Infrared and pinching singularities in out of equilibrium QCD plasmas

We examine collinear, infrared and pinching singularities in the production of weakly interacting particles from out of equilibrium relativistic plasmas. We show that collinear singularities cancel out in a scalar theory, exactly as at equilibrium. The same result holds in a quark-gluon plasma, provided the matter degrees of freedom are quantized in a physical gauge. However the cancellation does not hold in a covariant gauge; we comment on a possible explanation of this result. Finally we show that pinching singularities give contributions of order g ² δn, where δn is the deviation from equilibrium of the distribution function and g the QCD coupling constant.     

Relativistic distribution function for particles with spin at local thermodynamical equilibrium

We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of the global equilibrium case, that at local thermodynamical equilibrium particles acquire a net polarization proportional to the vorticity of the inverse temperature four-vector field. The obtained formula for polarization also implies that a steady gradient of temperature entails a polarization orthogonal to particle momentum. The single-particle distribution function in momentum space extends the so-called Cooper–Frye formula to particles with spin 1/2 and allows us to predict their polarization in relativistic heavy ion collisions at the freeze-out.     

Landau damping of longitudinal oscillation in ultra- relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.     

激光等离子体二维相对论电磁粒子模拟

研制了激光等离子体二维相对论电磁粒子模拟程序(2DCIC)。追踪几万甚至百万个模拟粒子在外加激光场和自洽场中运动,自洽地计算电荷和电流密度,求解完全的Maxwel方程,电子的相对论运动方程和离子的牛顿运动方程,辅以灵活的诊断研究波-波,波-粒子相互作用的发生、发展和饱和的细节以及时间演化规律。激光可以正入射,也可以斜入射;等离子体可以是均匀密度,也可以具有密度梯度;为了节约机时,还发展了并行运算。物理模型参数可调,既适用于研究激光聚变等离子体相互作用,也适用于超短脉冲超强激光等离子体相互作用和其它等离子体问题。经过多次试算检验,对等离子体平衡态进行了计算研究,对于超短脉冲超强激光的传播也进行了初步模拟计算。     

Relativistic BBGKY Theory and Collision Integral of Generalized Boltzmann Equation in a Relativistic Magnetized Plasma

Usually, only Coulomb interactions between charged particles which are independent of time are considered in BBGKY theory of a nonrelativistic plasma. In relativistic case, the induced electromagnetic forces between charged particles which are dependent on time obviously should be considered. A Lorentz-covariant generalized n-time Liouville equation for classical plasma is established. A convenient form applicable to the laboratory frame of this equation is also given. The relativistic BBGKY hierarchy is developed in which both Coulomb and electromagnetic forces between particles are included. A method for solving the relativistic pair correlation equation is given in polarization approximation. A new formula for calculating collision integral in terms of discrete particle Green functions is given. A number of generalized Boltzmann equations for relativistic plasmas are derived.     

Non-linear relativistic diffusions

We obtain a non-linear generalization of the relativistic diffusion. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution substantially restrict the class of admissible non-linear diffusion equations. We consider relativistic invariant as well as covariant frame-dependent diffusion equations with a drift. In the latter case we show that there can exist stationary solutions of the diffusion equation besides the equilibrium solution corresponding to the quantum or Tsallis distributions. We define the relative entropy as a function of the diffusion probability and prove that it is monotonically decreasing in time when the diffusion tends to equilibrium. We discuss its relation to the thermodynamic behavior of diffusing particles.     

DTA模型计算高温Mg等离子体的辐射不透明度

使用DTA(detailedtermaccounting)模型计算了温度为 5 6eV、密度为 0 .0 1g/cm3 的Mg等离子体的辐射不透明度以及Rosseland和Planck平均不透明度 .对于处于局域热动平衡 (LTE)下的Mg等离子体 ,利用Saha方程计算出各价离子的丰度 .MCHF方法得到Mg各价离子的能级以及束缚 束缚跃迁的振子强度 ,考虑了Doppler展宽和碰撞展宽 ,谱线线型采用Voigt线型 .束缚 自由以及自由 自由吸收截面使用AA模型得到. The spectral resolved opacity of high temperature Mg plasma at a temperature of 56 eV and a density of 0.01 g/cm 3 is calculated by the detailed term accounting (DTA) model. Saha equation is applied to obtain the population distribution of the plasma in local thermodynamic equilibrium. Atom levels and bound-bound absorption oscillator strengths are obtained from a multi-configuration Hartree-Fock (MCHF) calculation that includes Breit-Pauli relativistic correction. After ...     

Kinetics of isotropic expansion of an optically transparent plasma at the compton stage

An exact solution is obtained to the nonrelativistic Focker-Planck equation for electrons at the Compton stage of expansion. The electrons have a Maxwellian distribution whose temperature differs from the radiation temperature. A qualitative analysis is made of the correction to the equilibrium relativistic distribution, and it is shown that elastic collisions of ultrarelativistic and nonrelativistic particles in isotropic expansion do not result in the non-relativistic-particle spectrum.Translated from Izvestiya Vysshikh Uchebnykh, Zavedenii Fizika, No. 10, pp. 82–85, October, 1982.     

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example.     

