High-frequency sum-rule expansion for relativistic quasi-one-dimensional quantum plasma dielectric tensor IV: Radiation effect

A high-frequency sum-rule expansion for all transverse elements of the relativistic quasi-one-dimensional quantum plasma dielectric tensor with spin particles atT=0 K in a situation where the self-consistent magnetic radiation effect is appreciable is derived. It is found that radiation energy either reduces or enhances the dispersion for finitek, depending on the direction of propagation.     

High-frequency sum-rule expansion of relativistic quasi-one-dimensional quantum plasma dielectric tensor. II: Spin effect

A high-frequency sum rule for all elements of the relativistic quasi-one-dimensional quantum plasma with spins atT=0 K are derived. It is found that the spin either enhances or reduces the frequency of oscillation, depending on the orientation of the spin to the external magnetic field.     

High-frequency sum rules for the quasi-one-dimensional quantum plasma dielectric tensor

A high-frequency sum-rule expansion is derived for all elements of the spinless quasi-one-dimensional quantum plasma response tensor atT=0 K. As in the magnetized classical plasmas, we find that ₄ ¹³ is the only coefficient of ^–4 that has no correlational term. Further, we find that the correlations either enhance or reduce the negative quantum dispersion, depending on the direction of propagation. It is also noted that the quantum effect does not exist for the ordinary and the extraordinary modes for perpendicular and parallel propagation, respectively.     

High-frequency expansion of relativistic classical plasma dielectric tensor

A high-frequency sum-rule expansion is derived for the transverse elements of the relativistic classical plasma dielectric tensor in an isotropic system. The relativistic results are different from the nonrelativistic ones by a factor of ^–1(1 – ²/3c ²) for ₂ (k) and longitudinal plasmon and transverse photon frequencies, and by ^–2(1–2 ²/3c ²) for ₂ (k).     

High-frequency sum rules for the quasi-one-dimensional quantum plasma dielectric tensor. II. Spin effect

We derive a high-frequency expansion for all elements of the quasi-one-dimensional quantum plasma dielectric tensor atT=0 K for quantum particles with spins. In addition to the known results for spinless case, we find that _S.5 ^Emphasis>/12 (k) and _S.5 ²³ (k) are the only frequency moments of the dielectric tensor with spin terms. Further, we find that there is no spin effect on quantum plasma dispersion for both ordinary and transverse modes propagating either along or across the external field.     

The fully relativistic dielectric tensor for electron cyclotron interaction in a Maxwellian plasma

Summary A thorough analytical and numerical study of the fully relativistic dielectric tensor relevant to the electron cyclotron propagation and absorption in a Maxwellian plasma is presented for arbitrary values of the wave refractive index parallel to the equilibrium magnetic field. Both the Hermitian and the anti-Hermitian part are calculated relativistically and, in particular, as for the anti-Hermitian part, the finite Larmor radius effects are accounted for to any order. Limiting forms are obtained along with a detailed numerical comparison with the nonrelativistic form.

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Riassunto Si calcola, sia analiticamente che numericamente, il tensore dielettrico completamente relativistico di rilevanza nella propagazione e nell'assorbilnento ciclotronico elettronico in un plasma maxwelliano, per valori arbitrari dell'indice di rifrazione parallelo al campo magnetico di equilibrio. Si tien conto degli effetti relativistici sia nella parte Hermitiana che nella parte anti-Hermitiana, in questa ultima pure gli effetti di raggio di Larmor finito sono inclusi a tutti gli ordini. Si ottengono e si discutono limiti significativi e si presenta un dettagliato confronto numerico con la forma non relativistica del tensore dielettrico.

     

On the basic transcendental functions appearing in the dielectric tensor of a weakly relativistic Maxwellian plasma

Summary It is shown how to deduce in a straightforward way the class of transcendental functions which appear in the elements of the dielectric tensor of a weakly relativistic thermal plasma. The deduction is made directly from the second form of Trubnikov integrals and is valid for arbitrarily large values of the wave perpendicular refractive index.

