Chaotic electron trajectories in an electromagnetic wiggler free-electron laser with ion-channel guiding

Abstract

Chaotic behavior of an electron motion in combined backward propagating electromagnetic wiggler and ion-channel electrostatic fields is studied. The Poincaré surface-of-sections are employed to investigate chaotic behavior of electron motion. It is shown that the electron motion can exhibit chaotic behavior when the ion-channel density is low or medium, while for sufficiently high ion-channel density, the electron motion becomes regular (nonchaotic). Also, the chaotic trajectories decrease when the effects of self-fields of electron beam are taken into account and under Budker condition all trajectories become regular. The above result is in contrast with magnetostatic helical wiggler with axial magnetic field in which chaotic motion is produced by self-fields of electron beam. The chaotic and nonchaotic electron trajectories are confirmed by calculating Liapunov exponents.

Response to “Comment on ‘Chaotic electron trajectories in an electromagnetic wiggler free-electron laser with ion-channel guiding’” [Phys. Plasmas 17, 093103 (2010)]

“…In contrast with the authors of comment opinion, the variation of total energy is not permissive for initial conditions and during the electron motion because the electron total energy is a constant of motion as we have shown in Ref. 1. Note that, in the case of magnetostatic wiggler with axial magnetic field and in the absence of self-fields, the electron kinetic energy c is equal to the electron total energy and is a constant of motion (see, e.g., Fig.…”

“…1. For an electron beam with sufficiently low electron density (i.e., n b ¼ 0), self-fields can be neglected [see Eqs.…”

“…1, it has been assumed that the normalized mean axial velocity b b is constant equal to 0.93 to determine only the self-magnetic field. The assumption of a constant mean axial velocity has been used in the previous studies of chaotic dynamic (see e.g., Refs.…”

Effect of normalized plasma frequency on electron phase-space orbits in a free-electron laser

“…So far, a number of papers have been devoted to the study of the electron motion. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] Evidently, exploring the ways to irregulate phase-space orbits is of significance in improving the electron-beam transport quality and the FEL performance. Recent studies indicate that there are several ways to cause electron irregular motion and in consequence, what might be termed 'FEL chaos' has been found.…”

Electromagnetic Waves Dispersion and Interaction of an Annular Beam-Ion Channel System in Plasma Waveguide

“…In the past years, most of the published papers concentrated on the case of the relativistic electron beam (REB) with an external magnetic field guiding. In recent years, ion channel guiding has been put forward as an innovative focusing method for guiding the electron bunch transport [9,10]. To form an ion channel, the electron beam density and the plasma density must satisfy the matching condition / 2 ≤ < [9,11].…”