Theory of free electron laser instability in a relativistic annular electron beam

Abstract

A self-consistent theory of the free electron laser instability is developed for a hollow electron beam propagating through an undulator (multiple mirror) magnetic field. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations. It is assumed that the beam is thin, with radial thickness much smaller than the mean beam radius, and that ν/γb≪1, where ν is Budker’s parameter and γbmc2 is the characteristic energy of the electron beam. The dispersion relation describing the free electron laser instability in a hollow relativistic electron beam is obtained for an equilibrium distribution function in which all electrons have the same value of transverse energy and the same value of canonical angular momentum, and a Lorentzian distribution in axial momentum. It is shown that the influence of finite radial geometry plays a critical role in determining the detailed stability behavior. Moreover, the growth rate and bandwidth of the instability can be expressed in terms of Budker’s parameter ν, instead of the plasma frequency as in the case of a uniform density beam. Furthermore, it is found that free electron laser stability properties exhibit a sensitive dependence on axial momentum spread.

Effect of plasma and dielectric loading on the slow-wave properties of a traveling-wave tube

“…wherep 2 = (o?/c 2 -J3Q), q 2 = (w 2 f/c 2 -f3 2 0 ). In writing (6) and 7we have made use of the boundary condition at r = a that the tangential component of the electric field is continuous across the helix, i.e.,…”

“…J n , Y n are the Bessel functions of the first and the second kind, respectively, of order n (0, 1). The constants A and B in (6) and 7are evaluated with the boundary conditions written in (1) and (2). This gives…”

“…I N RECENT years there has been growing interest in high-power and high-frequency microwave devices for generating radiation at millimeter and submillimeter wavelengths. Microwave devices such as gyrotrons [1]- [4], magnetrons [5], and free-electron lasers [6], [7] make use of the synchronism of the electron beam with the fast waveguide modes. On the other hand, an electron beam propagating through a slow-wave structure couples with the slow electromagnetic modes of the system and emits coherent short-wavelength radiation.…”

<title>Three-Dimensional Theory Of The Raman Free-Electron Laser</title>

“…These orbits are axi-centered and, for orbits of either group I or group II, there is a unique mapping between y and X (i.e., the orbit radius) for given Bo, Bw, and X.,. Thus, it is sufficient to specify the class of (18) orbit and R0(Y0) in order to obtain y0(R0). In addition, a spread in radius AR of the beam is equivalent to an energy spread Ay given by Ay yó -1 AR Yo (1 + aa)Q(X0) R0 where Xo = kwRo.…”