Frequency-coordinate vector diagram

From the standpoint of circuit synthesis as well as for a fundamental comprehension of circuit behavior, it is desirable to be able to visualize the response of a circuit over an extended frequency range by means of a geometrical construction. Mathematically, the response of a circuit can be expressed with the La Place transform theory as a function of the complex frequency variable, p = α + jωw, in which a is the decrement and ω is the “real” angular frequency. Physically, the nature of the real-frequency response is usually not discernible by casual inspection of the mathematical function. This paper develops a means of visualizing this frequency response readily through the construction of a vector diagram from the response function.     

The electron mechanics of induction acceleration

The radial and axial motions of electrons in the betatron are described by means of a potential function of forces. Previously reported conditions of equilibrium, stability and damping of oscillations are derived for the region of parabolic variation of the potential. Extension of the analysis to, non-parabolic regions gives an account of the injection in conventional instruments in better agreement with experiment, particularly in regard to higher voltages of injection.Space charge limitations are discussed with the help of the Laplacian of the potential of forces.By means of an additional radial electric field electrons can be introduced as in the magnetron, without any asymmetry inherent in the conventional betatron circumferential injector. The analysis of the conditions of equilibrium and stability, greatly facilitated in this case by the notion of potential, shows that no substantial improvement in space charge limitations can be expected and that the required variations between the flux linking the electron orbits and the magnetic and electric fields at the orbits are difficult to realize on account of their complexity and narrow tolerances. The X-ray output of a small experimental double yoke instrument was measured by a phototube multiplier viewing an irradiated fluorescent screen and gave evidence of multiple group electron capture.