Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function f(x, v; t). Adopting an alternative approach, previously introduced for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Electrostatic waves in superthermal dusty plasmas: review of recent advancement

Real plasmas are often caracterized by the presence of excess energetic particle populations, resulting in a long-tailed non-Maxwellian distribution. In Space plasma physics, this phenomenon is usually modelled via a kappa-type distribution. This presentation is dedicated to an investigation, from first principles, of the effect of superthermality on the characteristics of dusty plasma modes. We employ a kappa distribution function to model the superthermality of the background components (electrons and/or ions). Background superthermality is shown to modify the charge screening mechanism in dusty plasmas, thus affecting the linear dispersion laws of both low- and higher frequency DP modes substantially. Various experimentally observed effects may thus be interpreted as manifestations of superthermality. Focusing on the features of nonlinear excitations (solitons) as they occur in different dusty plasma modes, we investigate the role of superthermality in their propagation dynamics (existence laws, stability profile) and characteristics (geometry).

Dynamical characteristics of solitary waves, shocks and envelope modes in kappa-distributed non-thermal plasmas: an overview

Space plasmas provide abundant evidence of highly energetic particle population, resulting in a long-tailed non-Maxwellian distribution. Furthermore, the first stages in the evolution of plasmas produced during laser-matter interaction are dominated by nonthermal electrons, as confirmed by experimental observation and computer simulations. This phenomenon is efficiently modelled via a kappa-type distribution. We present an overview, from first principles, of the effect of superthermality on the characteristics of electrostatic plasma waves. We rely on a fluid model for ion-acoustic excitations, employing a kappa distribution function to model excess superthermality of the electron distribution. Focusing on nonlinear excitations (solitons), in the form of solitary waves (pulses), shocks and envelope solitons, and employing standard methodological tools of nonlinear plasmadynamical analysis, we discuss the role of excess superthermality in their propagation dynamics (existence laws, stability profile), geometric characteristics and stability. Numerical simulations are employed to confirm theoretical predictions, namely in terms of the stability of electrostatic pulses, as well as the modulational stability profile of bright- and dark-type envelope solitons.

A Neutron Diffraction and Molecular Dynamics Investigation of Acetate-based Ionic Liquids as Solvents for Glucose

The liquid state structure of the ionic liquid, 1-ethyl-3-methylimidazolium acetate, and the solute/solvent structure of glucose dissolved in the ionic liquid at a 1: 6 molar ratio have been investigated at 323 K by molecular dynamics simulations and neutron diffraction experiments using H/D isotopically substituted materials. Interactions between hydrogen-bond donating cation sites and polar, directional hydrogen-bond accepting acetate anions are examined. Ion-ion radial distribution functions for the neat ionic liquid, calculated from both MD and derived from the empirical potential structure refinement model to the experimental data, show the alternating shell-structure of anions around the cation, as anticipated. Spatial probability distributions reveal the main anion-to-cation features as in-plane interactions of anions with imidazolium ring hydrogens and cation-cation planar stacking. Interestingly, the presence of the polarised hydrogen-bond acceptor anion leads to increased anion-anion tail-tail structuring within each anion shell, indicating the onset of hydrophobic regions within the anion regions of the liquid.

STEADY-STATE SOLUTIONS IN NONLINEAR DIFFUSIVE SHOCK ACCELERATION

Stationary solutions to the equations of nonlinear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean free path is thought to be an increasing function of energy, this condition is conventionally implemented as an upper cutoff in energy space-particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for the substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven nonresonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off-a diagnostic that is in principle accessible to observation.

Nakagami-m Phase Model: Further Results and Validation

This paper contributes to and expands on the Nakagami-m phase model. It derives exact, closed-form expressions for both the phase cumulative distribution function and its inverse. In addition, empirical first- and second-order statistics obtained from measurements conducted in a body-area network scenario were used to fit the phase probability density function, the phase cumulative distribution function, and the phase crossing rate expressions. Remarkably, the unlikely shapes of the phase statistics, as predicted by the theoretical formulations, are actually encountered in practice.

