Maxwellian Velocity Distribution Research Articles

Numerical simulation of deuterium-tritium fusion reaction rate in laser plasma based on Monte Carlo-discrete ordinate method

Inertial confinement fusion (ICF) is one of the possible ways to realize controlled thermonuclear fusion. The fusion neutron source term is one of the important parameters in the physical design and analysis of laser plasma. The accuracy of the fusion neutron source term directly affects the reliability of the analysis results. At present, the neutron source term of deuterium-tritium fusion reaction in ICF is mainly based on formula method. It has limited applications in temperature and reaction type. Because of a large quantity of data, it is impossible to simulate the fusion reaction of each particle. In this paper, the concept of particle cloud is introduced, that is, the collection of the like particles with the same position and speed, and it is considered that the action of particle cloud is the same reaction. Because the particles should satisfy the Maxwell velocity distribution at a certain temperature and the direction is all around the circumference angle, the collision cross sections between the incident particle and different target particles are different. Therefore, the design program takes all the possible velocities, polar angles and direction angles, reads the collision cross sections between deuterium and tritium and makes corrections, and obtains the multi-temperature differential correction cross sections of deuterium and tritium fusion with Doppler energy broadening. On these bases, Monte Carlo method and discrete ordinate method method are used. A numerical simulation program for the fusion rate of D-T particles in laser plasma is developed in this paper. It is found that there are significant differences between the DT, DD, TD cross sections and the original cross sections after Doppler broadening. In a range of plasma temperature between 20 keV and 100 keV, the simulation results are more consistent with the cross section data of ENDF/B-VI and ENDF/B-VII databases of deuterium-tritium fusion reaction than those from the analytical formula method. There is a large error between the numerical simulation results and the analytical formula method in the low energy region. It may be caused by the difference of calculation methods and too big difference among the used fusion cross sections at low temperature.

The impact of electron-capture supernovae on merging double neutron stars

Natal kicks are one of the most debated issues about double neutron star (DNS) formation. Several observational and theoretical results suggest that some DNSs have formed with low natal kicks ($\lesssim{}50$ km s$^{-1}$), which might be attributed to electron-capture supernovae (ECSNe). We investigate the impact of ECSNe on the formation of DNSs by means of population synthesis simulations. In particular, we assume a Maxwellian velocity distribution for the natal kick induced by ECSNe with one dimensional root-mean-square $\sigma_{\rm ECSN} = 0,7,15,26,265$ km s$^{-1}$. The total number of DNSs scales inversely with $\sigma_{\rm ECSN}$ and the number of DNS mergers is higher for relatively low kicks. This effect is particularly strong if we assume low efficiency of common-envelope ejection (described by the parameter $\alpha=1$), while it is only mild for high efficiency of common-envelope ejection ($\alpha{}=5$). In most simulations, more than 50 per cent of the progenitors of merging DNSs undergo at least one ECSN and the ECSN is almost always the first SN occurring in the binary system. Finally, we have considered the extreme case in which all neutron stars receive a low natal kick ($\lesssim{}50$~km~s$^{-1}$). In this case, the number of DNSs increases by a factor of ten and the percentage of merging DNSs which went through an ECSN is significantly suppressed ($<40$ per cent).

Nonlinear dust-acoustic wave propagation in a Lorentzian dusty plasma in presence of negative ions

In this paper we have studied the effect of the density and temperature of negative ions on the nonlinear dust-acoustic wave propagation in a Lorentzian dusty plasma. We have considered both adiabatic and non-adiabatic dust charge variation. The presence of both low and high populations of negative ions are considered. Separate models have been developed because the two populations give rise to opposite polarity of grain charges. In both models electrons are assumed to follow a kappa velocity distribution while the positive and negative ions satisfy a Maxwellian velocity distribution. Adiabatic dust charge variation shows the propagation of a dust-acoustic soliton in cases of both a high and low population of negative ions whose amplitude depends on the negative ion temperature and negative ion density. On the other hand, non-adiabatic dust charge variation generates a stable oscillatory dust-acoustic shock when the negative ion population is low. An unstable potential has been predicted from this analysis when the negative ion population is high and the dust charge variation is non-adiabatic.

