Lorentz Plasma Research Articles

Streaming instability in neutron star magnetospheres: No indication of soliton-like waves

Context. Coherent radiation of pulsars, magnetars, and fast radio bursts could, in theory, be interpreted as radiation from solitons and soliton-like waves. Solitons are meant to contain a large number of electric charges confined on long timescales and can radiate strongly via coherent curvature emission. However, solitons are also known to undergo a wave collapse, which casts doubts on the correctness of the soliton radio emission models of neutron stars. Aims. We investigated the evolution of the caviton type of solitons self-consistently formed by the relativistic streaming instability and compared their apparent stability in 1D calculations with more generic 2D cases, in which the solitons are seen to collapse. Three representative cases of beam Lorentz factors and plasma temperatures were studied to obtain soliton dispersion properties. Methods. We utilized 1D electrostatic and 2D electromagnetic relativistic particle-in-cell simulations at kinetic microscales. Results. We find that no solitons are generated by the streaming instability in the 2D simulations. Only superluminal L-mode (relativistic Langmuir) waves are produced during the saturation of the instability, but these waves have smaller amplitudes than the waves in the 1D simulations. The amplitudes tend to decrease after the instability has saturated, and only waves close to the light line, ω = ck, remain. Solitons in the 1D approach are stable for γb ≳ 60, but they disappear for low beam Lorentz factors, γb < 6. Conclusions. Our examples show that the superluminal soliton branch that is formed in 1D simulations will not be generated by the relativistic streaming instability when more dimensional degrees of freedom are present. The soliton model cannot, therefore, be used to explain the coherent radiation of pulsars, magnetars, and fast radio bursts – unless one can show that there are alternative plasma mechanisms for the soliton generation.

High power terahertz radiation generated by beam-plasma system in multi-filament regime

In the particle-in-cell simulation study of this paper, it is found that the high-power terahertz radiation at twice the plasma frequency can be generated by the interaction between a weakly relativistic, large-radius, focused electron beam and an overdense plasma. The terahertz radiation is emitted from a multi-filament structure in the electron beam, which is caused by the coupling of the longitudinal two-stream instability and the transverse filamentation instability. The analysis of the k space of the plasma waves indicates that the radiation can be explained by the mode coupling among a forward oblique mode, a backward oblique mode, and a second harmonic radiation mode. The influences of the beam Lorentz factor and plasma density on the radiation power, efficiency, and coherence are also investigated. The present results not only contribute to the development of novel megawatt-level narrowband terahertz radiation sources, but also propose a potential terahertz radiation mechanism for the fundamental research of the beam-plasma system.

Electronic transport coefficients from density functional theory across the plasma plane

We investigate the thermopower and Lorenz number of hydrogen with Kohn-Sham density functional theory (DFT) across the plasma plane toward the near-classical limit, i.e., weakly degenerate and weakly coupled states. Our results are in concordance with certain limiting values for the Lorentz plasma, a model system which only considers electron-ion scattering. Thereby, we clearly show that the widely used method of calculating transport properties via the Kubo-Greenwood (KG) formalism does not capture electron-electron scattering processes. Our discussion also addresses the inadequateness of assuming a Drude-like frequency behavior for the conductivity of nondegenerate plasmas by revisiting the relaxation time approximation within kinetic theory.

Study of Einstein-bumblebee gravity with Kerr-Sen-like solution in the presence of a dispersive medium

A Kerr-Sen-like black hole solution appears in the Einstein-bumblebee theory of gravity. The solution contains contains a Lorentz violating parameter in an explicit manner. We study the null geodesics in the background of this Kerr-Sen-like black hole surrounded by a dispersive medium like plasma. We investigate the effect of the charge of the black hole, the Lorentz violation parameter, and the plasma parameter on the photon orbits with the evaluation of the effective potential in the presence of both the Lorentz violation parameter and the plasma parameter. We also study the influence of the Lorentz violation parameter and plasma parameter on the emission of energy from the black hole due to thermal radiation. Besides, we compute the angle of deflection of massless particles with weak-field approximation in this generalized situation and examine how it varies with the Lorentz violation parameter in presence of plasma. Constraining the parameters of this Lorentz violating Kerr-Sen-like black hole is also attempted here with the result obtained from the observations of the Event Horizon Telescope (EHT) collaboration.

