Some closed-form expressions for relativistic cross-field electron trajectories
Equations for nonrelativistic cross-field motion are first repeated from prior work, in a form suitable for piecewise trajectory calculation in fields that need not be constant. They are then extended into the middle relativistic range, using a new method of expressing the relativistic cyclotron frequency in terms of the fields and the starting conditions. The extended equations are found to include second harmonic terms, but not third harmonic. Accuracy is tested by comparison with Runge-Kutta integration of the relativistic equations of motion, and is found to be adequate for many engineering purposes up to peak velocities in the region of 0.6 c, corresponding to cross-field tube operating voltages on the order of 400 kV. Speed is similar to or a little better than R-K integration on a per-step basis, but is substantially higher when the fieldsallow large step sizes to be taken, since the closed-form expressions have no inherent step size limitation. The tests covered conditions appropriate both to gyrotrons and to relativistic magnetrons.
Beam buildup in a DEMATRON amplifier
The operation of an RF triggered cold-cathode crossed-field amplifier is briefly described, and the problem is posed of how the beam builds up, since it is necessary for it to remain in an inherently debunching phase region for more than 20 successive impacts on the cathode. A partial answer is provided by numerical calculations showing that the velocity of a repeatedly impacting beam differs from E/B in a way which introduces a new phase-focusing mechanism. It is found that buildup can also occur without exact synchronism over a range of calculated voltages which agree closely with measurement. The principles of two computer programs are described, one covering the buildup region of negligible space charge, and the other the transition and power-generating regions where space charge becomes important. Quantitative conclusions are drawn concerning the velocity and direction of impacts on the cathode, which vary markedly as the space charge density changes.
Unity Identity Text Self
Abstract Understanding the receptivity of literature, how one work admits many readers, begins with an analogy: unity is to text as identity is to self. Unity here means the way all a text’s features can be related through one central theme. Identity describes a person’s sameness within different behaviors as variations on one identity theme (Lichtenstein). To find unity or identity, however, the interpreter himself plays a behavioral variation on his identity theme. In interpreting, his identity re-creates itself as he shapes the text to match his characteristic defenses, fantasies, and coherences. Thus, what a poet says about fictional, political, or scientific texts expresses the same identity theme as the poems he writes. To understand reading, criticism, and any knowing or making in symbols, then, we need to let go the Cartesian craving for objectivity and accept the themes in ourselves with which we construe the world—including literary works.