Electromagnetic linear dispersion relation for plasma with a drift across magnetic field revisited

A current across the magnetic field is formed in various situations in plasma. The relative drift between ions and electrons due to the cross-field current becomes a source of various microscopic instabilities. A fully electromagnetic and kinetic linear dispersion relation for plasma with a drift across magnetic field is derived by assuming a uniform background plasma. The dielectric permittivity tensor for shifted Maxwellian velocity distributions is also presented. Linear dispersion relations obtained by using the new dielectric permittivity tensor were confirmed by comparison with the previous studies and with particle-in-cell simulation results.

Brownian ensemble of random-radius buoyancy vortices and Maxwell velocity distribution in a turbulent convective mixed-layer

The stochastic ensemble of convective thermals (vortices), forming the fine structure of a turbulent convective atmospheric layer, is considered. The proposed ensemble model assumes all thermals in the mixed-layer to have the same determinate buoyancies and considers them as solid spheres of variable volumes. The values of radii and vertical velocities of the thermals are assumed random. The motion of the stochastic system of convective vortices is described by the nonlinear Langevin equation with a linear drift coefficient and a random force, whose structure is known for a system of Brownian particles. The probability density of the thermal ensemble in velocity phase space is shown to satisfy an associated K-form of the Fokker-Planck equation with variable coefficients. Maxwell velocity distribution of convective thermals is constructed as a steady-state solution of a simplified Fokker-Planck equation. The obtained Maxwell velocity distribution is shown to give a good approximation of experimental distributions in a turbulent convective mixed-layer.

General self-similar solution for expansion of non-Maxwellian plasmas

In this work, self-similar expansion of one-dimensional collisionless plasma into a vacuum has been calculated for non-Maxwellian particles. It is known that, during the expansion, the initial Maxwellian electron velocity distribution function (DF) is deformed. In this paper, this deformation is illustrated by the Vlasov simulation of plasma expansion. A part of deformation is associated with the appearance of high energy (super thermal) electrons. Therefore, a more complete and realistic plasma model has to include the effect of the super thermal electrons. It is found that the resulting DF of simulation has good consistency with the generalized Lorentzian (kappa) DF. Then the self-similar calculations were carried out for cold ions while the electrons having Lorentzian DF. Finally, it was found that, by increasing the population of energetic electrons, the expansion takes place faster and the ions are accelerated to higher energies.

Electron-impact excitation of forbidden and allowed transitions in Fe ii

Extensive calculations are reported for electron collision strengths, rate coefficients, and transitions probabilities for a wide range of transitions in Fe ii. The collision strengths were calculated in the close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method in connection with adjustable configuration expansions and a semiempirical fine-tuning procedure is employed for an accurate representation of the target wave functions. The energy correction was also used in the scattering calculations by adding to Hamiltonian matrices prior to transformation to intermediate coupling. The spin-orbit interaction term was added to the final Hamiltonian matrices in scattering calculations. The close-coupling expansion contains 340 fine-structure levels of Fe ii and includes all levels of the $3{d}^{6}4s$, $3{d}^{5}4{s}^{2}$, $3{d}^{7}$, and $3{d}^{6}4p$ configurations, plus a few lowest levels of the $3{d}^{5}4s4p$ configuration. The effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities at electron temperatures in the range from ${10}^{2}$ to ${10}^{5}$ K and are reported for all possible inelastic transitions between the 340 fine-structure levels. The present results are more extensive than the previous calculations and considerably expand the existing data sets for Fe ii, allowing a more detailed treatment of the available measured spectra from different space observatories. Comparison with other calculations for collision rates and available experimental radiative rates is used to place uncertainty bounds on our collision strengths and to assess the likely uncertainties in the existing data sets.

Effect of non‐extensivity parameter q on the damping rate of dust ion acoustic waves in non‐extensive dusty plasma

Kinetic theory has been applied to study the damping characteristics of dust ion acoustic waves (DIAWs) in a dusty plasma comprising q‐non‐extensive distributed electrons and ions, while the dust particles are considered extensive following the Maxwellian velocity distribution function. It is found that the results of the three‐dimensional velocity distribution function are more accurate compared to the results of the one‐dimensional velocity distribution function. The numerical solution of the dispersion relation is carried out to study the effect of the non‐extensivity parameter q on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λD) for which the DIAWs are weakly damped. It is found that the change in the value of the electron non‐extensivity parameter qe has a minor effect on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λD) for which the DIAWs are weakly damped, while on the other hand, ion non‐extensivity parameter qi has a strong effect on these arguments. The effect of other parameters, such as the ratio of electron to ion number density and ratio of electron to ion temperature, on the damping characteristics of DIAWs is also highlighted.