PETN spark-gap detonators

ABSTRACT The well-developed theory of Lorentz plasma that is dominated by electron–ion interactions is used to calculate the PETN arc characteristics. The spark-gap discharge current is a ramp with 10 to 25 ns rise time to peak and remaining constant subsequently. The approximate formulas for the arc channel conductivity, arc temperature, arc radius, and shock pressure from the arc are obtained from a system of nonlinear ordinary differential equations, which is the similarity solution of hydrodynamic equations similar to the Braginskii approximation. These arc parameters are given for the peak current ranging from 100 A to 1000 A and with different rise times. Representative cases are compared to the nonlinear ordinary differential equation code results. The shock pressures at the peak current are comparable to those from a typical commercial EBW bridgewire burst reported in the literature; the arc radius at the peak current is comparable to a typical bridgewire diameter of 0.0375 mm (e.g., RISI detonators, RP-1, and RP-80). The relevant Pop-Plot for low-density PETN is converted into an empirical detonation criterion, which is applicable to explosives subject to shocks of variable pressure. This criterion is then used to determine the detonation thresholds, which are comparable with test data obtained by Tucker, et al.

Characteristics of Welding and Arc Pressure in the Plasma–TIG Coupled Arc Welding Process

In this article, a novel hybrid welding process called plasma-TIG (Tungsten Inert Gas welding) coupled arc welding was proposed to improve the efficiency and quality of welding by utilizing the full advantage of plasma and TIG welding processes. The two arcs of plasma and TIG were pulled into each other into one coupled arc under the effect of Lorentz force and plasma flow force during welding experiments. The arc behavior of coupled arc was studied by means of its arc profile, arc pressure and arc force conditions. The coupled arc pressure distribution measurements were performed. The effects of welding conditions on coupled arc pressure were evaluated and the maximum coupled arc pressure was improved compared with single-plasma arc and single-TIG arc. It was found that the maximum arc pressure was mainly determined by plasma arc current and plasma gas flow. Compared with traditional hybrid welding method, the efficiency was obviously higher and the welding heat-input was lower. The epitaxial solidification of the weld was inhibited, the tensile strength of the welded joints was higher. According to the results, the proposed coupled arc welding process has both advantages of plasma arc and TIG method, and it has a broad application prospect.

Analytic non-Maxwellian electron velocity distribution function in a Hall discharge plasma

The electron velocity distribution function in the low-pressure discharges with the crossed electric and magnetic fields, which occur in magnetrons, plasma accelerators, and Hall thrusters with a closed electron drift, is not Maxwellian. A deviation from equilibrium is caused by a large electron mean free path relative to the Larmor radius and the size of the discharge channel. In this study, we derived in the relaxation approximation the analytical expression of the electron velocity distribution function in a weakly ionized Lorentz plasma with the crossed electric and magnetic fields in the presence of the electron density and temperature gradients in the direction of the electric field. The solution was obtained in the stationary approximation far from boundary surfaces, when diffusion and mobility are determined by the classical effective collision frequency of electrons with ions and atoms. The moments of the distribution function including the average velocity, the stress tensor, and the heat flux were calculated and compared with the classical hydrodynamic expressions. It was shown that a kinetic correction to the drift velocity stems from a contribution of the off-diagonal component of the stress tensor. This correction becomes essential if the drift velocity in the crossed electric and magnetic fields would be comparable to the thermal velocity of electrons. The electron temperature has three different components at a nonzero effective collision frequency and two different components in the limit when the collision frequency tends to zero. It is shown that, in the presence of ionization collisions, the components of the heat flux have additives that are not related to the temperature gradient, and arise because of the electron drift.