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Riassunto Si mostra come sia possibile dedurre in modo molto diretto la famiglia di trascendenti che appare negli elementi della matrice dielettrica di un plasma debolmente relativistico in condizioni di equilibrio termico. Il procedimento parte direttamente dalla così detta seconda forma degli integrali di Trubnikov ed è valido per valori arbitrariamente grandi dell’indice di rifrazione perpendicolare al campo magnetico nel quale è immerso il plasma.

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Резюме Мы показываем, как вывести непосредственным образом класс трансцендентных функций, которые появляются в элементах диэлектрического тензора для слабо релятивистской плазмы в условиях теплового равновесия. Вывод проводится непосредственно из второй формы интегралов Трубникова и справедлив для произвольно больших величин показателя преломления для волны, перпендикулярной магнитному полю, в которое помещена плазма.

     

Fluctuations in the relativistic quantum plasma

The fluctuations of various parameters of the relativistic quantum plasma are studied with the use of the covariant Wigner function techniques. The fluctuations of the covariant Wigner function of the ideal Fermi gas at thermal equilibrium are calculated. The result is a function of the one particle Wigner function and the anticommutator of the Dirac fields only. As a consequence second order correlation functions of the four-current and the momentum-energy tensor are obtained and analyzed. On the basis of the fluctuation-dissipation theorem, the polarization tensors at first order in e² of the magnetized and the non-magnetized electron gas are derived from the four-current fluctuations of the ideal plasma. Expressions are given for the magnetized vacuum polarization in two representations, integral and discrete sums over Landau levels, for arbitrary values of the photon four-momentum. The dispersion relations of the magnetized gas are studied in the limit of low frequencies and wavenumbers. It is shown that owing to relativistic quantum effects, the characteristic frequencies of the plasma modes (plasma and Larmor frequencies) split into effective transverse and longitudinal frequencies. The existence of an acoustic mode (zero sound) for the one-component plasma is also shown.     

二维相对论运动等离子体的介电率张量

定义了相对论性运动等离子体的物理模型.利用荷流体的微扰理论，研究了该系统二维扰动现象及背景离子下的束-波互作用问题，导出了该系统的介电率张量.研究表明，相对论运动等离子体系统属复杂的色散荷流体介质并呈复杂的空间电磁不均匀性.数值模拟计算给出了相对论运动等离子体系统的介电率对波频率、电子能量以及空间坐标的响应. 关键词： 等离子体 荷流体 介质 电磁理论     

Friedel oscillations in a relativistic quantum plasma

The linear responce of a two-component plasma to a static test charge is analyzed at large distances from the impurity. The electrons are considered relativistic and degenerate and the ions classical and non-relativistic. The results show that the electrons give the principal contribution to the response, which is long ranged and characterized by the Friedel oscillatory behavior.     

Transverse modes of a relativistic quantum plasma

The dispersion relation for long-wavelength transverse plasma weves propagating in a one-component relativistic quantum plasma is derived from the relativistic Boltzmann-Vlasov equation. The result is consistent with the one obtained from quantum electrodynamics by the method of dielectric response, but at variance with hydrodynamical calculations. The discrepancy is explained by making a distinction between collective and collision dominated plasmas.     

Wave propagation in quasi-one-dimensional quantum plasma in a magnetic field

A cold electron gas fills the lowest Landau level for high enough magnetic fields and for low enough densities. Such a situation is expected to occur for the Malmberg-O'Neil experiment and also for pulsar crusts and atmospheres. Such plasmas behave as a quasi-one-dimensional system and exhibit some peculiarities in their wave structure. We study the dispersion and damping of the low frequencies, i.e., the whistler mode, and the extraordinary mode for zero temperature. The behavior of the whistler mode depends critically on the filling number _Fc=_F/ , where _F is the Fermi energy and is the cyclotron frequency. The one-dimensional character of the system affects the pair excitation spectrum and thus the decay of modes. We find that, in contrast to the three-dimensional situation, the plasma mode and the extraordinary mode remain undamped, while the whistler mode is undamped for all but very highk values.     

