Radar System Engineering

SEC. 103] ELECTRON ORBITS AIVD THE SPACE CHARGE 331
anode segments. Inaddition, theelectron is part of aspace charge with
extreme variations in density. The resulting eIectron motion presentsa
problem of extreme complexity, and a detailed theory has not been
developed. A qualitative understanding insimple terms of the processes
responsible for the excitation of the magnetron is, however, possible.
Consider the simple case of a single electron in the interaction space
of a magnetron in the absence of any perturbing r-f fields. In crossd
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FIG. 1011.-Path
uf electron in nonosvillatiugmagnetron.
magnetic and electric fields, there is a force —eE, dueto the electric field,
and another, ~ v x H, due to the magnetic field, ~rhere E and H are the
electric and magnetic field strengths, e and v the charge and velocity of
the electron, and c the velocity of light. The resulting motion is approximately
represented by superposing a slow rotation around the cathode at
nearly constant radius Ro (the RO rotation), and a faster circular motion
with a smaller radius TO(the TOrotation). The resultant of these two
motions corresponds roughly to the motion of a point on the circumference
of a wheel as it rolls around a circle somewhat smaller than the cathode
in such a way that its center moves in a circle of radius RO (Fig. 10.11).
The speed of the slow R, rotation is given approximately by the ratio
E/H. The angular velocity of the fast rOrotation is determined by H