Stability of the poiseuille flow in a longitudinal magnetic field

The stability to small perturbations of a 2D flow of a conducting viscous fluid with large Reynolds numbers in a longitudinal magnetic field is investigated. A complete linearized system of magnetohydrodynamics equations is considered using the method of collocations and the differential sweep method. The dependences of the critical Reynolds numbers on the electrical conductivity are analyzed in detail. A new instability branch for large Reynolds numbers and a jumpwise variation of the critical Reynolds numbers are discovered.     

斜磁场中碰撞等离子体鞘层的玻姆判据

采用双流体模型研究了斜磁场作用下的碰撞等离子体鞘层的玻姆判据,讨论了磁场对鞘层玻姆判据的影响.结果表明:玻姆判据存在上限和下限,磁场强度、角度以及离子进入鞘层的状态都对离子马赫数的取值范围有影响.     

The sheath criterion for a collisional plasma sheath at the presence of external magnetic field

The Bohm sheath criterion is modified for collisional plasma containing Boltzmann electrons and cold fluid ions at the presence of external magnetic field. Based on fluid model, the effects of the strength and the orientation of an external magnetic field on the upper and lower limits of Bohm sheath criterion have been studied by considering the collision frequency between ions and neutrals. The results show that the sheath criterion depends on the orientation and magnitude of magnetic field and the ion flow velocity at the sheath boundary.     

Formation of compression shocks in a nonequilibrium plasma flow in a magnetic field

Plasma flow in a linearly widening, ideally sectioned, short-circuited magnetohydrodynamic (MHD) channel is studied. MHD flows are classified into two types: continuous flows and flows with a compressional MHD shock in plasmas that are stable and unstable against the onset of ionization instability. Specific features in the evolution of a stationary compression MHD shock are investigated, and its position as a function of the Stewart number is determined. It is found that, in a plasma flow in which ionization instability develops, a compression MHD shock arises at lower values of the MHD interaction parameter than in a stable plasma flow. An unidentified type of instability of MHD discontinuities is revealed.     

Transfer of electromagnetic radiation at a finite angle to the external magnetic field in a collisional plasma with large-scale irregularities

Using Monte Carlo simulations or numerical solution of radiation transfer equation in a random collisional plasma, we analyze the angular spectrum of a normal electromagnetic wave propagating at a finite angle to the external magnetic field. It was found that the anisotropy of absorption in the case of oblique wave propagation with respect to the external magnetic field leads to some specific effects which we call the anomalous growth in fluctuations. N. I. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol.43, No.1, pp. 28–37, January 2000.     

Stability of the flow of weakly electro-conductive fluid in the presence of a spiral magnetic field

The stability to small disturbances of the flow in a pipe of annular cross section is considered in the presence of a spiral magnetic field. The investigated duct configuration consists of two infinite coaxial cylinders between which a weakly electroconductive viscous incompressible fluid is placed, which moves under the axial pressure gradient. The azimuthal magnetic field is created by a current flowing through the central cylinder, and the longitudinal magnetic field is created by an external solenoid. The magnetohydrodynamic approximation is used. It is found that the introduction of the azimuthal magnetic field may lead to a flow destabilization as compared to the case of only the longitudinal magnetic field.     

Stability of rotating plasma with twisted magnetic field. II

The stability of a uniformly rotating cylindrical plasma configuration in dynamical equilibrium is discussed. Assuming an axial current and sheet currents for the plasma, we have obtained a dispersion relation for non-axisymmetric perturbations. The dispersion relation comes out to be a complex and implicit function of the frequency of perturbations. Here we have discussed the dispersion equation for the modem=1, with the help of numerical computations. It has been shown that rotation has a stabilizing influence, whereas the axial current destabilizes the cylinder.     

