Abstract
The characteristics of an axis-encircling electron beam using an annular Pierce-type electron gun are calculated analytically. The analytical calculation is carried out by considering the initial canonical angular momentum spreads at the cathode and the crossing of the electron beam with the magnetic flux line before the magnetic cusp. The analytically calculated characteristics of an axis-encircling electron beam such as the axial velocity spread, the velocity ratio, the Larmor radius, and the guiding center radius are in good agreement with the simulated result obtained using an electron trajectory program. In this comparison, a 30 kV, 1.0 A electron beam is used with a peak magnetic flux density of 4.38 kG using the magnetic field with a single cusp. The result obtained by this analysis also shows that the electron beam with a fairly low axial velocity spread of less than 1% can be realized by employing a suitable distance between the cathode and magnetic cusp.
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