Electronic transport of Lorentz plasma with collision and magnetic field effects**Project supported by the National Natural Science Foundation of China (Grant Nos. 11475026 and 11305010) and the NSAF of China (Grant No. U1530153).

The electronic transverse transport of Lorentz plasma with collision and magnetic field effects is studied by solving the Boltzmann equation for different electron density distributions. For the Maxwellian distribution, it is shown that transport coefficients decrease as Ω increases, Ω is the ratio of an electron’s magneto-cyclotron frequency to plasma collision frequency. It means that the electrons are possible to be highly collimated by a strong magnetic field. For the quasi-monoenergetic distribution with different widths, it is found that the transport coefficients decrease greatly as ɛ̄ decreases. In particular when the width approaches to zero the transverse transport coefficients are hardly affected by the magnetic field and the minimal one is obtained. Results imply that the strong magnetic field and quasi-monoenergetic distribution are both beneficial to reduce the electronic transverse transport. This study is also helpful to understand the relevant problems of plasma transport in the background of the inertial confinement fusion.

Numerical Investigation on the Impact of DBD Plasma Actuators on Temperature Enhancement in the Channel Flow

The present study indicates the impact of different arrangements of dielectric barrier discharge (DBD) plasma actuators on temperature field in a channel flow. The modified lumped circuit element electro‐static model was used to calculate induced Lorentz body force and plasma dissipation of the actuators. Different distributions of temperature in the modeled channel flow for each arrangement of actuators (one, two, and three attached actuators) are discussed. According to the numerical simulation, DBD plasma actuators are beneficial devices for increasing temperature in the channel flow, especially near the location of the actuators that can be considered for related applications. The actuators are modeled under an incompressible flow regime with low Reynolds number of 335, and the configurations of the actuators are set to be 3 KV for the peak voltage amplitude, 10,000 Hz for the voltage frequency, and Kapton as the dielectric.

Ion Contribution to Hydrogen Plasma Conductivity Beyond Born Approximation

AbstractA Lorentz plasma is considered. Within generalized linear response theory, the electrical conductivity is calculated for arbitrary degeneracy including higher orders of interactions (strong collisions, T matrix). The important quantity for the calculation of transport properties is the transport cross section. Assuming statically screened interaction, a fit formula for the electron – ion transport cross section is proposed which is valid for densities up to warm dense matter (WDM). This formula coincides with analytically known limits and reduces the high numerical effort of T matrix calculations at low densities and high temperatures. The plasma parameter regions are given where a Born approximation should be improved considering a T matrix approach. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Transport coefficients in Lorentz plasmas with the power-law kappa-distribution

Transport coefficients in Lorentz plasma with the power-law κ-distribution are studied by means of using the transport equation and macroscopic laws of Lorentz plasma without magnetic field. Expressions of electric conductivity, thermoelectric coefficient, and thermal conductivity for the power-law κ-distribution are accurately derived. It is shown that these transport coefficients are significantly modified by the κ-parameter, and in the limit of the parameter κ →∞ they are reduced to the standard forms for a Maxwellian distribution.

On the molecular forces acting between macroscopic bodies

The eigenfrequencies are identified for two electromagnetically coupled semi-infinite solids with plane-parallel surfaces (two half-spaces) separated by a third, polarizable body. The corresponding van der Waals–London and Casimir forces are calculated from the zero-point energy (vacuum fluctuations) of the normal modes. It is shown how the results can be extended to bodies of any shape; in particular, the force is given for a sphere interacting with a half-space. The calculations are performed using the well-known Drude–Lorentz (plasma) model of (non-magnetic) polarizable matter. The polarization degrees of freedom are explicitly introduced. It is shown that the polarization dynamical variables for the two bodies are coupled through the electromagnetic field, very similar with two infinite sets of coupled harmonic oscillators.

