Some observations on gyrotron interaction models III. Gyro-oscillators

Cavity loading in gyrotrons: approximate calculations

“…5 and 6 in Lindsay and Jones (1986)). For reasons of brevity, the coefficient of reflection p was assumed to be equal to Downloaded by [Purdue University] at 12:14 16 September 2013 unity in Lindsay and Jones (1986), so that the crucial eqn. (81) is valid for this particular value of p only.…”

“…The gyrotron interaction mechanism has already been discussed at some length in three earlier publications (Lindsay et al (1984(Lindsay et al ( , 1985 and Lindsay and Jones (1986)), the first two papers dealing with amplifiers and the third one with oscillators. In all cases, the model comprises a hollow electron beam which is assumed to interact with a circularly polarized electromagnetic field of constant amplitude and tra veiling in the direction of the beam axis.…”

“…In the case of a gyro-oscillator, the field is assumed to consist of two waves travelling in opposite directions, the ratio of the complex amplitudes of the two waves being given by a coefficient of reflection p (see eqns. (6) and (7) in Lindsay and Jones (1986)). The results of the investigations are summarized by plotting the normalized mean power transfer between the beam and the field as a function of the transit time through the cavity T and the 'slip' frequency W_, = W -Wee" where W'e1 = eBII/y, m o is the initial value of the relativitycorrected cyclotron frequency We.…”

“…(I) have already been fully discussed in Lindsay and Jones (1986). Here it is only necessary to point out that (P) represents the mean power exchanged between the field and the beam; (P) > 0 when the energy flows from the field to the beam (attenuation) and (P) < 0 when the energy flows in the opposite direction (amplification).…”

“…This 180°phase shift has been introduced quite inadvertently by choosing field components as shown in Lindsay and Jones (1986),eqns.…”