The viscosity of a plasma in a strong magnetic field

The viscosity of a plasma is studied under conditions in which a magnetic field influences particle collisions. The expressions obtained for the viscosity coefficients differ significantly from those obtained in the normal theory. It is shown that in sufficiently strong magnetic fields a temperature difference arises between the electron and ion plasma components which is proportional to the drift velocity and depends logarithmically on the magnetic field strength.     

The electric field in a circular semiconductor plate placed in a magnetic field

The current distribution in an isothermic isotropically conducting plate of circular form is investigated theoretically and experimentally, in the absence and in the presence of an external magnetic field that is perpendicular to the plate. The general solution of the Riemann-Hilbert boundary value problem has been obtained under these conditions. The analysis of this solution points to experimental possibilities of determining parameters of a crystal under consideration such as the specific electric conductivity (in the absence and in the presence of an external magnetic field), the mobility of current carriers in it, and others.All the basic results of the calculations undertaken were experimentally verified and quantitatively confirmed in a series of tests carried out on homogeneous monocrystalline n-germanium (with the specific resistivity of 1.1 ohm cm) at room temperature.It is known that investigations into the galvanomagnetic phenomena (longitudinal and transverse magneto-resistance, the usual, planar and longitudinal Hall effects and others) at the present time constitute not only a means of determining the characteristics of the parameters of the crystals in question (concentration of current carriers, their mobility, etc.) [1], but serve also as a proven and simple means of obtaining important information about the zone structure of crystals [2–5].Such broadening of the circle of problems affecting the sphere of galvanomagnetic investigations already begins not to correspond to the established traditions of carrying out these investigations on test pieces of rectangular shape (as a rule, in the form of parallelepipeds). This lack of correspondence is greater due to a number of completely logical causes, certain requirements as to the geometrical dimensions of such test pieces (the ratio of length to width) [6] can far from always be satisfied. We note in this connection that in the study of galvanomagnetic phenomena in impulsive magnetic fields, for example, the use of test pieces of circular form would simplify the use of working volumes of small diameter. This, in the final analysis, is equivalent to broadening the scale of magnetic fields that can be used. The replacement of a rectangular plate by a circular disc enables us also to simplify a measurement of the parameters of semiconductor crystals which usually are obtained in circular form.Below we present theoretical and experimental investigations into the problem of measuring the galvanomagnetic effects in conducting crystals having a circular form.The authors thank V. V. Gaiduchenko for his help in carrying out the tests.     

Experimental study of the microwave radiation from a relativistic electron beam in a strong magnetic field

The results are given of an experimental study of the microwave radiation from a powerful relativistic electron beam in a longitudinal magnetic field. The design and the characteristics of the bandpass microwave filters used in the analysis of the radiation spectra are described. Radiation spectra have been obtained for different values of magnetic field. It is shown that the observed radiation is in fact cyclotron radiation from the beam. The reasons for the high radiation intensity are discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–6, May–June, 1976.In conclusion, the authors wish to express their gratitude to D. D. Ryutov and B. N. Breizman for fruitful discussion and interest in this work, and V. S. Koidan and V. V. Konyukhov for valuable advice and assistance in carrying out the experiments.     

Limiting viscosity of ferromagnetic suspensions in a strong magnetic field

The effective viscosity of a suspension of ferromagnetic particles with anisotropy of the “easy-axis” type is calculated. The case considered is that in which the magnetic field in which the suspension is flowing greatly exceeds the internal anisotropy field, and the concept of the “frozen” magnetic moments of the particles is inapplicable. The relationship between the viscosity and the anisotropy field is established. The question as to the magnitude of the viscosity for an arbitrary ratio of the internal and external fields is discussed.     

Magnetohydrodynamic flow past a porous rotating disk in a circular magnetic field

This paper studies the effects of a circular magnetic field on the flow of a conducting fluid about a porous rotating disk. Using modern quasi-Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths, suction and injection velocities and Alfven and disk speeds. Results are presented graphically in terms of three non-dimensional parameters. There is excellent agreement with previous work and asymptotic formulae.     

