Quasiclassical distribution function of electrons in a homogeneous magnetic field

Vlasov's equation is used to find the classical nonrelativistic and relativistic distribution functions that describe an electron beam of bounded radius in a homogeneous magnetic field. In the quasiclassical approximation, by means of the exact wave functions of an electron in a homogeneous magnetic field, the quantum relativistic distribution function with allowance for the electron spin is found. The mean physical quantities that characterize the radially bounded electron beam are found as functions of the temperature and electron spin.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 50–56, July, 1976.It is a pleasant duty to thank Professor V. G. Bagrov for discussing the results.     

Neutron flux from nondegenerate nonrelativistic neutron gas polarized by a magnetic field

The effect of a strong magnetic field on the average neutron velocity both in an equilibrium neutron system and in a beam of particles flowing from the system is assessed in the context of the statistical thermodynamics of equilibrium systems. The calculations are based on the Maxwell-Boltzmann distribution for a nondegenerate, nonrelativistic, magnetized neutron gas with allowance for Pauli paramagnetism. Byelorussian State University, Brest State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 44–48, April, 2000.     

Collisional effect on the Weibel instability in the limit of high plasma temperature

The Weibel instability (WI) of relativistic electron beam (REB) penetrating an infinite collisional plasma was studied in the following models: (i) REB model, where the total equilibrium distribution function f ₀($ \vec p $ \vec p ) is approximated by nonrelativistic background electron and REB distribution functions and (ii) relativistic monoenergetic beam (RMB) model, where f ₀($ \vec p $ \vec p ) is approximated by nonrelativistic background electrons and RMB distribution functions.     

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.     

Cold dense hydrogen in a strong magnetic field

The equation of state of a hydrogen plasma in a magnetic field that is quantizing for charged fermions is obtained within the framework of the statistical thermodynamics of systems in equilibrium for a model of extremely degenerate, ideal Fermi gases. Values of the mass density corresponding to nonrelativistic and relativistic electrons are considered, as well as densities exceeding the threshold for neutronization of cold, magnetized, electron-proton matter. Brest State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 57–59, October, 1997.     

射频腔光阴极注入器发射度研究

 在激光驱动的光阴极注入器产生的高亮度电子束中，空间电荷引起发射度的增长。分析了射频腔中引起发射度增长的因素以及解决这个问题的办法——在射频腔的阴极附近加一个螺旋聚焦磁场进行补偿，也给出了补偿后电子束的发射度并和数值模拟结果进行比较，实验测试表明，所得结果比较符合。     

A Distribution Function for the Particles in an Anisotropic Relativistic Plasma

The particles making up a plasma are usually not in equilibrium, and their energies are often relativistic and anisotropically distributed, especially if the plasma is in a d.c. magnetic field. Thus, the usual methods for developing particle distribution functions based on equilibrium conditions are not applicable. A development of a particular anisotropic relativistic distribution function that may describe the particles in a plasma is made.     

相对论性电子束的类Tokamak平衡

本文对具有双δ函数速度分布的相对论性电子束,考察了其环形平衡性质。通过对反环径比展开,得到了关于磁通函数及电势的一级近似解析解。还讨论了电子漂移轨道的近似描述。 关键词：     

Schematic diagram and calculation of the magnetic analyzer of electrons for investigations in relativistic atomic physics with internal targets of the Nuclotron

A specialized magnetic analyzer providing a possibility of experimental research in the field of relativistic atomic physics by means of registration of electrons from the internal target of the Nuclotron is proposed and calculated. At the selection of δ electrons, it provides a possibility of on-line (in each accelerator cycle) monitoring of the absolute intensity of the interaction of nuclei of the circulating beam with the target.     

导电栅网对相对论速调管中电子束的约束作用

介绍利用导电栅网约束相对论速调管(RKA)中强流电子束的理论分析及实验结果.用近似的空间电荷场分布分析导电栅网约束实心电子束稳定传输时的电子运动情况，讨论束流稳定传输的条件；并介绍在一台直线感应加速器上利用导电栅网约束未调制强流束(约400kV，2.5kA)长距离(约60cm)传输的实验结果，同时给出利用导电栅网约束RKA中调制电子束的实验结果.理论分析及实验研究表明，导电栅网对实心束的约束作用对电子束能量相对不敏感；导电栅网可有效地用于RKA中取代磁场系统约束强流相对论电子束.     

Kinetic equation for a relativistic electron beam propagating along an external magnetic field in dense and rare gas-plasma media

A kinetic equation that describes the transverse dynamics of an axisymmetric paraxial relativistic electron beam propagating along an external magnetic field in a gas-plasma medium is derived with allowance for the influence of the self-consistent electromagnetic field on the beam, the effects related to the nonlaminar motion and rotation of the beam electrons at the exit from the injector, and the scattering and energy loss of the beam electrons in their collisions with the neutral particles of the background gas.     