A finite element/Fourier treatment of the Fokker–Planck equation

A method is proposed for a finite element/Fourier solution of the Fokker–Planck (FP) equation describing Coulomb collisions between particles in a fully ionized, spatially homogeneous plasma. A linearized FP equation is obtained by assuming collisions between test particles and a static background are more important than between the test particles themselves. A full 3D velocity space dependence is maintained using cylindrical coordinates (v‖,v⊥,γ). When a magnetic field exists, v‖ is aligned with it and γ corresponds to gyroangle. Distribution functions are approximated by a Fourier representation in the azimuthal angle, γ, and by a 2D finite element representation in the parallel and perpendicular directions. The FP equation can be solved in a fully implicit manner allowing large, stable timesteps and simulations that arrive quickly at equilibrium solutions. The results of several test problems are discussed including a calculation of the resistivity of a Lorentz plasma, the heating and cooling of a test particle distribution, the slowing down of a beam of test particles and the acquisition of a perpendicular flow for a non-flowing Maxwellian test distribution. Robust convergence upon refinement of the finite element/Fourier representation is highlighted.

Non-inertial electromagnetic effects in matter. Gyromagnetic effect

Non-inertial electromagnetic effects in matter, i.e. electromagnetic fields created by a non-inertial motion of material bodies, are discussed within the Drude–Lorentz (plasma) model of matter polarization. It is shown that an oscillatory motion of a point-like body, or wavelike motion in an extended body gives rise to electromagnetic fields with the same frequency as the frequency of the original motion, while shock-like movements of a point-like body generate electromagnetic fields with the characteristic (atomic scale) frequency of the bodies. The polarization of a rigid body induced by rotations is discussed in various circumstances. A uniform rotation produces a static electric field in a dielectric and a stationary current (and a static magnetic field) in a conductor. The latter corresponds to the gyromagnetic effect (while the former may be called the gyroelectric effect). Both fields are computed for a sphere and the gyromagnetic coefficient is derived. A non-uniform rotation induces emission of electromagnetic fields. The equations of motion for the polarization are linearized for slight non-uniformities of the angular velocity and solved both for a dielectric and a conducting sphere. The electromagnetic field emitted by a dielectric spherically shaped body in (a slightly) non-uniform rotation has the characteristic (atomic scale) frequency of the body (slightly shifted by the uniform part of the angular frequency). In the same conditions, a conducting sphere emits an electromagnetic field whose frequency is double the uniform part of the angular frequency.

Dielectric function beyond the random-phase approximation: Kinetic theory versus linear response theory

Calculating the frequency-dependent dielectric function for strongly coupled plasmas, the relations within kinetic theory and linear response theory are derived and discussed in comparison. In this context, we give a proof that the Kohler variational principle can be extended to arbitrary frequencies. It is shown to be a special case of the Zubarev method for the construction of a nonequilibrium statistical operator from the principle of the extremum of entropy production. Within kinetic theory, the commonly used energy-dependent relaxation time approach is strictly valid only for the Lorentz plasma in the static case. It is compared with the result from linear response theory that includes electron-electron interactions and applies for arbitrary frequencies, including bremsstrahlung emission. It is shown how a general approach to linear response encompasses the different approximations and opens options for systematic improvements.

A gyrokinetic collision operator for magnetized Lorentz plasmas

A gyrocenter collision operator for magnetized Lorentz plasmas is derived using the Fokker–Plank method. The gyrocenter collision operator consists of drift and diffusion terms in the gyrocenter coordinates, including the diffusion of the gyrocenter, which does not exist for the collision operator in the particle phase space coordinates. The gyrocenter collision operator also depends on the transverse electric field explicitly, which is crucial for the correct treatment of collisional effects and transport in the gyrocenter coordinates. The gyrocenter collision operator derived is applied to calculate the particle and heat transport fluxes in a magnetized Lorentz plasma with an electric field. The particle and heat transport fluxes calculated from our gyrocenter collision operator agree exactly with the classical Braginskii’s result [S. I. Braginskii, Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1, p. 205: P. Helander and D. J. Sigmar, Collisional Transport in Magnetized Plasmas (Cambridge University, Cambridge, 2002), p. 65], which validates the correctness of our collision operator. To calculate the transport fluxes correctly, it is necessary to apply the pullback transformation associated with gyrocenter coordinate transformation in the presence of collisions, which also serves as a practical algorithm for evaluating collisional particle and heat transport fluxes in the gyrocenter coordinates.

