Beam divergence with harmonic gyroresonance in focusing wiggler and axial field

Abstract

The transport of a relativistic electron beam was studied experimentally and numerically in a magnetic field configuration which consists of a focusing wiggler as well as an additional axial guide field. A new beam divergence was found for the lower side of the magnetoresonance. It was identified as due to the effect of the second harmonic mode of the cyclotron frequency in the resonance, determined by /jft i i -A^rn for n =2. The harmonic resonance was detected for the planar wiggler first, and it could appear also for the helical one. PACS numbers: 41.75.Ht, 41.85.Ja, 52.75.MsSuccessful operation of a Raman free electron laser (FEL) using a relativistic electron beam (REB) has been reported for both planar and helical wiggler configurations [1][2][3][4]. To obtain a high-power performance of the FEL, a stable transport of the beam in the wiggler is one of the key issues. The introduction of an axial uniform guide field superimposed on the wiggler is usually required to keep the orbital stability in the transport, while it will involve some other complex features like the magnetoresonance between the cyclotron motions and the wiggling of the electrons [5]. It is well recognized that the beam diverges and spills out when the electron cyclotron frequency flu in the guide field B g approaches the wiggling frequency K w v\\, where k w is a wiggler wave number, Clw^eBg/yorrie, yo = {l "~ (v 2 /c 2 )} _1 *, v and c are electron and light speed, respectively, and the suffix II indicates axial components [6].In this Letter we describe an experimental and numerical study on the transport of a REB (£6~~0.8 MeV and /6~300 A) through a combination of a focusing type planar wiggler [7] and an axial field: We retain a relatively low additional B g to control the beam dynamics at the entrance of the wiggler and the FEL performance. We found a new type of beam loss at an axial field far lower than the value of B g corresponding to the fundamental magnetoresonance flii^&wm; e.g., the loss is in the parameter region of the so-called group I. Therefore it clearly differs from the "harmonic" gyroresonance which was predicted to occur in group II at flu ^nk w v\\ (n an integer) by Chu and Lin [8], where ft H is a timeaveraged cyclotron frequency in B\\. We need another explanation for the new resonance. We made an analytical study and a numerical simulation on the resonance and its effect on the beam transport through the wiggler. We carried out a similar numerical study for the case of a helical wiggler and the result suggests we will also have the same kind of resonance and beam degradation. The magnetic field in a planar focusing wiggler with a uniform field B g G z is given by B(r) = s

Hybrid planar free-electron maser in the magnetoresonance regime

“…Although, as mentioned at the beginning of this article, a number of approaches to the linear theory of a hybrid FEM have been already formulated, a new one presented here allowed us to both provide a consistent and unified analytical description of electron dynamics for all values of the guide magnetic field and, more importantly, to find an efficient characterization of the dynamical chaos present in the system. It is also worth mentioning that the zones of suppressed beam transport found in [12] are in good correspondence with our (semi)analytical calculations for the zones of dynamical chaos (cf. Fig.…”

“…This is achieved because the method of Lindshtedt employed by us to obtain test individual electron trajectories in the magnetostatic field of a hybrid planar FEM is capable of high precision in analytical calculations. It should be also mentioned that this method is sufficiently general to be applicable to describe the motion of charged particles in spatially inhomogeneous static magnetic fields like, for example, that in [12,29].…”

“…Magnetostatic fieldB p ðrÞ consists of a guide (uniform longitudinal) magnetic fieldB k and planar spatially periodic undulator magnetic field [12,29]:…”

“…Experimentalists [10][11][12][13] reported a considerable loss of electron beam current and microwave power for a hybrid FEM for a certain range of values of the guide magnetic field. A study of chaotic particle dynamics in free-electron lasers was undertaken in papers [14,15], where the authors investigated effects of the high-current (high-density) regime and the transverse spatial gradients in the applied wiggler magnetostatic field, and in Refs.…”

Stability Analysis of Relativistic Electron Beams in a Wiggler with Harmonic Gyro-Resonance Using the Lie Perturbation Method

“…To further increase the beam current, Sakamoto et al [3] superposed an axial guiding field on the selffocusing wiggler and demonstrated the advantages of this configuration. Meanwhile, they also observed a deterioration of beam propagation due to the resonance between the wiggler and cyclotron motions.…”