Surface waves on the relativistic quantum plasma half-space

We present a theoretical investigation on the propagation of surface waves on the relativistic quantum plasma half-space. The dispersion relations of surface plasmon polaritons (SPPs) and electrostatic surface waves containing relativistic quantum corrected terms are derived. Results show that the frequency of SPPs has a blue-shift, and surface Langmuir oscillations can propagate on the cold plasma half-space due to quantum effects. Numerical evaluation indicates that quantum effects to SPPs and electrostatic surface waves are significant and observable.     

Thermodynamical properties of the relativistic quantum scalar plasma

The thermodynamical properties of the relativistic quantum scalar plasma (i.e. a system of spin one-half baryons interacting through a scalar field) are studied in the Hartree approximation.     

High-frequency surface waves in quantum plasmas with electrons relativistic degenerate and exchange-correlation effects

The propagation characteristics of high-frequency surface waves are studied in spin-1/2 quantum plasmas by considering the electron relativistic degenerate and exchange-correlation effects. Using the quantum fluid equations of magnetoplasmas in the presence of the quantum Bohm potential, spin magnetization energy, relativistic degenerate pressure, and exchange-correlation effects, a generalized dispersion relation is derived. The analytical and numerical results show that the relativistic degenerate and exchange-correlation effects significantly modify the propagation properties of high-frequency surface waves. It is found that under the influence of exchange-correlation effects, the frequency spectrum of high-frequency surface waves will be down-shifted. It is also indicated that the dispersion curve shifts up with the increase of relativistic gamma factor. Furthermore, the phase speed of the high-frequency surface waves increases with increasing electron number density. The current research is helpful to understand the propagation of the high-frequency surface waves in quantum plasmas, such as those in dense astrophysical environment.     

Bifurcation and Lorentz-factor scaling of relativistic magnetized plasma expansion

We report the long-term results of 2 1/2-dimensional particle-in-cell simulations of the relativistic expansion of strongly magnetized electron-positron plasmas. When the simulation is carried to >150 light-crossing time of the initial plasma, the plasma pulse exhibits a number of remarkable properties. These include the repeated bifurcation of the pulse profile, development of a power-law momentum distribution with low-energy cutoff, and a simple scaling law for the peak Lorentz factor.     

Normal modes of a relativistic quantum plasma; The one-component plasma

The normal modes of a relativistic electron gas are studied on the basis of the Boltzmann-Vlasov kinetic equation via a projection operator formalism. A general framework is constructed in which the fully relativistic Vlasov self-consistent force term appears as a symmetric operator acting in the Hilbert space of one-particle states. The plasma-dynamical equations are obtained by projecting onto the subspace consisting of the charge, energy and momentum densities, plus the nonconserved current density. The eigenmodes of these equations include two transverse and two longitudinal plasma modes, and one damped heat mode. They are explicitly calculated up to second order in the wave vector and to first order in the collision frequency.     

Wave propagation in strongly coupled quasi-one-dimensional quantum plasma in a magnetic field

A cold electron gas fills the lowest Landau level for superstrong magnetic fields and very low densities. In such cases, in general, the potential energy of the particles is equal to or greater than their kinetic energy (strongly coupled plasmas), and a special approach is called for. The STLS (Singwi, Tosi, Land, and Sjolander) approximation scheme is used to study the dispersion and damping of the low-frequency modes, i.e., the whistler and the extraordinary modes for zero temperature. The lowest order dispersion for all modes in consideration are unaffected by correlations, but for undamped plasmas the correlation term is of the ordera ² c ^–2. Further,( ²) for the whistler mode becomes infinite at=3; its behavior critically depends on the filling number _Fc = _F/, where _F is the Fermi energy and is the electron cyclotron frequency.     

弱电离尘埃等离子体的介电张量研究

忽略磁场作用,通过求解含BGK碰撞项的Boltzmann方程和尘埃粒子充电方程导出了弱电离尘埃等离子体介电张量的表达式.证明了“冷”尘埃等离子体的纵向介电张量系数与横向介电张量系数相等.完善了弱电离尘埃等离子体电磁特性的理论模型. 关键词： 弱电离尘埃等离子体 Boltzmann方程 充电方程 介电张量     

Local products for relativistic quantum fields

A definition of local functions of generalized free fields is suggested. Their concrete form is determined in a fairly general setting by analysing realizations of locality. A huge class of new models of relativistic quantum fields results in this way.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.