No abstract

It has been observed experimentally that the application of a radio-frequency voltage (10 kc/sec–50 Mc/sec) to any one of several electrode configurations around the outside of a plasma discharge tube results in a constriction of the luminous portion of the plasma away from the inner walls of the glass tube. This investigation has established that the phenomenon is basically a radio-frequency rectification effect, leading to the formation of thick ion sheath. The interaction is described mathematically in terms of a differential equation which has an approximate solution that fits qualitatively all the observed characteristics of the phenomenon. The differential equation, in its most general form, has also been solved numerically and the solution is shown to quantitatively fit our experimental observations for both radio-frequency sine and square wave signals. An application of this phenomenon as a possible external diagnostic probe technique is proposed.

It is shown that a pressure theory, modified to take into account ion generation, can be used to describe the steady-state collisionless discharge. Both planar and cylindrical geometry one-dimensional cases are solved for various types of ion generation using this fluid-type of approach. The parameters found by this approximate technique are shown to be in good agreement with the values obtained from the more exact formulation developed by Langmuir. The analysis leads to partial differential equations which are easily generalized to describe two-dimensional problems. For the particular case of ion generation proportional to electron density, the discharge parameters of a two-dimensional rectangular box and a finite-length cylinder are obtained.

We have developed a new photothermal technique to investigate electronic phase transitions associated with high temperature superconductivity and charge density waves (CDW). The phase shift of the thermal wave yields the anisotropic thermal diffusivity coefficient of the sample. The amplitude of the photothermal signal is sensitive to electronic phase transitions of the second kind and measures directly the effect of thermodynamic fluctuations near the transitions. This noncontacting high-definition technique is well suited to measurements of small and fragile samples. Good comparisons between our experimental results and second-order phase transition theory are obtained on a high-Tc superconductor and a CDW sample.

The equations for irrotational, electrostatic laminar space-charge flow (no thermal velocities or normal magnetic field at the cathode) are set up in terms of the action function. The resulting nonlinear partial differential equation is first reduced, by the method of the separation of variables in cylindrical polar coordinates, to the solution of a set of first-order, nonlinear, ordinary differential equations in one coordinate. It is shown that it is possible to predict axially symmetric, electrostatic, hollow beams from the inside of hollow cylindrical cathodes with space-charge-limited emission which asymptote, theoretically, to other extremely thin cylinders—though thermal velocities would, in practice, limit such a convergence. The characteristics of a particular beam, and the electrode system to produce it are shown. The beams which result from the separation of variables in other coordinate systems are described. In spherical polar coordinates one obtains hollow axially symmetric beams from a conical cathode, which may asymptote to other cones; in a less familiar coordinate system, spiral coordinates, sheet beams from equiangular spiral cathodes result. Finally, it is shown how the method may be extended to include magnetic fields transverse to the cathode. Some new solutions to space-charge flow in crossed electric and magnetic fields from a space-charge-limited cathode are mentioned.