Implications of Superstatistics for steady-state plasmas

Colissionless plasmas are non-extensive systems which, due to the long-range interaction between their components, are incapable of reaching thermal equilibrium, even in a steady state. These systems cannot, therefore, be described statistically by a single canonical distribution with well-defined inverse temperature β = 1/kBT and are commonly described via two alternative approaches: namely Tsallis statistics and Superstatistics. The use of Superstatistics in describing steady-state plasmas has been proposed by several authors, more recently Ourabah et al. In this work we study the consequences of this assumption of Superstatistics for steady-state plasmas. We explicitly show that only the ensembles characterized by the condition P(x|ρ) = ρ(H(x)) are consistent with a generalized definition of temperature introduced recently. We show how this formalism is employed in the case of plasma, considering interaction with external electromagnetic fields as well as between particles in the plasma. Our results clearly illustrate why low-energy particles tend to the Maxwellian distribution of velocities, while high-energy particles contribute to the long tails of the velocity distribution.

The Influence of the Motion of a Strongly Magnetized Plasma on Radiation from a Traveling-Wave Antenna

We consider the problem of radiation from a traveling-wave antenna in a warm electron plasma which moves along a strong magnetic field at a constant velocity. To describe the electromagnetic properties of the plasma, we use the diagonal tensor of dielectric permittivity, which is calculated for a magnetized plasma with the Maxwellian electron velocity distribution allowing for collisions of electrons with neutral molecules. The dispersion relation is analyzed numerically, and expressions for the field amplitudes in the wave zone are obtained. The radiation resistance of the antenna is calculated. It is shown that as the phase velocity of the traveling current wave in the antenna approaches the average velocity of the plasma motion, the radiation field decreases exponentially with distance from the source as a result of the efficient transfer of the wave energy to the plasma electrons due to collisionless interaction.

Transition and Electron Impact Excitation Collision Rates for O iii

Abstract Transition probabilities, electron excitation collision strengths, and rate coefficients for a large number of O iii lines over a broad wavelength range, from the infrared to ultraviolet, have been reported. The collision strengths have been calculated in the close-coupling approximation using the B-spline Breit–Pauli R-matrix method. The multiconfiguration Hartree–Fock method in combination with B-spline expansions is employed for an accurate representation of the target wave functions. The close-coupling expansion contains 202 O2+ fine-structure levels of the , , , and configurations. The effective collision strengths are obtained by averaging electron excitation collision strengths over a Maxwellian distribution of velocities at electron temperatures ranging from 100 to 100,000 K. The calculated effective collision strengths have been reported for the 20,302 transitions between all 202 fine-structure levels. There is an overall good agreement with the recent R-matrix calculations by Storey et al. for the transitions between all levels of the ground configuration, but significant discrepancies have been found with Palay et al. for transitions to the 1 S 0 level. Line intensity ratios between the optical lines arising from the − 1 D 2 transitions have been compared with other calculations and observations from the photoionized gaseous nebulae, and good agreement is found. The present calculations provide the most complete and accurate data sets, which should allow a more detailed treatment of the available measured spectra from different ground and space observatories.

Quasi-static surface modes of plasma layer with anisotropic electron temperature

Quasi-static surface wave propagation in a plasma layer with anisotropic electron temperature is considered. The case is analyzed where the electron temperature in the direction normal to the plasma boundary is considered to be zero, while in the direction along the boundary, electrons are described by the Maxwellian velocity distribution. It is shown that the modes of such a layer are described by equations for bulk plasma waves with renormalization of the electron density affecting the surface wave dispersion and damping.

Can Substorm Particle Acceleration Be Applied to Solar Flares?

