time correlation functions for cellular automata

Hydrodynamic excitations in lattice gas cellular automata are described in terms of equilibrium time correlation functions for the local conserved variables. For large space and time scales the linearized hydrodynamic equations are obtained to Navier-Stokes order. Exact expressions for the associated susceptibilities and transport coefficients are identified in terms of correlation functions. The general form of the time correlation functions for conserved densities in the hydrodynamic limit is given and illustrated by some examples suitable for comparison with computer simulation. The transport coefficients are related to time correlation functions for the conserved fluxes in a way analogous to the Green-Kubo expressions for continuous fluids. The general results are applied for a one-component fluid and several types of binary diffusion. Also discussed are the effects of unphysical slow modes such as staggered particle or momentum densities.     

Nonlinear closures for hydrodynamical semiconductor transport models

Linear and nonlinear closures are explicitly determined for a model of 13 moment equations for carrier transport in semiconductors in the case of a Fermi electron gas.     

A collisional approach to the calculation of time correlation functions. Transport coefficients of gases

A method of successive approximations is proposed for the evaluation of the time-correlation functions such as those that give the thermal transport coefficients of gases. The method is based on a calculation of the changes in correlations of appropriate functions of the molecular velocity which are a result of collisions in the gas. The decaying rates of the correlations are expressed as integrals of the differential collision cross section. When the first approximation is introduced in the expressions for thermal transport coefficients, results are obtained for the coefficient of binary diffusion and the viscosity and thermal conductivity of single-component systems which are identical with those of the first Chapman-Enskog solutions of the Boltzmann and Enskog equations. For the coefficients of viscosity and thermal conductivity in multicomponent systems, it is shown that the first approximation leads to expressions of the form of the Sutherland and Wassiljewa relations, respectively.     

Full phase diagram of the massive Gross-Neveu model

The massive Gross-Neveu model is solved in the large-N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi elliptic functions. It contains three parameters which are determined by transcendental equations. Self-consistency of the scalar potential is proved. The phase diagram for non-zero bare quark mass is found to contain a kink-antikink crystal phase as well as a massive fermion gas phase featuring a cross-over from light to heavy effective fermion mass. For zero bare quark mass, we recover the three known phases kink-antikink crystal, massless fermion gas, and massive fermion gas. All phase transitions are shown to be of second order. Equations for the phase boundaries are given and solved numerically. Implications on condensed matter physics are indicated where our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.     

Two-dimensional electron transport in AlGaN/GaN heterostructures

We present a theoretical study of electron transport properties of two-dimensional electron gas in AlGaN/GaN heterostructures. By assuming a drifted Fermi–Dirac distribution and taking into account all major scattering mechanisms, including polar optical and acoustic phonons, background impurities, dislocation and interface roughness, the momentum- and energy-balance equations derived from Boltzmann equation are solved self-consistently. The dependence of the electron drift velocity and electron temperature as a function of the applied electric field are obtained and discussed.     

Chapman–Enskog solutions to arbitrary order in Sonine polynomials I: Simple,rigid-sphere gas

The Chapman–Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosities, the thermal conductivities, and diffusion coefficients. The Chapman–Enskog solutions are also useful for computation of the associated slip and jump coefficients near surfaces. Generally, these solutions are expressed in terms of Sonine polynomial expansions. While it has been found that relatively, low-order expansions (of order 4) can provide reasonable precision in the computation of the transport coefficients (to about 1 part in 1000), the adequacy of the low-order expansions for computation of the slip and jump coefficients still needs to be explored. Also of importance is the fact that such low-order expansions do not provide good convergence (in velocity space) for the actual Chapman–Enskog solutions even though the transport coefficients derived from these solutions appear to be reasonable. Thus, it is of some interest to explore Sonine polynomial expansions to higher orders. It is our purpose in this paper to report the results of our investigation of high-order, standard, Sonine polynomial expansions for the viscosity and the thermal conductivity related Chapman–Enskog solutions for a simple, rigid-sphere gas where we have carried out our calculations using expansions to order 150 and where our reported values for the transport coefficients have been demonstrated to converge to at least 25 significant digits. We note that, for a rigid-sphere gas, all of the relevant integrals needed for these solutions are evaluated analytically as pure fractions and, thus, results to any desired precision may be obtained. This work also indicates how results may be obtained in a similar fashion for realistic intermolecular potential models, and how gas-mixture problems may also be addressed with some additional effort.     

