Wiggler Free-electron Laser Research Articles

Nonlinear analysis of the efficiency and saturation length of free electron laser with realistic helical wiggler and ion-channel guiding

A nonlinear study of the efficiency, power, and the saturation length of a free-electron laser with realistic helical wiggler and ion-channel guiding using numerical simulation is presented. A set of coupled nonlinear differential equations is derived using the Lorentz force equation for the ensemble of electrons and Maxwell’s equations for radiation waves. To calculate the efficiency, power, and the saturation length of the amplifier, these equations are solved simultaneously using a code developed in this study. By choosing different values of the plasma frequency of ion-channel guiding, the dominant mode for the group I and group II orbits is found. The effect of ion-channel guiding on efficiency and saturation length was studied, and the results show that ion-channel guiding increases efficiency and reduces saturation length. Moreover, the efficiency increases, and the saturation length decrease when the annular electron beam is substituted for a solid electron beam. Finally, the results show that the efficiency of a realistic wiggler free-electron laser is higher than that of an idealized one, while the saturation length is lower.

Interaction of a relativistic electron beam with a laser pulse in the presence of a magnetized plasma medium

Significant progress has been made using plasma channels to guide relativistic e-beams in magnetostatic wiggler free-electron lasers (FELs). In this regard, we study the interaction of an intense laser pulse (as a laser wiggler) with a relativistic electron beam embedded in a background of magnetized plasma. The short wavelength of the laser wiggler ( ∼ µm) allows a higher radiation frequency to be obtained than from conventional magnetostatic wigglers. Laser-plasma interaction in a magnetized plasma channel has been studied. Numerical results reveal that the laser self-focusing and self-compression can be enhanced with increasing the external axial magnetic field strength, which leads to a decrease in the spot size of the laser beam. Hence, we employ the laser beam as a suitable laser wiggler in a FEL-device. Injection of plasma in the interaction region of a laser-wiggler-FEL suggests the possibility of producing short wavelengths ( ∼ x-ray) using lower energy beams ( ∼ O(10) MeV). Furthermore, this configuration has a higher tunability by controlling the plasma density in addition to the e-beam energy tunability of the conventional FELs. Effects of the external axial guide magnetic field and plasma medium on the gain of the FEL have been studied. It is found that by increasing the plasma frequency the FEL-gain increases. The effects of e-beam self-electric and self-magnetic fields on the laser gain have also been investigated in the presence of various plasma frequencies. The results indicate that in the presence of beam self-fields, the sensitivity of the gain increases in the vicinity of resonance regions. Besides, the normalized wiggler-induced self-magnetic field has been obtained which reveals that it is a positive parameter, i.e., it can act as a paramagnetic correction to the wiggler magnetic field, therefore, the gain enhancement can be due to the paramagnetic effect of the self-magnetic field. This concept opens a path toward a new source of soft x-ray pulse based on table-top plasma loaded laser wigglers.

Interaction of a relativistic dense electron beam with a laser wiggler in a vacuum: self-field effects on the electron orbits and free-electron laser gain.

Employing laser wigglers and accelerators provides the potential to dramatically cut the size and cost of X-ray light sources. Owing to recent technological developments in the production of high-brilliance electron beams and high-power laser pulses, it is now conceivable to make steps toward the practical realisation of laser-pumped X-ray free-electron lasers (FELs). In this regard, here the head-on collision of a relativistic dense electron beam with a linearly polarized laser pulse as a wiggler is studied, in which the laser wiggler can be realised using a conventional quantum laser. In addition, an external guide magnetic field is employed to confine the electron beam against self-fields, therefore improving the FEL operation. Conditions allowing such an operating regime are presented and its relevant validity checked using a set of general scaling formulae. Rigorous analytical solutions of the dynamic equations are provided. These solutions are verified by performing calculations using the derived solutions and well known Runge-Kutta procedure to simulate the electron trajectories. The effects of self-fields on the FEL gain in this configuration are estimated. Numerical calculations indicate that in the presence of self-fields the sensitivity of the gain increases in the vicinity of resonance regions. Besides, diamagnetic and paramagnetic effects of the wiggler-induced self-magnetic field cause gain decrement and enhancement for different electron orbits, while these diamagnetic and paramagnetic effects increase with increasing beam density. The results are compared with findings of planar magnetostatic wiggler FELs.