Motion of an incompressible conducting liquid in a strong self-consistent magnetic field

One of the common regimes of operation of many laboratory and industrial magnetohydrodynamic (MHD) devices using liquid metals as working medium is the regime for which the Alfvén number A, the ratio of the magnetic and kinetic energy densities, appreciably exceeds unity. For example, for a typical MHD device [1] with characteristic length 0.1 m of the working region, velocity 1 m/sec of the medium, and magnetic induction 1 T (the medium is molten sodium at temperature 330°C) the Alfvén number is A - 900. To simplify the investigation of the processes in such devices, one can use the approximation of a strong magnetic field proposed by Somov and Syrovatskii [2] to describe certain types of hydrodynamic flows of a dissipationless plasma in a magnetic field. In the present paper, the approach to the analysis of the self-consistent magnetohydrodynamic problem in this asymptotic approximation is extended to the case of an incompressible liquid with finite conductivity. A study is made of the closed reduced system of MHD equations obtained from the complete model in the zeroth order in the small parameter A^–1, in which the magnetic field is a force-free field. An investigation is made of the free diffusion of force-free magnetic field with constant coefficient a of proportionality between the current density and the magnetic induction in a spatially unbounded liquid, and the kinematic properties of a velocity field of the liquid in which the force-free nature of the magnetic field is maintained during the damping process are determined. It is shown that the complete class of such velocity fields is represented by the group of rigid-body motions of the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–9, January–February, 1991.     

Influence of the hall effect on plasma compressibility in a strong toroidal magnetic field

The development of the tearing instability is studied in the presence of a high toroidal magnetic field and a high plasma conductivity. The variation of the plasma density is shown to be significant in this case. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 3–9, March–April, 1998.     

Liquid metal flow in a simple manifold with a strong transverse magnetic field

This paper treats a liquid-metal flow through a simple manifold connecting one duct to two parallel ducts. The manifold consists of an infinitely long, constant-area, rectangular duct with a uniform, transverse magnetic field and with a semi-infinite middle wall at the plane of symmetry which is perpendicular to the magnetic field. The magnetic flux density is sufficiently large that inertial effects can be neglected everywhere and that viscous effects are confined to boundary layers and to an interior layer along the magnetic field lines through the end of the middle wall. The purpose of this paper is to illustrate an approach with eigenfunction expansions which will be useful for manifolds with many parallel ducts. In the present simple manifold, the principal three-dimensional effect is a transfer of flow to the inviscid core region from the high-velocity jets adjacent to the sides which are parallel to the magnetic field. There is also an important redistribution of flow along magnetic field lines inside the side-wall boundary layers.     

Flow of a conductive gas in a circular tube in a strong axiosymmetric magnetic field

The flow of a conductive gas along a channel in an external axiosymmetric magnetic field with a finite value of the magnetogasodynamic parameter N is examined. Numerical flow calculations are performed for a circular tube in such a field. Gas dynamic parameter fields, total pressure losses, and electric current intensities with the presence of transsonic zones and highly compressed regions are determined. Through comparison of the results obtained with linear theory data, the range of applicability of the latter is determined. Of the works dedicated to study of flow in external magnetic fields with N1, we should take note of [1], in which the process of entry of the gas into a transverse magnetic field was examined; [2], which studied one-dimensional transient motion with shock waves; and [3], where mixed flow in a Laval nozzle with an axiosymmetric homogeneous magnetic field was studied. Flow in a circular tube was examined in [4]; but the analysis performed by the characteristic method permitted calculation of only the initial supersonic flow zone. Motion in circular tubes in the presence of an axiosymmetric, magnetic field was studied in the linear formulation in [4, 5].Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–155, September–October, 1972.     

Boundary layer on a flat plate with strong longitudinal magnetic field

The influence of a magnetic field on the boundary layer on a flat plate in a sufficiently strongly ionized gas stream is studied. The magnetic field is parallel to the plate and to the velocity of the free stream, and it is so strong that the transport coefficients become anisotropic (the cyclotron rotation frequency of the charged particles is greater than or equal to the order of the frequency of the particle collisions). Using the results of [1–3] it is shown that the effect of the strong longitudinal magnetic field with a sufficiently high degree of gas ionization leads to a reduction in the thermal flux to the plate. For low degrees of ionization this effect is very small, since the viscosity and heat conduction in this case are determined by the neutral component of the gas.Results are presented of numerical calculations of the considered problem with account for the dependence of the transport coefficients on the thermodynamic parameters. It is assumed throughout that the magnetic Reynolds number is small (R_m1).     

