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.
Peniotron oscillator operating performance
Performance results are presented for two 8 GHz peniotron oscillators operating in the funda mental rotational mode. To form the rotating hollow beam, a non-rotating hollow beam is generated by an immersed Pierce-type gun, and the beam is caused to rotate at cyclotron frequency by a field reversal. The resonant cavity consists of a section of waveguide with a double pair of ridges, short-circuited at each end. The first device tested was loosely coupled to the external load, and the second was much more tightly coupled to increase circuit efficiency. Observed performance is in quite good agreement with calculated performance. Extension of the peniotron to higher frequencies and to amplifier operation is discussed.
ASSESSING AGE AND GENDER DIFFERENCES IN PERCEIVED RISK AND FEAR OF CRIME
Much of the research on fear of crime indicates that women and older persons are highly afraid of crime. These findings, especially older persons' fear of crime, are widely communicated in the scientific and popular media. This study examines age and gender differences in perceived risk and fear of crime. The data are from telephone interviews of 320 randomly selected residents in a southeastern metropolitan area of the United States. The relationships of age and gender to fear of crime are compared using a National Crime Survey (NCS) measure of fear of crime and 11 alternative indicators of fear of specific offenses. Women reported signifcantly greater perceived risk and fear of crime than men regardless of how fear of crime was measured and older adults reported the greatest fear of crime when the NCS measure was used. but not when the alternative individual measures of fear of crime were used. A LISREL model with latent constructs for fear of personal crime and fear of property crime also indicates that older adults do not have higher levels of fear of crime. In short, the extent of fear in the everyday lives of most older persons has been overestimated in many previous studies because of measurement problems.