Abstract Using test particle studies in the electromagnetic fields of three-dimensional magnetohydrodynamic (MHD) simulations of magnetic reconnection, we study the energization of charged particles in the context of the standard two-ribbon flare picture in analogy to the standard magnetospheric substorm paradigm. In particular, we investigate the effects of the collapsing field (“collapsing magnetic trap”) below a reconnection site, which has been demonstrated to be the major acceleration mechanism that causes energetic particle acceleration and injections observed in Earth’s magnetotail associated with substorms and other impulsive events. We contrast an initially force-free, high-shear field (low beta) with low and moderate shear, finite-pressure (high-beta) arcade structures, where beta represents the ratio between gas (plasma) and magnetic pressure. We demonstrate that the energization affects large numbers of particles, but the acceleration is modest in the presence of a significant shear field. Without incorporating loss mechanisms, the effect on particles at different energies is similar, akin to adiabatic heating, and thus is not a likely mechanism to generate a power-law tail onto a (heated or not heated) Maxwellian velocity distribution.

Dispersion relation for electrostatic waves in plasmas with isotropic and anisotropic Kappa distributions for electrons and ions

Velocity distribution functions which feature extended tails with power-law dependence have been consistently observed in the solar wind environment and are frequently modelled by the so-called Kappa distributions. Different forms of Kappa distributions are commonly employed in analytical studies, and despite their similarities, they can produce different effects on the dispersion properties that occur in a plasma. We consider two different and widely used forms of Kappa distributions, in both isotropic and anisotropic cases, and systematically discuss their effects on the dispersion relations of Langmuir and ion-sound waves. It is shown that in the case of Langmuir waves, one of the forms leads to the expression for the Bohm–Gross dispersion relation, valid for plasmas with Maxwellian velocity distributions, while the other form of Kappa functions leads to a dispersion relation with significant difference regarding the Maxwellian case, particularly in the case of small values of the kappa index. For ion-sound waves, the dispersion relations obtained with the different forms of Kappa distributions are different among themselves, and also different from the Maxwellian case, with difference which increases for small values of the kappa index. Some results obtained from numerical solution of the dispersion relations are presented, which illustrate the magnitude of the perceived differences. Some results obtained with relativistic particle-in-cell simulations are also presented, which allow the comparison between the dispersion relations obtained from analytical calculations and the frequency–wavelength distribution of wave fluctuations which are observed in numerical experiments.

Interfacing MHD Single Fluid and Kinetic Exospheric Solar Wind Models and Comparing Their Energetics

An exospheric kinetic solar wind model is interfaced with an observation-driven single fluid magnetohydrodynamic (MHD) model. Initially, a photospheric magnetogram serves as observational input in the fluid approach to extrapolate the heliospheric magnetic field. Then semi-empirical coronal models are used for estimating the plasma characteristics up to a heliocentric distance of 0.1AU. From there on a full MHD model which computes the three-dimensional time-dependent evolution of the solar wind macroscopic variables up to the orbit of the Earth is used. After interfacing the density and velocity at the inner MHD boundary, we compare with the results of a kinetic exospheric solar wind model based on the assumption of Maxwell and Kappa velocity distribution functions for protons and electrons respectively, as well as with \textit{in situ} observations at 1AU. This provides insight on more physically detailed processes, such as coronal heating and solar wind acceleration, that naturally arise by inclusion of suprathermal electrons in the model. We are interested in the profile of the solar wind speed and density at 1AU, in characterizing the slow and fast source regions of the wind and in comparing MHD with exospheric models in similar conditions. We calculate the energetics of both models from low to high heliocentric distances.

Numerical solutions of sheath structures around a moderate negative biased electron-emitting cylindrical probe in low-density isotropic plasma

The potential structures around a moderate negative biased electron-emitting cylindrical probe in low-density isotropic plasma are calculated in the collisionless sheath region. The formalisms, equations, and solutions for the entire electron emitting range (i.e., subcritical, critical, and supercritical) from the cylindrical emitter and collector surface are discussed. The plasma-electron and emitted-electron are assumed to have half Maxwellian velocity distributions at their respective sheath entering boundaries with cold plasma ions. Poisson's equation is solved numerically in the sheath region for the subcritical, critical, and supercritical emissions. The I-V characteristics for these three cases are presented in tabular form. The results show that we need very high emitted-electron current to solve Poisson's equation for the critical and spercritical emissions. Thus, the floating potential is far away in these scenarios. Also, the number density of emitted-and plasma-electron are comparable at the sheath edge so we cannot neglect the density of former in comparison with latter at the sheath edge.