Plasma and cyclotron frequency effects on output power of the plasma wave-pumped free-electron lasers

Significant progress has been made employing plasmas in the free-electron lasers (FELs) interaction region. In this regard, we study the output power and saturation length of the plasma whistler wave-pumped FEL in a magnetized plasma channel. The small wavelength of the whistler wave (in sub-μm range) in plasma allows obtaining higher radiation frequency than conventional wiggler FELs. This configuration has a higher tunability by adjusting the plasma density relative to the conventional ones. A set of coupled nonlinear differential equations is employed which governs on the self-consistent evolution of an electromagnetic wave. The electron bunching process of the whistler-pumped FEL has been investigated numerically. The result reveals that for a long wiggler length, the bunching factor can appreciably change as the electron beam propagates through the wiggler. The effects of plasma frequency (or plasma density) and cyclotron frequency on the output power and saturation length have been studied. Simulation results indicate that with increasing the plasma frequency, the power increases and the saturation length decreases. In addition, when density of background plasma is higher than the electron beam density (i.e., for a dense plasma channel), the plasma effects are more pronounced and the FEL-power is significantly high. It is also found that with increasing the strength of the external magnetic field frequency, the power decreases and the saturation length increases, noticeably.

Dispersion relation and growth rate of a relativistic electron beam propagating through a Langmuir wave wiggler

In this study, a theory of free-electron laser (FEL) with a Langmuir wave wiggler in the presence of an axial magnetic field has been presented. The small wavelength of the plasma wave (in the sub-mm range) allows obtaining higher frequency than conventional wiggler FELs. Electron trajectories have been obtained by solving the equations of motion for a single electron. In addition, a fourth-order Runge–Kutta method has been used to simulate the electron trajectories. Employing a perturbation analysis, the dispersion relation for an electromagnetic and space-charge waves has been derived by solving the momentum transfer, continuity, and wave equations. Numerical calculations show that the growth rate increases with increasing the e-beam energy and e-beam density, while it decreases with increasing the strength of the axial guide magnetic field.

自由电子激光摇摆器磁测系统

自由电子激光摇摆器磁测系统

Effects of electron beam temperature on radiation growth rate in a realistic helical wiggler with ion-channel guiding

We study the effects of electron beam parameters such as electron beam temperature and Lorentz relativistic factor (or electron energy) on growth rate in a realistic (three-dimensional) helical wiggler free-electron laser with ion-channel guiding. A generalized dispersion relation is derived by considering the interaction between the radiation fields and electron beam when the effects of electron beam self-fields are taken into account. The growth rate is then calculated, and it is found that, for group I orbits, there is an optimum value for electron beam density at which the growth rate goes to its maximum. Also, there is an optimum value for Lorentz relativistic factor. The effect of beam temperature is also investigated, and it is shown that the growth rate decreases considerably as beam temperature increases.

Steady-state electron trajectories in a free electron laser with ion-channel and axial magnetic field in the presence of self-fields

A theory of self-fields in a one-dimensional helical wiggler free electron laser with ion-channel guiding and axial magnetic field is presented. The steady-state orbits under the influence of self-field are derived and discussed. The Φ function that determines the rate of change of axial velocity with energy is derived. The numerical results show the effects of self-fields and the two electron-beams guiding devices (ion-channel and axial magnetic field) on the trajectories when used separately and simultaneously. The study shows that new unstable orbits, in the first part of the group I and II orbits, are found. A detailed stability analysis of orbits is presented.

Effects of self-fields on electron trajectory and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding

The effects of self-fields on electron trajectories and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding are investigated. An analysis of the two-stream quasi-steady-state electron trajectories is given by solving the equation of motion in the presence of ion-channel guiding and the planar wiggler. The electron trajectories and the gain are derived. The stability of the trajectories, the characteristics of the linear gain, and the normalized maximum gain are studied numerically. The numerical calculations show that there are eight group trajectories rather than the two groups reported in the absence of the self-fields. It is also shown that the normalized gain group seven (G7) decreases while the rest increases with the increase in normalized ion-channel frequency. The two-stream instability and the self-field lead to a decrease in the maximum gain, except for G7.