圆柱形阳极层霍尔等离子体加速器的质点网格方法模拟

对圆柱形阳极层霍尔加速器内的放电等离子体运用二维质点网格方法（particle in cell）进行数值模拟,用蒙特卡罗碰撞方法处理带电粒子与中性粒子之间的碰撞. 得到了放电通道内离子与电子的分布以及离子流的运动,并且对出口外侧的能量分布进行了统计. 结果发现圆柱形阳极层等离子体加速器的磁场对电子有明显的约束作用,电子集中于阳极附近很小的区域内. 由于电磁场的特殊分布,离子流呈现出双峰式的分布. 离子能量范围从放电电压的20%到接近放电电压,平均能量在放电电压的40%—50%之间. 关键词： 质点网格方法 蒙特卡罗碰撞 数值模拟 阳极层霍尔等离子体加速器     

The anomalous penetration of intense circularly polarized electromagnetic beam through overdense magnetized plasma

The steady state nonlinear propagation of an intense, circularly polarized electromagnetic beam in an inhomogeneous magnetized plasma has been investigated in paraxial approximation. The laser induces a large oscillatory velocity on electrons, raising their mass and lowering the plasma frequency. Further, rising due to cyclotron resonance effect. The propagation of the electromagnetic waves in magnetized plasma in both the extraordinary and ordinary mode is analyzed. The nonlinearity in dielectric function is considered in presence of external magnetic field due to saturation effects for arbitrary large intensity, which leads to focusing/defocusing of the beam. The focusing effect along with magnetic field helps in the process of anomalous penetration of the beam by enhancing the depletion of the plasma from the axial region. The penetration increases with the incident beam power up to some critical value beyond which it rises abruptly when all electrons have been driven out of the axis. The cyclotron resonance effect awfully supports the laser beam to propagate inside the overdense plasma region. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction applicable for underdense and overdense plasma.     

Ionization equilibrium of atoms in a strong magnetic field (the saha formula)

The effect of an external magnetic field on the ionization equilibrium of atoms in the nondegenerate nonrelativistic plasma is examined. When taken into account that the interaction of the magnetic moments of electrons with the magnetic field immediately changes their kinetic energy, which is incorrect, the degree of ionization of atoms will increase with increase in the magnetic field strength compared to the atomic concentration in the absence of a magnetic field at the same temperature. When taken into account that this energy changes in view of the Pauli principle and spontaneous minimization of the quantum system, the degree of ionization must decrease with increase in the external magnetic field strength, that is, a strong magnetic field suppresses ionization of atoms in the nonrelativistic plasma at a given temperature. Byelorussian State University; Brest State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 36–39, July, 1999.     

Suppression of degeneracy of Fermi gases of charged particles in a strong magnetic field

The suppression of degeneracy of ultrarelativistic electron and nonrelativistic proton gases is considered as a function of temperature and magnetic field strength. It is shown that at absolute zero the degeneracy of nonrelativistic proton and relativistic electron gases of equal concentrations is suppressed at the same values of magnetic field strength exceeding considerably the values at which these particles fill the lower Landau level completely.Education Institute, Brest. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 85–90, June, 1992.     

A Cyclic Induction Accelerator

The main feature of the examined cyclic induction accelerator is the separation of control and accelerating electromagnetic fluxes. The control magnetic field is formed by analogy with the magnetic field of a weakly focusing synchrotron, and the accelerating vortex electric field is generated by electromagnetic cores – inductors. Such a design of the cyclic induction accelerator allows the active steel volume and the power of a supply unit to be reduced significantly, and the separation of control and accelerating magnetic fluxes allows the energy lost by particles by synchrotron emission to be compensated using a relatively simple method. Recent investigations have demonstrated that in this accelerator, electrons can be accelerated to energies exceeding 300 MeV.     

The processes of formation and nonstationary dynamics of a virtual cathode in a nonrelativistic electron beam in the decelerating field (two-dimensional approximation)

We present the results of studies within the framework of a two-dimensional numerical model of nonlinear nonstationary processes in a nonrelativistic electron beam in the mode of formation of a virtual cathode in the decelerating field without focusing of the electrons by a magnetic field (low-voltage vircator). The results of numerical simulation were qualitatively confirmed by the experiment. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 843–852, October 2006.     

Stability of equilibrium orbits in isochronous ultrarelativistic cyclotron I

The paper deals with an investigation into the equilibrium orbits of charged particles in one variant of the isochronous ultrarelativistic cyclotron, i.e. accelerator with time independent, axially increasing magnetic field and strong focusing for accelerating charged particles at constant orbital time. The author finds phenomena well known from the theory of oscillations of non-linear mechanical systems (in a certain region of the parameters of a magnetic field there exist substantially two equilibrium orbits, while in another region none exist), which have no analogy in other accelerators. A variant of the ultrarelativistic cyclotron with axially scalloped equilibrium orbit is proposed.     

Generalization of the Bennett equilibrium condition for a relativistic electron beam propagating in the Ohmic plasma channel and ion focusing regime along an external magnetic field

The problem of formulating the generalization of the Bennett equilibrium condition is considered for a relativistic electron beam propagating in the Ohmic plasma channel, as well as in the ion focusing regime in the presence of an external longitudinal uniform magnetic field. We assume that the electron component of the background plasma is not completely removed from the region occupied by the beam. This equilibrium condition is derived using the mass and momentum transport equations obtained for a paraxial monoenergetic beam from the Fokker–Planck kinetic equation.