Initial Energy Modulation Research Articles

Suppression of microbunching instability with magnetic bunch length compression in a linac-based free electron laser

The aim of this paper is to investigate the effect of the magnetic bunch length compression on the development of the microbunching instability. It will be shown that, after removing the linear energy chirp required for the compression, an additional and properly tuned ${R}_{\mathbf{56}}$ transport matrix element is able to dilute the initial energy modulation and to suppress the current spikes created by the microbunching instability without affecting the bunch length. A by-product of the study is the observation that a single compressor is more effective than the two-compressors scheme in reducing the unwanted modulations caused by the microbunching instability. The study is based on analytical calculations and on the simulation code elegant.

Echo-enabled harmonic generation free electron laser

In this paper, we systematically study the echo-enabled harmonic generation (EEHG) free electron laser (FEL). The EEHG FEL uses two modulators in combination with two dispersion sections that allow one to generate in the beam a high harmonic density modulation starting with a relatively small initial energy modulation of the beam. After presenting an analytical theory of the phenomenon, we address several practically important issues, such as the effect of incoherent synchrotron radiation in the dispersion sections, and the beam transverse size effect in the modulator. Using a representative realistic set of beam parameters, we show how the EEHG scheme enhances the FEL performance and allows one to generate a fully (both longitudinally and transversely) coherent radiation. As an example, we demonstrate that 5 nm coherent soft x rays with GW peak power can be generated directly from the 240 nm seeding laser using the proposed EEHG scheme.

Propagation characteristics of a premodulated electron beam

The propagation properties of an electron beam whose energy and current are simultaneously premodulated at the cathode are investigated by computer simulation using the two-dimensional (2-D) particle-in-cell code, MAGIC. The simulation is carried out to investigate the influence of the initial energy modulation and the phase difference between current and energy modulation. With appropriate initial energy modulation, the amplitude of the downstream current modulation can be kept as high as the initial modulation level. Appreciable growth of high harmonic components is also observed as the electron beam debunches. The simulation data are compared with results obtained from a nonlinear theory of the current modulation in an electron beam propagating through a drift tube. It is shown that the simulation data agree remarkably well with the analytical theory.

Propagation characteristics of a premodulated electron beam

The propagation properties of an electron beam whose energy and current are simultaneously premodulated at the cathode are investigated by computer simulation using the two-dimensional particle-in-cell code, MAGIC. The simulation is carried out to investigate the influence of the initial energy modulation and phase difference between current and energy modulation. With appropriate initial energy modulation, amplitude of the downstream current modulation can be kept as high as the initial modulation level. Appreciable growth of high harmonic components is observed as the electron beam debunches. The maximum amplitude of the fundamental mode (m=1) occurs at the propagation distance, where all the other modes vanish or have a very small amplitude.

Propagation properties of a relativistic electron beam with premodulated energy and current

This paper considers an electron beam whose energy and current are simultaneously premodulated at the injection point of a drift tube. A theoretical model is developed for the subsequent current and energy modulations which propagate downstream. A closed integrodifferential equation for the normalized beam current is obtained in terms of time and propagation distance. To make the nonlinear current modulation analytically tractable, a small signal theory is introduced into the modulation calculation. The current modulation in the linear regime is a linear combination of the forward and backward waves of the initial current and energy modulations. It is shown that the initial energy modulation is a very effective means for downstream current modulation. The downstream energy modulation is also expressed by a linear combination of the forward and backward waves of the initial current and energy modulations. In general, the maximum current modulation occurs at the propagation distance where the energy modulation is minimum. Properties of the current and energy modulations are numerically investigated from the integrodifferential equation for a broad range of system parameters. Numerical data even for a large initial current and energy modulations agree reasonably well with analytical results predicted by the linear theory.

Influence of initial energy modulation on premodulated electron beam propagating through a drift tube

Influence of the initial energy modulation caused by the self-potential depression on the premodulated electron-beam propagation through a drift tube is investigated. The potential depression κ can significantly vary because of the initial current modulation. Thus, beam’s kinetic energy at the injection varies accordingly. A self-consistent nonlinear theory of current modulation of the premodulated electron beam is developed. It is shown that the initial energy modulation caused by the self-potential depression at injection plays a significant role in the current modulation for long range propagation. It is also found from a small signal theory that reduction of the beam’s kinetic energy due to its potential depression accelerates debunching process of the initial current modulation. Although the initial current modulation is debunched quickly for high current beam, amplitude of the current modulation never becomes zero because of the initial energy modulation.

A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam

A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall klystron, in which a relativistic electron beam is modulated at the first cavity and propagates downstream through the resistive wall. Because of the self-excitation of the space charge waves by the resistive-wall instability, a highly nonlinear current modulation of the electron beam is accomplished as the beam propagates downstream. A partial integrodifferential equation is obtained in terms of the initial energy modulation (ε), the self-field effects (h), and the resistive-wall effects (κ). Analytically investigating the partial integrodifferential equation, a scaling law of the propagation distance zm at which the maximum current modulation occurs is obtained. It is found in general that the self-field effects dominate over the resistive-wall effects at the beginning of the propagation. As the beam propagates farther downstream, the resistive-wall effects dominate. Because of a relatively large growth rate of the instability, the required tube length of the klystron is short for most applications.

Nonlinear analysis of the two-stream instability for relativistic annular electron beams

A nonlinear theory is developed for the two-stream interaction of two relativistic annular electron beams propagating through a grounded cylindrical conducting tube. The theory is based on the assumption that the beams experience energy modulation at a cavity before they enter the drift tube. Two coupled integrodifferential equations are derived which describe beam current modulation in terms of time t and propagation distance z. The evolution of the fundamental mode in the current modulation is investigated analytically by making use of these coupled equations. The amplitude of the fundamental mode, which is a function of the propagation distance, is expressed explicitly in terms of the initial energy modulation, the growth rate of the instability, and the beam intensity. It is found that self-field effects dominate two-stream effects at the beginning of the propagation. As the beams propagate further, the two-stream effects start to dominate and then the perturbations grow exponentially. The saturation mechanism is identified as multimode coupling. A theoretical model describing the mode coupling in the current modulation is also developed. The theory is verified by detailed comparisons between analytical and particle-in-cell simulation results.

A theoretical investigation of the plasma klystron amplifier

The plasma klystron amplifier concept is investigated. The plasma klystron consists of a relativistic annular electron beam propagating through a space between a plasma column and drift tube wall. The annular electron beam, premodulated at the first cavity in the klystron, enters the space. An axial electric field accompanied by the modulated beam excites space charge waves in the plasma column, which acts like an inductive medium amplifying the electrostatic waves. The physical mechanism of self‐amplification of the electrostatic waves is the two‐stream instability, which is investigated in detail. Instability criteria indicate that the plasma should be opaque to sustain instability. A theoretical model to describe current modulation of the annular electron beam propagating through the space is developed. The electron beam current is modulated by the amplifying electric field fed by the plasma column. Saturation distance of the current modulation is a weakly dependent function of the initial energy modulation at the first cavity. Thus, a relatively low‐power microwave input may well excite the two‐stream instability and deliver a highly modulated beam to the extraction cavity. Due to a relatively large growth rate of the instability, required interaction length of the beam and plasma column is short for most applications.