Free-electron laser with a plasma wave wiggler propagating through a magnetized plasma channel

A plasma eigenmode has been employed as a wiggler in a magnetized plasma channel for the generation of laser radiation in a free-electron laser. The short wavelength of the plasma wave allows a higher radiation frequency to be obtained than from conventional wiggler free-electron lasers. The plasma can significantly slow down the radiation mode, thereby relaxing the beam energy requirement considerably. In addition, it allows a beam current in excess of the vacuum current limit via charge neutralization. This configuration has a higher tunability by controlling the plasma density in addition to the γ-tunability of the standard FEL. The laser gain has been calculated and numerical computations of the electron trajectories and gain are presented. Four groups (I–IV) of electron orbits have been found. It has been shown that by increasing the cyclotron frequency, the gain for orbits of group I and group III increases, while a decrease in gain has been obtained for orbits of group II and group IV. Similarly, the effect of plasma density on gain has been exhibited. The results indicate that with increasing plasma density, the orbits of all groups shift to higher cyclotron frequencies. The effects of beam self-fields on gain have also been demonstrated. It has been found that in the presence of beam self-fields the sensitivity of the gain increases substantially in the vicinity of gyroresonance. Here, the gain enhancement and reduction are due to the paramagnetic and diamagnetic effects of the self-magnetic field, respectively.

The Gain Equation of a Helical Wiggler Free Electron Laser with Ion-Channel Guiding and/or an Axial Magnetic Field

Electron motion in the combined ion-channel, helical wiggler and axial magnetic fields is analyzed in the absence of a radiation field. Detailed analysis of the gain equation in a free-electron laser is presented. Numerical calculations are made to illustrate the effects of the two electron-beam guiding devices on the gain when applied separately and simultaneously.

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

The chaotic electron dynamics in a free-electron laser with electromagnetic-wave wiggler and ion-channel has been recently reported by A. Taghavi et al. [Phys. Plasmas 17, 093103 (2010)]. We comment on the authors use of a set of initial condition that is not correct based on the dispersion relation and steady-state orbits.

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

Nasr and Hasanbeigi in their comment [Phys. Plasmas 17, 093103 (2010)] have claimed that, in our recent paper [Phys. Plasmas 17, 093103 (2010)], incorrect initial conditions have been used based on dispersion relation (or normalized electromagnetic wave frequency ω−w) and mean axial velocity βb. We use a self-consistent method to calculate more accurate values of ω−w and βb and show that all results presented in our recent paper are correct.

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

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.

Self-field effects on electron dynamics in a three-dimensional helical wiggler free-electron laser with axial magnetic field

An analytic linear theory of the electron dynamics in a three-dimensional helical wiggler free electron laser (FEL) with axial magnetic field is presented. Orbits are obtained by perturbing the steady state-trajectories in order to determine the characteristic frequencies Ω± of the FEL. The effect of the self-fields on electron dynamics is studied and modified steady-state orbits and their stabilities have been analysed considering variation of electron energy and density. Among the features encountered is that in both group-I and group-II, one of the characteristic frequencies may have either signs affecting then the stability of the motion, while in group-II operation a repulsion of the frequencies at a pseudocrossing leads to highly perturbed trajectories when the wiggler frequency is approximately half the cyclotron frequency. Self-fields effects can significantly impair the stability of the electron orbits. For group-I orbits, they are more important for higher wiggler frequencies and lower beam energies. For group-II orbits, they remain less important for higher wiggler frequencies and lower beam energies before reaching the inversion zone, then they behave as for group-I orbits. It should be remarked that self-fields shift the inversion zone towards higher cyclotron frequencies the thing that is obtained by either decreasing the wiggler frequency or increasing the beam energy. It is shown that the axial velocity-induced self-magnetic field has a diamagnetic effect for both groups orbits, while the wiggler-induced self-magnetic field has a diamagnetic effect for group-I orbits and a paramagnetic effect for group-II orbits. The paramagnetic and diamagnetic effects are more important for higher beam energies and densities.

