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.
Experimental energy barriers to anions transporting through nanofiltration membranes.
Environmentally relevant contaminants fluoride, chloride, nitrate, and nitrite face Arrhenius energy barriers during transport through nanofiltration (NF) membranes. The energy barriers were quantified using crossflow filtration experiments and were in the range of 7-17 kcal·mol(-1), according to ion type and membrane type (Filmtec NF90 and NF270). Fluoride faced a comparatively high energy barrier for both membranes. This can be explained by the strong hydration energy of fluoride rather than other ion properties such as bare ion radius, fully hydrated radius, Stokes radius, diffusion coefficient, or ion charge. The energy barrier for fluoride decreased with pressure, indicating an impact of directional force on energy barriers. The influence of temperature-induced pore radius variability and viscosity on energy barriers was considered. The novel link between energy barriers and ion properties emphasizes the importance of ion hydration and/or partial dehydration mechanisms in determining transport in NF.