Coupled Mode Theory of Electron‐Beam Parametric Amplification

Abstract

A theory of parametric amplification in a filamentary electron beam by transverse fields is developed in coupled mode form. Space charge effects are neglected. In addition to beam modes at the signal frequency, beam modes at frequencies ωₙ = ω + ωₚ, n = 0, ±1, ±2…, where ωₚ is the pump frequency, are coupled together. A discussion of the general form of the equations is given and reveals the circumstances under which exponential gain or periodic energy transfer between various modes can occur. When applied to quadrupole electric pump fields, a description of the quadrupole amplifiers of Adler, Wade, and Gordon is obtained. This theory is then used to evaluate the noise contribution from synchronous beam modes and higher cyclotron idler modes. Coupling by axially symmetric electric fields and by axially symmetric magnetic fields is discussed, and other amplification schemes suggested. The theory of coupling by axially symmetric fields can also be used to study lens effects on noise in the gun region.