Electron trajectory and growth rate in two-stream electromagnetically pumped free-electron lasers with ion-channel guiding

A theory of the two-stream electromagnetic wave wiggler free-electron lasers (TSEMWFEL) with ion-channel guiding is proposed and investigated. An analysis of the two-stream steady-state electron trajectories is done by solving the equation of motion in the electromagnetic wave wiggler and ion-channel guiding. Numerical calculations show that there are seven groups of trajectories rather than the two groups reported for the conventional free-electron laser (FEL). The dispersion relation is derived by employing linear fluid theory. The characteristics of the dispersion relation are analyzed numerically. The results show that employing two streams rather than a single stream in an FEL with ion-channel guiding gives rise to an enhancement in the growth rate, and using ion-channel guiding instead of an axial magnetic field in a two-stream FEL causes the growth rate to increase. Our numerical study of the normalized maximum growth rate and maximum wavenumber as a function of ion-channel frequency for different trajectories is presented.

Electron trajectory and growth rate in a two-stream electromagnetically pumped free electron laser and axial guide field

The effects of two-stream on electromagnetic wiggler free electron lasers (TSEMWFEL) with an axial guiding magnetic field are studied. An analysis of the two-stream steady-state electron trajectories is given by solving the equation of motion in the axial guiding magnetic field and the electromagnetic wiggler. Numerical calculations are made to illustrate the effects of the dual electron beam on the trajectories. The dispersion relation is derived employing linear fluid theory. The characteristics of the dispersion relation are analyzed numerically. The result shows that the growth rate is considerably enhanced in comparison with single-stream. The maximum growth rate is studied numerically as a function of axial guiding magnetic field for multiple electron trajectories. It is shown that the maximum growth rate of TSEMWFEL increases and decreases with respect to the axial guiding field for different trajectories.

The effects of the guide field and tapered wiggler in free-electron laser

The interaction between electromagnetic field and electron beam was investigated numerically in a free-electron laser, using a new simulation code which consist of the three-dimensional electron motion, amplitude and phase of emitted radiation. The maintenance of the quality and stability of electron beam and the resonance condition through the wiggler is important to obtain the high gain and the high efficiency. But the electron orbits diverge and become unstable, and the resonance condition is not preserved because of the three-dimensional effects on the off-axis electron and the conversion of electron energy to electromagnetic field. To prevent those defects and improve the efficiency compared with the conventional case, we used the new methods such as the axial-guide field and tapered wiggler.

Kinetic description of a planar wiggler free electron laser with ion-channel guiding

A theoretical study of electron trajectories and gain in a planar wiggler free electron laser (FEL) with ion-channel guiding is presented. A kinetic description is given. The linearized Vlasov–Maxwell equations are solved to investigate the growth rate in a tenuous-beam limit for perturbation about a general beam equilibrium distribution function, and generated harmonics are discussed. Linear gain corresponding to FEL resonance for the case of mono-energetic beam is derived and continuous tuning by varying the ion-channel density, for the fundamental mode, is illustrated.

Unified model of electron beam shot noise and coherent spontaneous emission in the helical wiggler free electron laser

A numerical algorithm for simulating electron beam shot noise in free electron lasers (FELs) is presented. Shot noise is a source of spontaneous emission that may be amplified in the self-amplified spontaneous emission regime of operation. This regime is of great importance to XUV and x-ray FELs where the spontaneous emission is currently the only effective source available for amplification. The algorithm uses a quasiuniform phase-space distribution of appropriately charge weighted macroparticles. The statistical properties of the macroparticles are derived directly from the temporal Poisson statistical properties of the real electron distribution. Unlike previous algorithms, ours does not rely upon any averaging over a resonant radiation period time scale and so more correctly describes the underlying physics. The algorithm also allows shot noise to be modeled self-consistently in unaveraged FEL models which are able to describe subwavelength phenomena such as coherent spontaneous emission (CSE). The algorithm is used in the unaveraged 1D FEL numerical simulation code FemFel and demonstrates spontaneous emission due to shot noise and CSE in both rectangular and Gaussian electron pulse current profiles. The preliminary results show good qualitative and quantitative agreement with theory.