Steady-state and transient electronic transport properties of β-(AlxGa1-x)2O3/Ga2O3 heterostructures: An ensemble Monte Carlo simulation

The steady-state and transient electron transport properties of $\beta $-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$/Ga$_{2}$O$_{3}$ heterostructures were investigated by Monte Carlo simulation with the classic three-valley model. In particular, the electronic band structures were acquired by first-principles calculations, which could provide precise parameters for calculating the transport properties of the two-dimensional electron gas (2DEG), and the quantization effect was considered in the $\varGamma $ valley with the five lowest subbands. Wave functions and energy eigenvalues were obtained by iteration of the Schrödinger-Poisson equations to calculate the 2DEG scattering rates with five main scattering mechanisms considered. The simulated low-field electron mobilities agree well with the experimental results, thus confirming the effectiveness of our models. The results show that the room temperature electron mobility of the $\beta $-(Al$_{0.188}$Ga$_{0.812}$)$_{2}$O$_{3}$/Ga$_{2}$O$_{3}$ heterostructure at 10 kV$ \cdot$cm$^{-1}$ is approximately 153.669 cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$, and polar optical phonon scattering would have a significant impact on the mobility properties at this time. The region of negative differential mobility, overshoot of the transient electron velocity and negative diffusion coefficients are also observed when the electric field increases to the corresponding threshold value or even exceeds it. This work offers significant parameters for the $\beta$-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$/Ga$_{2}$O$_{3}$ heterostructure that may benefit the design of high-performance $\beta$-(Al$_{x}$Ga$_{1-x}$)$_{2}$O$_{3}$/Ga$_{2}$O$_{3}$ heterostructure-based devices.     

Theory of fluctuations in non-equilibrium Fermi gas

We present the equations for the equal-time two-particle correlation functions in degenerate electron gas. In association with the Onsager-type equation for the time-displaced correlation function, the equations constitute the basis of the theory of fluctuations in non-equilibrium degenerate electron gas. Thanks to the prevalence of the small-angle inter-electron scattering, the theory takes a rather simple form.     

Electron crystallization using localized representation

The character of the ground state of the electron crystal—an electron gas with periodic density and/or spin density is investigated. Calculations for non-magnetic, ferromagnetic and anti-ferromagnetic electron crystals based on the Koster-Kohn variational principle for direct calculation of Wannier functions are presented. The Wannier function is approximated by a symmetrically orthonormalized Gaussian. The orbital exponent of the Gaussian is used as a variational parameter. The effect of the positive background is suitably taken into account. The results of our calculation support Wigner’s prediction of electron crystallization.     

Streamer discharge simulation in flue gas

Streamer discharges are formed in a dielectric-barrier discharge used for nonthermal plasma generation. The results of simulation of streamer type discharge in a flue gas mixture is reported. A Monte Carlo simulation is done to obtain the transport and appropriate rate coefficients. The transport and rate coefficients calculated from the Monte Carlo is used to solve the conservation equations for electron, positive and negative ions, together with the Poisson's equation. The G-factor (radicals produced per 100 eV of electrical energy input to the discharge) obtained for Townsend-type discharge is higher as compared to a streamer-type discharge. Also experimental results of the SO₂ removal efficiency is compared to theoretical predictions     

The Influence of Dynamical Screening on the Transport Properties of Dense Plasmas

We investigate the effects of dynamical screening on the static transport properties. We review the low density expansion for the electron‐electron and electron‐ion correlation functions and give results for a 6‐moment approach within linear response theory. The expansion coefficients are given. The convergence of thermoelectric transport coefficients is examined in dependence of the rank of the collision term determinant. The results are compared with previous calculations and experiments. Effective Debye screening radii derived from the Gould‐DeWitt scheme for the inclusion of strong collisions as well as dynamical effects are discussed. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Derivation of the nonlinear hydrodynamic equations using multi-mode techniques

A general mode-mode coupling theory is developed for the microscopic mass, energy and momentum densities of a simple classical fluid. A projection operator method is employed to derive a generalized Langevin equation that contains nonlinearities of all orders with both convective and dissipative terms. A general nonequilibrium ensemble average, which contains local equilibrium as a special case, is employed to derive nonlinear transport equations that are nonlocal in both space and time.The nonlinear Euler and Navier-Stokes equations are recovered using a factorization procedure based on an inverse system size approximation. We show that in the context of mode-mode coupling theory, nonlinearities of all orders must be retained to derive the full nonlinear transport equations. We also slow that the space and time dependent nonequilibrium pressure and transport coefficients are functions of the nonequilibrium mass and internal energy densities. The thermodynamic closure relationships follow as a natural consequence of mode-mode coupling theory. For a system linearly displaced from equilibrium we demonstrate the role of the corrections to our factorization approximation in renormalizing the transport coefficients.