Re-examining the Cairns-Tsallis model for ion acoustic solitons

Recently, a hybrid distribution function was proposed to describe a plasma species with an enhanced superthermal component. This combines a Cairns-type "nonthermal" form with the Tsallis theory for nonextensive thermodynamics. Using this alternative model, the propagation of arbitrary amplitude ion acoustic solitary waves in a two-component plasma is investigated. From a careful study of the distribution function it is found that the model itself is valid only for a very restricted range in the q-nonextensive parameter and the nonthermality parameter, a. Solitary waves, the amplitude and nature of which depend sensitively on both q and a, can exist within a narrow range of allowable Mach numbers. Both positive and negative potential structures are found, and coexistence may occur. © 2013 American Physical Society.

Ergodic Capacity of Cognitive TAS/GSC Relaying in Nakagami-m Fading Channels

We examine the impact of transmit antenna selection with receive generalized selection combining (TAS/GSC) for cognitive decode-and-forward (DF) relaying in Nakagami-m fading channels. We select a single transmit antenna at the secondary transmitter which maximizes the receive signal-to-noise ratio (SNR) and combine a subset of receive antennas with the largest SNRs at the secondary receiver. In an effort to assess the performance, we first derive the probability density function and cumulative distribution function of the end-to-end SNR using the moment generating function. We then derive new exact closed-form expression for the ergodic capacity. More importantly, by deriving the asymptotic expression for the high SNR approximation of the ergodic capacity, we gather deep insights into the high SNR slope and the power offset. Our results show that the high SNR slope is 1/2 under the proportional interference power constraint. Under the fixed interference power constraint, the high SNR slope is zero.

Cognitive Single Carrier Systems: Joint Impact of Multiple Licensed Transceivers

In this paper, the impact of interference from multiple licensed transceivers on cognitive underlay single carrier systems is examined. Specifically, the situation is considered in which the secondary network is limited by three key parameters: 1) maximum transmit power at the secondary transmitter, 2) peak interference power at the primary receivers, and 3) interference power from the primary transmitters. For this cognitive underlay single carrier system, the signal-to-interference ratio (SIR) of the secondary network is obtained for transmission over frequency selective fading channels. Based on this, a new closedform expression for the cumulative distribution function of the SIR is evaluated, from which the outage probability and the ergodic capacity are derived. Further insights are established by analyzing the asymptotic outage probability and the asymptotic ergodic capacity in the high transmission power regime. In particular, it is corroborated that the asymptotic outage diversity gain is equal to the multipath gain of the frequency selective channel in the secondary network. The asymptotic ergodic capacity also gives new insight into the additional power cost for different network parameters while maintaining a specified target ergodic capacity. Illustrative numerical examples are presented to validate the outage probability and ergodic capacity under different interference power profiles.

Advanced Modelling and Optimization of Infared Oven in Injection Stretch Blow-moulding for Energy Saving

In the production process of polyethylene terephthalate (PET) bottles, the initial temperature of preforms plays a central role on the final thickness, intensity and other structural properties of the bottles. Also, the difference between inside and outside temperature profiles could make a significant impact on the final product quality. The preforms are preheated by infrared heating oven system which is often an open loop system and relies heavily on trial and error approach to adjust the lamp power settings. In this paper, a radial basis function (RBF) neural network model, optimized by a two-stage selection (TSS) algorithm combined with partial swarm optimization (PSO), is developed to model the nonlinear relations between the lamp power settings and the output temperature profile of PET bottles. Then an improved PSO method for lamp setting adjustment using the above model is presented. Simulation results based on experimental data confirm the effectiveness of the modelling and optimization method.

Generalized Selection Combining for Cognitive Relay Networks over Nakagami-m Fading

We consider transmit antenna selection with receive generalized selection combining (TAS/GSC) for cognitive decodeand-forward (DF) relaying in Nakagami-m fading channels. In an effort to assess the performance, the probability density function and the cumulative distribution function of the endto-end SNR are derived using the moment generating function, from which new exact closed-form expressions for the outage probability and the symbol error rate are derived. We then derive a new closed-form expression for the ergodic capacity. More importantly, by deriving the asymptotic expressions for the outage probability and the symbol error rate, as well as the high SNR approximations of the ergodic capacity, we establish new design insights under the two distinct constraint scenarios: 1) proportional interference power constraint, and 2) fixed interference power constraint. Several pivotal conclusions are reached. For the first scenario, the full diversity order of the
outage probability and the symbol error rate is achieved, and the high SNR slope of the ergodic capacity is 1/2. For the second scenario, the diversity order of the outage probability and the symbol error rate is zero with error floors, and the high SNR slope of the ergodic capacity is zero with capacity ceiling.