Dynamic strain of a conducting half space with a cavity in a strong magnetic field

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 16–20, November–December, 1991.     

Stress concentration in the multiple-notched rim of a disk

A photoelastic study shows the effect of notch radius and spacing on the stress-concentration factor in a multiple-notched, parallel-sided disk, for thermal and rotational stress distributions.     

Flows of a conducting incompressible liquid in an arbitrary region with a strong magnetic field

A general solution is obtained describing the flow of a conducting liquid in an arbitrary region, which is bounded by nonconducting walls, in the case when it is possible to neglect inertial and viscous forces in comparison with the magnetic field, as well as the induced magnetic field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 144–150, May–June, 1973.     

Three-dimensional concentration field measurements in a mixing layer using magnetic resonance imaging

Magnetic resonance imaging (MRI) was used to measure the three-dimensional, time-averaged concentration distribution in a turbulent two-stream mixing layer. Test fluids and MRI scanning parameters were chosen to give good signal linearity, and a calibration/normalization procedure was developed to reduce the concentration measurement uncertainty. Plain deionized water mixing with a solution of 0.8% gadopentetate dimeglumine in deionized water were selected as test fluids. The concentration of the marked water was measured on an array of 220,000 0.69 mm³ voxels covering the entire flow apparatus. Planar laser-induced fluorescence experiments were performed on the flow centerplane to provide validation data. The uncertainty of a single voxel measurement was estimated to be less than 12% with the largest source of uncertainty being turbulent dephasing. Averaging two runs in which the marked water was switched between the two streams reduced the uncertainty to only 4%. The complete magnetic resonance concentration (MRC) procedure including the adjustment of scanning parameters, a background run, two reference/calibration runs, and multiple concentration measurement runs can be completed in 2–3 h. This work establishes MRC as a viable technique for studying the mixing in complex turbulent liquid flows.     

Calculating the parameters of an electron beam that drifts across a strong homogeneous magnetic field

Electron drift in specified fields has been examined in [1] and, as applied to a magnetron, in [2–4] with the averaging method. In [1,2], a first- and in [3,4] in a second-order approximation of the small parameter ) E/²L was used. Here and below, E and H=(c/) are the field strengths, L is the characteristic dimension of the field heterogeneity, is the charge-mass ratio of an electron (>0), and c is the velocity of light. An attempt to construct similar approximations for a drifting electron beam with allowance for the space-charge field, within the framework of the averaging method, involves considerable mathematical difficulties. This paper describes an attempt to solve the latter problem for a stationary monoenergetic beam that drifts under the influence of a plane electric field with potential (x,y) across a strong homogeneous magnetic field H_z H=const. Solutions are constructed by the method of successive approximations, in powers of the parameter =h/L, where h is the Larmor electron radius for narrow beams with a width on the order of 2h.I thank A. N. Ievlevu for assistance in the computational and graphical work, V. Ya. Kislov for a discussion of the results, and L. A. Vainshtein for suggesting the problem examined in §3 and for critical comments.     

Determination of a magnetic field with rotational symmetry about a given line of magnetic force

In certain technical applications when a magnetic field with rotational symmetry has to be calculated, it is often a principal requirement that a given line should be a magnetic line of force (or more accurately, that a given surface of rotation should coincide with a surface of magnetic force).An exact particular solution of the problem is found in the case when the given line of force is straight. This solution is subsequently generalized to the case of an arbitrary smooth line, approximating it by a broken line. A method is also proposed for producing and calculating a magnetic field satisfying the above conditions.The solution of this problem may be used in questions of magneto-hydrodynamics and plasmadynamics as the first approximation for the magnetic field in the case of small magnetic Reynolds numbers, when it is required that a certain line of fluid flow should coincide with a magnetic line of force.The authors would like to mention that it was due to the constant interest of E. S. Kuznetsov and his valuable advice that the present paper was completed.