Uniform Magnetic Field Parallel Research Articles

Reflection of a Weak Shock Wave in a Perfectly Conducting Gas

Regular reflection of a weak plane shock wave propagating in a homogeneous, perfectly conducting gas from a solid wall, in the presence of a uniform magnetic field parallel to the wall, is discussed. A mathematical derivation is presented. It is found that the presence of the magnetic field tends to enlarge the range of the shock angle in which regular reflection can occur. (L.N.N.)

On Cylindrical Magnetohydrodynamic Shock Waves

If an axial rod is surrounded by an ionized gas, an expanding cylindrical shock wave can be produced by passing through the gas a current which returns along the rod. The azimuthal magnetic field of the current acts like a piston, pushing the plasma away from the rod and leaving behind a cylindrical vacuum region. The case considered is that where a uniform magnetic field parallel to the axis is initially present in the gas; in this case a transverse magnetohydrodynamic shock wave results from the current discharge. The flow is analyzed under the assumptions that the plasma is a nonviscous, nonheat-conducting, ideal gas of infinite electrical conductivity, and that the discharge current increases linearly with time. The analysis is made first on the basis of the ``snowplow'' theory of Rosenbluth, and then from a similarity solution of the full magnetohydrodynamic equations. The results of the two solutions are compared for the case γ = 7/5. It is found that the speed predicted by the snowplow theory is in very good agreement with the speed of the contact front obtained from the solution of the full equations over the entire range of shock strength, but that the snowplow speed is a good approximation to the shock speed only in the limit of strong shocks. The effect on the flow of varying the axial field is discussed.

Effect of a Magnetic Field upon the Stability of Free Boundary Layers between Two Uniform Streams

The stability of free boundary-layer flows of a viscous, incompressible, electrically conducting fluid is investigated. It is found generally that a uniform magnetic field parallel to the steady flows has an effect of stabilizing the flows. When the magnetic field is weak, i.e. when the Alfven number A is less than unity, the flows are unstable with zero critical Reynolds number ( R c =0). But when the magnetic field is so strong that A >1, the flows are absolutely stable ( R c =∞) provided R m / R >1 where R m is the magnetic Reynolds number. For small values of R m / R , the flows are unstable even for A >1, so long as ( R m / R ) A 2 ≪1. It is also shown that an oblique magnetic field cannot stabilize the flow, however strong it may be.

Hydromagnetic Resonators

The behavior of hydromagnetic waves in a cylindrical resonator of arbitrary cross section is examined. The conducting fluid inside the resonator is permeated with a steady uniform magnetic field parallel to the generators of the cylinder. The equation describing the eigenfrequency spectrum is derived for all possible modes and types of waves. It is shown that a TLA (transverse longitudinal acoustic) type wave when reflected from a rigid conducting termination generates an accompanying TLM (transverse longitudinal magnetohydrodynamic) type wave and vice versa. Energy losses due to the finite viscosity and electrical conductivity of the fluid as well as to the finite conductivity of the walls are then estimated for the case of T (purely transverse) type waves. A Q factor for T type waves is subsequently calculated.

Stability of parallel flow in a parallel magnetic field at small magnetic Reynolds numbers

The hydromagnetic stability of a basic two-dimensional parallel flow of an incompressible conducting fluid in a uniform magnetic field parallel to the flow is considered. By use of the generalization of the Orr–Sommerfeld equation for an electrically conducting fluid, it is shown that any given small wave disturbance can be stabilized by a sufficiently strong magnetic field if the Reynolds number is finite and the magnetic Reynolds number small.Stability of velocity profiles with a point of inflexion at small magnetic Reynolds number and infinite Reynolds number is considered in detail. Perturbation methods are developed to find stability characteristics in two cases, when the magnetic field is weak, and when the disturbance is a long wave. These methods are applied to the jet and the half-jet, which are both found to be unstable to long-wave disturbances, however strong the magnetic field. Nonetheless, these two flows can be stabilized for any given harmonic disturbance of finite wavelength. The analysis of the jet reveals the surprising result that the magnetic field makes inviscid long-wave disturbances more unstable.

