An analytic theory of spatial power deposition profiles in gyro-device collectors

Summary form only given, as follows. The spiraling beams employed in gyrodevices can create regions of enhanced local heating in the collector as a result of the turning-point behavior of the electron orbits. This hot-spotting is exacerbated by small transverse or angular misalignments between the collector axis and the system magnetic axis, or by transverse magnetic fields in the electron gun. The ability to easily predict the spatial power deposition profile in a gyro-device collector would be a useful capability during the design of high average power, millimeter-wave gyroamplifiers, which often stress the limits of collector power loading. Such an analysis can aid in designing the collector cooling, in setting transverse magnetic field and mechanical alignment tolerances, or designing depressed collectors for gyrotron oscillators. A new procedure to generate synthetic collector maps in small-orbit gyrodevices has been developed based on adiabatic theory. The fringing magnetic field from a semi-infinite solenoid is used as a realistic model for the field in the impact area of the collector. The adiabatic equations for electron motion in this field profile are solved exactly, yielding analytic expressions for radius and gyrophase angle as a function of axial position. When combined with expressions for the location of the cylindrical collector wall, one obtains a characteristic equation that describes the impact locations of a single beamlet of electrons. The locus of impacts is exactly solvable for a perfectly aligned collector, and the more general misaligned case can be evaluated with simple root-finding techniques. To create a complete collector map, the locus of impact sites is computed assuming realistic distributions of Larmor radii, guiding center azimuthal angles, and guiding center radii. This new procedure eliminates the need for numerical integration of millions of electron trajectories.