For a three-dimensional (3-D) Cherenkov laser composed of a dielectric-loaded rectangular waveguide and a finite-width planar relativistic electron beam, the nonlinear characteristics and efficiency enhancement are investigated with the aid of particle simulation, allowing for the nonlinear properties of the electron beam. The numerical results obtained in the paper are compared with those obtained in the two-dimensional (2-D) analysis. The efficiency enhancement scheme, which was previously proposed for the 2-D case, is found to be effective also for the 3-D case.

Three-dimensional analysis of a Cherenkov laser via particle simulation

The effectiveness and limitation of the periodic boundary condition (PBC) in the analysis of single-pass electron beam devices are discussed. A Cherenkov traveling-wave amplifier consisting of a dielectric-loaded parallel plate waveguide and a planar relativistic electron beam is picked up as an example of electron beam devices. The numerical results obtained without the PBC are compared with those obtained with the PBC. Then, errors caused by the approximation are found to be mainly attributed to two factors. One is caused by the initial condition, which is inherent to the analysis with the PBC. The other factor is the magnitude of the growth rate. The upper bound for the growth rate is given for which the analysis with the PBC is valid. The analysis with the PBC could be effective for estimating energy transfer efficiency because of its relatively small error and significantly low computational cost.

Effectiveness and limitation of the periodic boundary approximation in the analysis of single-pass electron beam devices

In the theoretical treatment of beam-wave interactions, the fluid model or the single-particle model has been used for representing the relativistic electron beam, as described in the foregoing chapters. However, it is very difficult to clarify the details of complicated beam-wave interactions, which are generally nonlinear in essence, only with the aid of purely theoretical approaches based upon either of these models. In fact, with the rapid development of digital computers in recent years, computer simulation has become a powerful tool for the research of nonlinear physical phenomena in various electron beam devices. In this chapter, we describe a typical branch of computer simulation, what is called particle simulation [8.1–8.3], which treats resonant interactions between a collection of charged particles and electromagnetic waves in plasmas or electron beams. In this method, the Maxwell equations and the relativistic equation of motion are discretized in space and time for numerical analysis of electromagnetic wave propagation and particle motion. Thus the interaction of a collection of charged particles and electromagnetic waves is temporally followed with the aid of the finite-difference time-domain (FDTD) method [8.4, 8.51.

FDTD Analysis of Beam-Wave Interaction

Using a method for computer simulation, called particle simulation, this paper investigates in detail nonlinear characteristics (whose analytical treatment has been difficult to date) for a Cerenkov laser composed of a parallel plate waveguide loaded with a dielectric sheet and a planar relativistic electron beam focused with infinite magnetostatic field. The main results obtained here are summarized as follows. First, the growth of an electromagnetic wave is found to be due to energy transfer from the kinetic energy of an electron beam to the electromagnetic energy. Initially, the amplitude of an electromagnetic wave grows exponentially, and then nonlinearity gradually begins to dominate as electrons composing the electron beam are trapped in the electric field of the electromagnetic wave. In the final stage where most of the electrons are trapped, the amplitude of the electromagnetic wave gets saturated. In the early stage where the wave amplitude grows exponentially, the results obtained from particle simulation agree well with those obtained from linear analysis. In this paper, the efficiency of energy conversion from the electron beam to the electromagnetic wave is also estimated with the use of the energy carried by the electromagnetic wave at saturation.

Masaki Sanda

Papers

Analysis of characteristics of a čerenkov laser via particle simulation

Analysis of Characteristics of a Cherenkov Laser via Particle Simulation