Electron-acoustic solitons in an electron-beam plasma system with kappa-distributed electrons

Interaction of a stream of high-energy electrons with the background plasma plays an important role in the astrophysical phenomena such as interplanetary and stellar bow shock and Earth's foreshock emission. It is not yet fully understood how electrostatic solitary waves are produced at the bow shock. Interestingly, a population of energetic suprathermal electrons were also found to exist in those environments. Previously, we have studied the properties of negative electrostatic potential solitary structures exist in such a plasma with excess suprathermal electrons. In the present study, we investigate the existence conditions and propagation properties of electron-acoustic solitary waves in a plasma consisting of an electron beam fluid, a cold electron fluid, and hot suprathermal electrons modeled by a kappa-distribution function. The Sagdeev pseudopotential method was used to investigate the occurrence of stationary-profile solitary waves. We have determined how the electron-acoustic soliton characteristics depend on the electron beam parameters. It is found that the existence domain for solitons becomes narrower with an increase in the suprathermality of hot electrons, increasing the beam speed, decreasing the beam-to-cold electron population ratio. These results lead to a better understanding of the formation of electron-acoustic solitary waves observed in those space plasma systems characterized by kappa-distributed electrons and inertial drifting (beam) electrons.

X-ray Polarization Measurements of Dense Plasmas Heated by Fast Electrons

The detailed knowledge of fast electron energy transport following interaction with high-intensity, ultra-short laser pulses is a key area for secondary source generation for ELI. We demonstrate polarization spectroscopy at laser intensities up to 10(21) Wcm(-2). This is significant as it suggests that in situ emission spectroscopy may be used as an effective probe of fast electron velocity distributions in regimes relevant to electron transport in solid targets. Ly-alpha doublet emission of nickel (Z = 28) and sulphur (Z = 16) is observed to measure the degree of polarization from the Ly-alpha(1) emission. Ly-alpha(2) emission is unpolarized, and as such acts as a calibration source between spectrometers. The measured ratio of the X-ray sigma- and pi-polarization allows the possibility to infer the velocity distribution function of the fast electron beam.

Electron-acoustic solitons in an electron-beam plasma system with kappa-distributed electrons

We investigate the existence conditions and propagation properties of electron-acoustic solitary waves in a plasma consisting of an electron beam fluid, a cold electron fluid, and a hot suprathermal electron component modeled by a k-distribution function. The Sagdeev pseudopotential method was used to investigate the occurrence of stationary-profile solitary waves. We have determined how the soliton characteristics depend on the electron beam parameters. It is found that the existence domain for solitons becomes narrower with an increase in the suprathermality of hot electrons, increasing the beam speed, and decreasing the beam-to-cold electron population ratio.

X-ray Polarization Spectroscopy from Ultra-Intense Interactions

Detailed knowledge of fast electron energy transport following the interaction of ultrashort intense laser pulses is a key subject for fast ignition. This is a problem relevant to many areas of laser-plasma physics with particular importance to fast ignition and X-ray secondary source development, necessary for the development of large-scale facilities such as HiPER and ELI. Operating two orthogonal crystal spectrometers set at Bragg angles close to 45 degrees determines the X-ray s- and p-polarization ratio. From this ratio, it is possible to infer the velocity distribution function of the fast electron beam within the dense plasma. We report on results of polarization measurements at high density for sulphur and nickel buried layer targets in the high intensity range of 10(19) - 10(21) Wcm(-2). We observe at 45 degrees the Ly-alpha doublet using two sets of orthogonal highly-orientated pyrolytic graphite (HOPG) crystals set in 1(st) order for sulphur and 3(rd) order for nickel.