Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

:488 FREQUENCY MODULATION, Volume Ivector potential of the nt\i mode, i.e., A 0n, corresponding to the frequencya> .0n If a uniform beam of electrons is introduced into thecavity, then we may calculate a first approximation to the currentinside the cavity by calculating the electron trajectories that would beproduced by the unperturbed or zeroth-order fieldexisting before theelectrons were introduced. Let the first-order approximation to thecurrent density inside the cavity be denoted by SJ 1(r,t). S is aparameter introduced to indicate the order of smallness of the current.The corresponding first approximation to the charge distribution inthe cavity can be denoted by 8p 1 (r, t) . The first-order current andcharge can be substituted in (56a) and (56b) and these equationssolved to obtain a first approximation for the vector and scalar potentialswhich may be denoted by A ln and ln. In principle this procedurecan be repeated and would be expected to yield a convergent series(when J 1 is not too large) which would give a solution of the problemwith any desired accuracy.Carrying out this procedure, the first-order approximation for thevector and scalar potentials will be found by solving the followingequationsV•VA ln (r,t) —t!iA u ,(r,t) =- /iS/ lre (r, t) + p.c grad ln (r, t) (60)8pi„(r, t)V 2