Global kinetic hybrid simulation for radially expanding solar wind

AbstractWe present the results of a 1‐D global kinetic simulation of the solar wind in spherical coordinates without a magnetic field in the region from the Sun to the Earth's orbit. Protons are considered as particles while electrons are considered as a massless fluid, with a constant temperature, in order to study the relation between the hybrid and hydrodynamic solutions. It is shown that the strong electric field in the hybrid model accelerates the protons. Since the electric field in the model is related to electron pressure, each proton in the initial Maxwellian velocity distribution function moves under the same forces as in the classical Parker Solar wind model. The study shows that the hybrid model results in very similar velocity and number density distributions along the radial distance as in the Parker model. In the hybrid simulations, the proton temperature is decreased with distance in 1 order of magnitude. The effective polytropic index of the proton population slightly exceeds 1 at larger distances with the maximum value ∼1.15 in the region near the Sun. A highly non‐Maxwellian type of distribution function is initially formed. Further from the Sun, a narrow beam of the escaping protons is created which does not change much in later expansion. The results of our study indicates that already a nonmagnetized global hybrid model is capable of reproducing some fundamental features of the expanding solar wind shown in the Parker model and additional kinetic effects in the solar wind.

Temperature anisotropy relaxation of the one‐component plasma

The relaxation rate of a Maxwellian velocity distribution function that has an initially anisotropic temperature (T‖≠T⊥) is an important physical process in space and laboratory plasmas. It is also a canonical example of an energy transport process that can be used to test theory. Here, this rate is evaluated using molecular dynamics simulations of the one‐component plasma. Results are compared with the predictions of four kinetic theories; two treating the weakly coupled regime, namely (a) the Landau equation, and (b) the Lenard–Balescu equation, and two that attempt to extend the theory into the strongly coupled regime, namely (c) the effective potential theory and (d) the generalized Lenard–Balescu theory. The role of dynamic screening is studied, and is found to have a negligible influence on this transport rate. Oscillations and a delayed relaxation onset in the temperature profiles are observed at strong coupling, which are not described by the kinetic theories.

Collective transport of Lennard–Jones particles through one-dimensional periodic potentials**Project supported by the Natural Science Foundation of Guangdong Province, China (Grant No. 2014A030313367) and the Fundamental Research Fund for the Central Universities, China (Grant No. 11614341).

The surrounding media in which transport occurs contains various kinds of fields, such as particle potentials and external potentials. One of the important questions is how elements work and how position and momentum are redistributed in the diffusion under these conditions. For enriching Fick’s law, ordinary non-equilibrium statistical physics can be used to understand the complex process. This study attempts to discuss particle transport in the one-dimensional channel under external potential fields. Two kinds of potentials—the potential well and barrier—which do not change the potential in total, are built during the diffusion process. There are quite distinct phenomena because of the different one-dimensional periodic potentials. By the combination of a Monte Carlo method and molecular dynamics, we meticulously explore why an external potential field impacts transport by the subsection and statistical method. Besides, one piece of evidence of the Maxwell velocity distribution is confirmed under the assumption of local equilibrium. The simple model is based on the key concept that relates the flux to sectional statistics of position and momentum and could be referenced in similar transport problems.

Electron recombination with tungsten ions with open f-shells

We calculate the electron recombination rates with target ions , q = 18–25, as functions of electron energy and electron temperature (i.e. the rates integrated over the Maxwellian velocity distribution). Comparison with available experimental data for , , and is used as a test of our calculations. Our predictions for , , , , and (where the experimental data are not available) may be used for plasma modeling in thermonuclear reactors. The results for the temperature-dependent rates for each ion are fitted with the standard analytical expressions to make them easy to use. All of these ions have an open electron f-shell and an extremely dense spectrum of chaotic many-electron compound resonances, which enhance the recombination rates by 2–3 orders of magnitude in comparison with the direct electron recombination. Conventional dielectronic recombination theory is not directly applicable in this case. Instead, we developed a statistical theory based on the properties of chaotic eigenstates. This theory describes a multi-electronic recombination (extension of the dielectronic recombination) via many-excited-electron compound resonances.