Lewi Tonks

Photon Avalanches from a Population Inversion

High‐power lasers encounter increasing losses of stored energy from stimulated emission by once‐through avalanches of photons as higher powers are sought. This occurs even without resonance buildup. Even in the simple geometry of a thin rod, a satisfactory analysis would require elaborate machine calculation. A very crude model has, however, produced rough results from which some guidance is obtainable.The model exhibits the expected linear increase of outgoing photon flux near the end of the rod and the huge depletion of excited atom population away from the rod equator. A criterion has been developed for the maximum useful excitation relative to emission parameters, rod length and rod cross section. It is concluded that this excitation level is fairly insensitive to aspect ratio (radius/length) but that internal reflection from the rod cylindrical surface can markedly lower this level by increasing the effective aspect ratio enormously.

Filamentary Standing‐Wave Pattern in a Solid‐State Maser

The filamentary maser action in a ruby is explained as caused by minute randomly distributed variations in index of refraction. Relations are derived for the density of filaments and their size in terms of a Fourier resolution of the inhomogeneities. These are so small that it seemed that thermal motion might play a part, but this is shown to be orders of magnitude too small at room temperature.

IMPEDANCE CHARACTERISTICS OF LOADED LECHER SYSTEMS

Simple formulas are developed for the impedance of short lengths of Lecher system terminated by resistances. This impedance is most simply expressible as a multiple of the surge impedance. The variation of impedance with system length is traced and certain simple relationships are found. It is shown that any system of loads across a Lecher system is equivalent to a certain length of system terminated by a certain resistance. The formulas account for Takagishis double hump phenomenon and this phenomenon is applied to finding the bridge shortening of an actual bridge. A method of calculating resistance from a resonance curve is derived.

Theoretical Isotherms for Adsorption on a Square Lattice

A method which is not self‐consistent has been used by J. K. Roberts to calculate the adsorption isotherm of adatoms, which are larger than the spacing of the adsorption sites on the substrate so that each adatom excludes all others from neighboring sites. It consists in completely formulating the internal statistics of a sample of the film surface and allowing for the effect of the rest of the film by introducing one or more “environmental” parameters as undetermined functions. These are determined by the requirement that each site of the sample shall be an average site. The failure of this method is traceable to the fact that these functions, when determined, are found to vary with surface concentration in a manner inconsistent with the physical requirements. The same difficulty is found to be latent in Peierls’ treatment of adsorption with interaction between adatoms and in Bethe’s treatment of superlattices. The adsorption isotherms for two cases with no interaction between neighbor adatoms are here c...

Note on earnshaw's theorem

Many have seen the “electromagnetic levitator” in the General Electric Companys “House of Magic” demonstration lectures. In this demonstration, an aluminum disk is stably supported in an alternating magnetic field under the repulsive force between the induced eddy currents and field.5 Another and related problem is reflected in several recent and serious, but inevitably (utile, attempts to achieve stable suspension in space under the forces of permanent magnets alone. This article sheds further light on the basic theory involved, which was formulated a century ago by Samuel Earnshaw and seems quite largely to have been overlooked.

Diffusion through a Finite Plasma in a Uniform Magnetic Field

The anisotropic diffusion of ions and electrons in a nonmultiplying partially ionized plasma lying in a strong uniform magnetic field has been analyzed to zero and first order in the parameter Ω−1, where Ω2 is the ratio of the reduction of transverse electron mobility to the reduction of transverse ion mobility due to the magnetic field. This obviates the need for an earlier erroneous assumption. Potential distribution and electron and ion current flows have been formulated for two‐dimensional flow, using a lowest‐harmonic charged‐particle distribution in a rectangular space and various wall‐current conditions. The encroachment of sheaths inward from the walls has not been considered on the basis that, in principle, the charged‐particle concentration could always be assumed to be large enough to keep this complication small.

FLOW OF IONS THROUGH A SMALL ORIFICE IN A CHARGED PLATE

ABSTRACT Measurements of ion and electron current densities and temperatures in a low pressure arc may be made with a collector which is screened by a close parallel electrode pierced with uniform circular holes. The electrostatic potential distribution in the neighborhood of a pierced electrode , pierced with either slit or hole, has been worked out. The volt-ampere characteristic for random electrons is exponential for the higher retarding voltages and the exponent gives a temperature slightly too high. When the anode drop is known the current density of electrons can be calculated. The volt-ampere characteristic for positive ions is linear for small accelerating voltages. For small retarding voltages the characterisitc is not a pure exponential. The characteristic gives anode drop, ion current density, “transverse” ion temperature and “longitudinal” ion temperature. The limitations and possible errors are discussed.

The Complete Solution of the One‐Velocity Diffusion Problem at Intermediate and Large Distances

An approximate evaluation of the branch‐cut integral which occurs in the rigorous solution of the Boltzmann equation for intermediate and large distances is of importance in shielding problems. Such an evaluation leads to Eq. (20) for the point source and Eq. (24) for the plane source. Equation (20) is actually 23 percent high for zero absorption (f=0) and rσ=7, but the error decreases with increasing rσ and f. It is seen that the branch‐cut term is not simply the contribution of noncollided neutrons.Figure 2 is a plot of the region in the f−rσ plane where the two terms are comparable.

On the instability and rupture of droplets and bubbles in strong electric fields

Abstract An approximate quantitative theory of the equilibrium of a bubble or droplet in a uniform electric field is developed and applied to earlier experimental results. An explanation of the oscillation of bubbles in strong fields and the difference in behavior of positive and negative bubbles is explained on the basis of the discharge of electricity from points.