Microwave Tube Research & Development Centre, Bangalore - 560 013.
Nomenclaturea
Radius of the beam-tunnel
bRadius of the electron beam
βeElectronic propagation constant
ηeCharge-to-mass ratio of an electron at rest
εoPermittivity of free-space
InModified Bessel function of first-kind of order n
JnOrdinary Bessel function of first-kind of order n
KnModified Bessel function of second-kind of order n
RPlasma frequency reduction factor
ρoCharge density of the un-modulated electron beam
ωpPlasma frequency
ωqReduced plasma frequency
A simple formula for plasma frequency reduction factor for a solid cylindrical electron beam in a metallic tunnel has been developed by means of a 3-D curve fitting to the standard results of Branch and Mihran with accuracy > 1.7 per cent, over the parametric regime of normalised beam-radius and beam-filling factor applicable for linear-beam microwave tubes. An artificial neural network algorithm was used for the curve-fitting following the approach of universal approximation. The formula is simple and amenable to easy computation, even using a scientific calculator.
Artificial neural network, plasma oscillation, plasma frequency reduction factor, solid electron beam, metallic tunnel