Optical response of single‐wall carbon nanotube sheets in the far‐infrared spectral range from 1 THz to 40 THz

AbstractThe optical properties of single‐wall carbon nanotube sheets in the far‐infrared have been investigated with THz time‐domain spectroscopy. Over a wide frequency range from 1 THz to 40 THz, the complex dielectric function of the nanotube sample has been derived. Our data can be excellently reproduced by a Drude–Lorentz model function. The extracted fit parameters such as Lorentz resonance frequency and plasma frequency are consistent with values obtained by scanning tunneling techniques. We discuss the origin of both the Lorentz and Drude contribution in terms of direct and indirect optical transitions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analytic electrical-conductivity tensor of a nondegenerate Lorentz plasma.

We have developed explicit quantum-mechanical expressions for the conductivity and resistivity tensors of a Lorentz plasma in a magnetic field. The expressions are based on a solution to the Boltzmann equation that is exact when the electric field is weak, the electron-Fermi-degeneracy parameter Theta>>1, and the electron-ion Coulomb-coupling parameter Gamma/Z<<1. (Gamma is the ion-ion coupling parameter and Z is the ion charge state.) Assuming a screened 1/r electron-ion scattering potential, we calculate the Coulomb logarithm in the second Born approximation. The ratio of the term obtained in the second approximation to that obtained in the first is used to define the parameter regime over which the calculation is valid. We find that the accuracy of the approximation is determined by Gamma/Z and not simply the temperature, and that a quantum-mechanical description can be required at temperatures orders of magnitude less than assumed by Spitzer [Physics of Fully Ionized Gases (Wiley, New York, 1962)]. When the magnetic field B=0, the conductivity is identical to the Spitzer result except the Coulomb logarithm ln Lambda(1)=(ln chi(1)-1 / 2)+[(2Ze(2)/lambdam(e)v(2)(e1))(ln chi(1)-ln 2(4/3))], where chi(1) identical with 2m(e)v(e1)lambda/ variant Planck's over 2pi, m(e) is the electron mass, v(e1) identical with (7k(B)T/m(e))(1/2), k(B) is the Boltzmann constant, T is the temperature, lambda is the screening length, variant Planck's over 2pi is Planck's constant divided by 2pi, and e is the absolute value of the electron charge. When the plasma Debye length lambda(D) is greater than the ion-sphere radius a, we assume lambda=lambda(D); otherwise we set lambda=a. The B=0 conductivity is consistent with measurements when Z greater, similar 1, Theta greater, similar 2, and Gamma/Z less, similar 1, and in this parameter regime appears to be more accurate than previous analytic models. The minimum value of ln Lambda(1) when Z> or =1, Theta> or =2, and Gamma/Z< or =1 is 1.9. The expression obtained for the resistivity tensor (B not equal 0) predicts that eta( perpendicular )/eta( parallel ) (where eta( perpendicular ) and eta( parallel ) are the resistivities perpendicular and parallel to the magnetic field) can be as much as 40% less than previous analytic calculations. The results are applied to an idealized 17-MA z pinch at stagnation.

Electromagnetic waves in a suddenly created Lorentz medium and plasma

The dispersion relations for the new waves excited by a suddenly created Lorentz media are derived and presented by the use of a Brillouin-like diagram. The amplitude and power transmission and reflection coefficients for these new modes are derived and discussed. It is shown that less than 4% of the pump wave power is transferred to the reflected modes.

Electron distribution function in a Lorentz plasma with a time‐varying electric field

In this paper, the effect of a harmonically varying electric field on the runaway electrons in a Lorentz plasma is studied. It will be shown that runaway electrons are inhibited even for a moderate value of the frequency of the applied electric field, compared with the collision frequency, provided that the magnitude of the field is much smaller than the Dreicer field.