Magnetohydrodynamic Flow past a Sphere

The flow of an incompressible, viscous, electrically conducting fluid past a sphere in the presence of a uniform magnetic field parallel to the undisturbed flow is investigated using Oseen approximation. The drag coefficient is calculated up to the second order of magnitudes of parameters: the Reynolds number R , the magnetic Reynolds number R m and the Hartmann number M . Its numerical values are shown graphically for a few typical cases. It is found that the drag coefficient is continuous at the pressure number S =1, whereas it changes there abruptly in the two-dimensional case. The flow pattern changes remarkably according as the pressure number \(S{\gtreqqless}1\).

Flow over Thick Plate with Circular Hole

Formulas are derived for the scalar potential of a uniform magnetic field parallel to the plane face of an infinite nonpermeable medium in which a circular hole of radius, a, is drilled normally. Outside the hole the formula is an oblate spheroidal harmonic series for which eleven coefficients are given, and inside it is a Bessel function series for which twenty coefficients are given. The case of a flat-bottomed hole whose depth is greater than its diameter is included. All series converge slowly in the plane of the opening but rapidly elsewhere. When a plane electromagnetic wave falls on such a hole, the fraction of the energy scattered is approximately 11.7(2a/λ)4 cosθ if the wavelength λ is much greater than 2a and θ is the angle of incidence. Such a hole in the thick plane wall of a resonant cavity, at a point where H is uniform and E is zero, decreases the resonance frequency ω by 0.2366μa3H2Wm−1ω where Wm is the magnetic energy in the cavity when H is measured. A lug of radius a affixed to the plane face of a cylindrical rod of the same material, length l and cross section A changes the resistance in the ratio [1+0.3154a3/(Al)]−1.

Problems Related to Measuring the Field Strength of High-Frequency Electromagnetic Fields

Discussion and comparison of the analysis of two cases of an electron of uniform velocity acted on by a uniform magnetic field parallel to the electron direction, and a high-frequency electromagnetic field with the electric component transverse to the beam, shows that, for both a plane parallel-plate field and a rectangular cavity field, the field amplitude may be expressed quite simply in terms of easily measurable parameters. The simple relationship in question requires that certain velocity conditions on the electron velocity be observed, and that the cyclotron frequency ǀeǀ H/mc be equal to the frequency of the alternating electromagnetic field.

The cut-off characteristic of the single anode magnetron

For the purpose of the present discussion the magnetron will be defined as a diode thermionic tube, having concentric cylinders as electrodes, in which there is a uniform magnetic field parallel to the axis of the electrodes. An electron emitted from the cathode travels towards the anode in a path which is bent by the action of the magnetic field. If the anode has radius a and is at potential V with respect to the cathode of radius b, then it is well known that electrons emitted without velocity from the cathode will just graze the anode when the uniform and axial magnetic field has a value H such that

The Blackening of Photographic Emulsions by Low Speed Electrons

New type of electron spectrograph.---Electrons from an oxide coated filament are accelerated to a cylindrical anode, coaxial with the filament, having a narrow slit for one of its elements. The whole system is placed in a uniform magnetic field parallel to the filament. Those electrons which pass through the slit focus in the plane normal to that containing the filament and the slit. 22 volt electrons have been focused sharply. An extremely accurate direct determination of $\frac{e}{m}$ should be possible with this arrangement.The results indicate that the blackening of photographic emulsions by low speed electrons is due to radiation produced by electron impact on the surface of the emulsion and is a discontinuous function of the electron speed. For electrons with speeds below 100 volts, the blackening apparently depends upon the grain size and gelatine thickness of the emulsion. A thin film of fluorescent lubricating oil on the emulsion greatly increases its sensitivity. Schumann plates have an enormous sensitivity.