Distribution function of an electron beam in a focusing magnetic field

The distribution function of electrons moving in an axially symmetric focusing magnetic field is constructed. The macromotion and self-field of the beam are taken into account. The nonrelativistic and relativistic limits are discussed. Upon switching off the magnetic field the distribution functions obtained change into the Maxwell-Boltzmann distribution. The motion of charged particles in a focusing magnetic field is the simplest model for investigation of a beam of particles, for example, electrons, in storage or accelerator rings. In accordance with the well-known theorem of N. Bohr, a magnetic field has no effect on the distribution function for a one-dimensional distribution of electrons with respect to the momenta. However, the situation is altered if macromotion occurs in a static system, for example, the revolution of electrons in storage or accelerator rings. Maintaining the focusing of the beam in an equilibrium orbit, the magnetic field thereby affects the electron distribution function. For an actual electron beam the distribution function is determined by the initial conditions of formation of the beam; however, as a result of scattering processes it will approach some steady-state equilibrium distribution function. We will discuss the problem of finding such a distribution function in the nonrelativistic and relativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 35–40, July, 1978.The author thanks Professor I. M. Ternov of Moscow University for his constant interest in this research and Professor V. G. Bagrov of Tomsk University for help in the research.     

Die Verteilungen des elektrischen und magnetischen Mikrofeldes im relativistischen Plasma

The probability distributions of the electric and magnetic microfield at a fixed space point in a relativistic, non-degenerate, homogeneous, and isotropic plasma in thermodynamic equilibrium are determined using the Markov-method and neglecting the particle interaction. They are found to be Holtsmarkians like the electricnon-relativistic microfield distribution, but the characteristic field strengths are increasing functions of temperature which are calculated.     

Motions of particles in an oscillating plasma

An alternative consideration of oscillations and waves in plasma is suggested based on equations for small deflections of particles from their equilibrium trajectories instead of equations for perturbations of distribution functions and fields, so that average values are calculated with equilibrium distribution functions. Instead of the Maxwell equations for an electromagnetic field their solutions in the Lienard-Wiechert form are used. All the known results of the linear kinetic theory of plasma oscillations are shown to be derivable in this way, and small correlations for dispersion relations of the first order in the plasma parameter due to the Debye screening have been obtained. A simplified consideration of a rarefield plasma in a strong magnetic field is given showing a non-cyclotron character of the motion of the particles. Such a combination of statistical and dynamical approaches may be useful in many problems of plasma physics.     

Quark-gluon plasma diagnostics in a successive equilibrium scenario

The relativistic Fokker-Planck equation has been used to study the evolution of the quark distribution in the quark-gluon phase expected to be formed in ultra-relativistic heavy-ion collisions. The effect of thermal masses for quarks and gluons is incorporated to take account of the in-medium properties. We find that the kinetic equilibrium is achieved before the system reaches the critical temperature of quark-hadron phase transition. We find that chemical equilibrium is not achieved during this time. We have evaluated the electromagnetic probes of quark-gluon plasma from the non-equilibrated quark-gluon phase and compared them with those in completely equilibrated scenario. The hard QCD production rates for the electromagnetic ejectiles as well as the heavy quark production rates are also calculated.     

Local thermalization in d+Au collisions

The extent of a locally equilibrated parton plasma in d+Au collisions at √s _NN =200 GeV is investigated as a function of centrality in a nonequilibrium-statistical framework. Based on a three-sources model, analytical solutions of a relativistic diffusion equation are in precise agreement with recent data for charged-particle pseudorapidity distributions. The moving midrapidity source indicates the size of the local thermal equilibrium region after hadronization. In central d+Au collisions it contains 19% of the produced particles.     

Magnetic properties of a relativistic plasma

On the basis of thermodynamic functions calculated in closed form, the magnetic properties of an equilibrium relativistic plasma in fields of arbitrary magnitude are studied in both the Boltzmann and quantum cases. It is shown that, for a relativistic degenerate gas of free electrons, the de Haas-van Alphen effect will remain.     

Criterion for long-wavelength electromagnetic instability of a homogeneous relativistic plasma

Electromagnetic instability of an unmagnetized homogeneous relativistic plasma with an anisotropic velocity distribution having a center of symmetry is analyzed. A stability criterion is derived for slowly varying long-wavelength perturbations. The criterion is formulated as a set of equalities that are not valid for ellipsoidal velocity distributions, but can be satisfied for other anisotropic distributions. The relativistic case is special only in that the rest mass is replaced with the relativistic one.     

Wigner function and normal ordering

The Wigner function is calculated for a relativistic system of interacting scalar particles and anti-particles in thermal equilibrium. It is pointed out that the prerequisite for obtaining the correct result is normal ordering, as opposed to the customary process of symmetrization of the field operators, whether combined with a vacuum subtraction or not.     

Relativistic thermal equilibrium of non-neutral plasmas

Finite temperature effects on the relativistic radial equilibrium of a non-neutral plasma are analyzed. An equation for an effective potential governing the self-consistent radial density profile is derived in the case of global thermal equilibrium. The effect of a finite temperature turns out to be particularly strong for the fast mode of rigid plasma rotation, where the density profile can extend beyond the cold limiting radius.     

Au激光等离子体X射线发射光谱的理论研究

采用细致组态(detailed configuration accounting,DCA)方法和碰撞辐射模型(collisional radiative equilibriummodel),Cowan的相对论的原子结构理论程序,选取与初、末离子组态有关的平均组态,取Hartree-Fock-Slater自洽势,考虑了非局域热动力学平衡条件下等离子体的主要原子动力学过程,建立了描述等离子体中碰撞辐射模型的离子布居和能级布居的速率方程,得到了Au元素的离子分布和能级分布,电荷态分布和平均电离度,并模拟出Au激光等离子体的5f-3d跃迁的X射线发射光谱的谱线强度,计算得出的谱线强度与实验数据相比符合得较好.