Influence of the magnetic field on the angular power spectrum of an electromagnetic wave multiply scattered in a turbulent collisional magnetized plasma

We consider a small-amplitude plane electromagnetic wave incident on a semi-infinite layer of a collisional turbulent magnetized plasma. The system of differential equations for the statistical moments of the angular power spectrum of the normal wave is derived in the narrow-angle approximation of radiation transfer theory. The dependence of the center of mass, variance, and asymmetry of the normal-wave spectrum on the distance from the plasma boundary is studied numerically. The results for different refraction angles of the illuminating wave and magnitudes and directions of the external magnetic field are presented. The nonmonotonic dependences of the variance and the third central moment on the distance from the plasma boundary are revealed. These dependences are shown to become more nonmonotonic if the absorption of the scattered waves becomes more isotropic, in particular, if the strength of the external magnetic field increases. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 12, pp. 1165–1171. December 1999.     

外加磁场微波等离子推力器内流场数值模拟

为了提高微波等离子推力器性能，改善等离子体对电磁波能量的吸收状况，提高核心区温度，提出外加磁场的方案，并对热等离子体进行了数值模拟.假设局域热平衡条件，采用Navier-Stokes，Maxwell和Saha方程，利用压力修正的半隐格式和时域有限差分求解方法，建立了径向磁镜场下推力器内等离子体流场的数值计算模型.数值模拟结果表明：外加磁场后的磁感应强度小于0.5 T时，推力器内热等离子体核心区最高温度随磁感应强度的增加而迅速提高.外加磁场后的磁感应强度大于0.5 T时，核心区最高温度随磁感应强度的增加而缓慢提高.磁感应强度为0.5 T时，热等离子体核心区最高温度与不加磁场相比提高了24%.外加磁场对等离子体流场速度分布影响不大. 关键词： 等离子体模拟 等离子体相互作用 等离子体流动     

Stability of quantum spins in a magnetic field

Continuous representations of the dynamical group, and the corresponding generalized coherent states, are used to conjugate dynamics of a system of quantum spins to that of a classical Hamiltonian system. Stability of the Hamiltonian system obtained are studied, using linear stability analyses and results from the perturbation theory. Quantum evolution of any of the compound‐spins components is described exactly by classical Hamilton's equations. No semiclassical asymptotics in the analyses or explicit time‐dependence has been involved.     

Ultracold plasma expansion in a magnetic field

We measure the expansion of an ultracold plasma across the field lines of a uniform magnetic field. We image the ion distribution by extracting the ions with a high-voltage pulse onto a position-sensitive detector. Early in the lifetime of the plasma (<20 micros), the size of the image is dominated by the time-of-flight Coulomb explosion of the dense ion cloud. For later times, we measure the 2D Gaussian width of the ion image, obtaining the transverse expansion velocity as a function of the magnetic field (up to 70 G). We observe that the expansion velocity scales as B(-1/2), explained by a nonlinear ambipolar diffusion model with anisotropic diffusion in two different directions.     

Stability of bipolarons in the presence of a magnetic field

The stability of large Fröhlich bipolarons in the presence of a static magnetic field is investigated with the path integral formalism. We find that the application of a magnetic field (characterized by the cyclotron frequence ω _c) favors bipolaron formation: (i) the critical electronphonon coupling parameter α _c (above which the bipolaron is stable) decreases with increasing ω _c and (ii) the critical Coulomb repulsion strength U _c (below which the bipolaron is stable) increases with increasing ω _c. The binding energy and the corresponding variational parameters are calculated as a function of α, U and ω _c. Analytical results are obtained in various limiting cases. In the limit of strong electron-phonon coupling (α ? 1) we obtain for ω _c ? 1 that E _estim ? E _estim(ω _c = 0) + c(u)ω _c/α ⁴ with c(u) an explicitly calculated constant, dependent on the ratio u = U/α where U is the strength of the Coulomb repulsion. This relation applies both in 2D and in 3D, but with a different expression for c(u). For ω _c ? α ²? 1 we find in 3D E _estim ? ω _c - α ² A(u) ln²(ω _c/α ²), (also with an explicit analytical expression for A(u)) whereas in 2D E _estim ^2D ? ω _c - α√ω _cπ(u-2-√2)/2. The validity region of the Feynman-Jensen inequality for the present problem, bipolarons in a magnetic field, remains to be examined.