Undulator Magnetic Field Research Articles

Waveguide tapering for FEL in the high gain regime

A free electron laser (FEL) operation in the far infrared or millimeter wave region of the spectrum requires the use of a waveguide to confine the radiation. A new tapering scheme for the operation in the high gain regime, in the amplifier configuration, can thus be utilized in which the waveguide gap is varied while the undulator magnetic field and period are kept constant. The results of a numerical code are presented.

The gain and efficiency enhancement in double-undulator FELs induced betatron oscillations

A new construction of a free-electron laser using induced betatron oscillations to increase the FEL gain or efficiency is proposed. Induced betatron oscillations are driven by an additional space-periodic magnetic field with a period close to that of electron betatron oscillations in an undulator magnetic field. The induced oscillation amplitude proves to be sensitive to electron energy variation. In the result one more mechanism causing electron grouping in a ponderomotive wave takes place. This mechanism can cause the increase of the gain in a small-signal regime or the realization of an amplification regime close to an autoresonance when FEL efficiency grows essentially.

Correlation between measured undulator magnetic fields and x-ray spectraa)

Electron storage ring insertion devices, especially undulators, are designed using ideal device theory and the resulting x-ray spectra are reasonably close to predictions in most cases. However, magnetic field errors result in nonideal x-ray spectra. These effects can be calculated theoretically, and may also be measured. Here we present a study of an undulator whose magnetic fields and x-ray spectra have been measured carefully. We compare experiment and theory and explain the deviation from ideal of the shape of the undulator’s spectral peaks in terms of magnet errors.

Undulators and Free-Electron Lasers

Bibliographical note Early developments Overview of the general operational principles Motion of an electron in an undulating magnetic field Undulator radiation Small-signal, small-gain free-electron laser Large gain Saturation Tapered undulators Undulator operation Magnet design Experiments and applications Appendix A. Concepts of Hamiltonian relativistic mechanics Appendix B. Effective mass Appendix C. Undulator and FEL formulary.

Quantum mechanical theory of spontaneous emission in a magnetic wiggler by a high-energy electron beam

Unstimulated bremsstrahlung in a transverse undulating magnetic field («magnetic wiggler») by a relativistic electron beam is investigated by means of relativistic quantum kinetics in which the incident laser wave is the first-order perturber to the electron motion, while the magnetic wiggler is treated as a classical field, which wiggles the electrons in the transverse direction. Thus, the unper-turbed state is represented by the solution of the first-order Dirac equation describing the motion of a relativistic electron in the magnetic wiggler approximated as an electromagnetic wave, and the solution is derived from the Volkov solution. It is found that the spontaneous-emission power in the laser-axis direction scales as the cube of the electron energy.

Enhanced emission of high frequency radiation from an electron beam in an undulator by backward wave resonance

For an electron moving in an undulating magnetic field, there are two frequencies of radiation that can produce a resonance. There is a forward wave which corresponds to the free electron laser (FEL) resonance and there is also a backward wave. In the electron frame of reference these two resonances are identical except for the direction of the Poynting vector of the radiation. In the lab frame, however, the frequency of the forward wave appears upshifted and the frequency of the backward wave seems downshifted. Because of the correspondence between the two resonances, the backward wave can be used to stimulate incoherent emission of radiation at the frequency of the forward wave. A scheme is proposed for the utilization of the correspondence of these resonances. A backward wave at near twice the undulator wavelength can be used to produce incoherent radiation at the frequency of the forward resonance, which for sufficiently energetic electron beams could be in the XUV spectral region. The process could be used to enhance the radiation power over self-amplified spontaneous emission in single-pass XUV FELs. Some computer simulations are performed to estimate the amount of enhancement possible.

The study of interaction of electrons with an electromagnetic wave in an undulator

The results of an experimental investigation of electron beam spectral distribution after interaction with external electromagnetic waves in an undulator are given. The initial electron energy was 12 MeV, external electromagnetic wave power was 50 MW, the wavelength being 10 μm. A helical 20-cm-long undulator with a period length of 9.5 mm was used. The dependence of spectral distribution maximum change on undulator magnetic field strength was measured. The results are in good agreement with estimated findings taking into account the real parameters of the experimental setup. Electron energy maximum change was ±20 keV which is a result of electron acceleration or deceleration by the electromagnetic wave in the undulator.

Free electron lasing in a longitudinal electric wave

It is shown that stimulated bremsstrahlung in the transverse undulating magnetic field alone decreases with the electron energy. The amplification of a laser wave by single-photon stimulated bremsstrahlung in an longitudinal electric wave propagating in the lasing beam direction (traveling longitudinal electric wiggler) is calculated from relativistic quantum-mechanical principles. It is found that the single-pass gain by stimulated bremsstrahlung of a lasing bunch in an envisioned two-beam wake-field cavity is sufficiently great to generate a coherent radiation in the soft X-ray region.

Free electron lasing in a transverse undulating magnetic field

It is shown that stimulated bremsstrahlung in a transverse undulating magnetic field (“magnetic wiggler”) is a quantum effect which relativistic electrons cannot exhibit by the correspondence principle. It is suggested that free electron lasing in a magnetic wiggler is due to stimulated bremsstrahlung in the longitudinal space-charge electric field associated with density bunching produced by the magnetic wiggler. The laser gain and wavelength of free electron lasing in the magnetic wiggler by an electron beam in the single-electron interaction regime is formulated.

Net acceleration of high-energy electrons by net inverse Bremsstrahlung of a laser wave in a uniform magnetic field and a transverse undulating magnetic field

The nonzero net dc force acting on relativistic beam electrons traveling in a uniform magnetic field, a laser wave, and transverse undulating magnetic field (magnetic wiggler) is calculated by using quantum-kinetics in accordance with the correspondence principle. It is found that the average of this force can be as strong as the Lorentz force of the laser wave in an electron energy region beyong energies for free electron lasing, and decreases linearly with the inverse of the electron energy far beyond this energy region.

Quantum-kinetic calculation for net acceleration of high-energy electrons by a transverse undulating magnetic field and an electromagnetic wave

The average force acting on a highly relativistic electron beam traveling in a laser wave and a transverse undulating magnetic field (magnetic wiggler) is calculated using quantum kinetics. The quantum-kinetic calculation shows that the net dc force due to net inverse bremsstrahlung in the magnetic wiggler (“inverse free electron lasing”) increases linearly with the beam energy, and can be greater than the Lorentz force of the laser wave.

Dispersion equation of FEL with combined undulator and uniform magnetic field

A general quintic dispersion equation, describing the linear stage of the amplification of an electromagnetic wave in FEL-ubitrons with a combined spiral undulator and longitudinal uniform magnetic field, is derived. It is shown that the relativistic electron beam in such an undulator has four normal waves: two longitudinal waves (fast and slow waves of space charge) and two transverse waves, which in the limiting case of vanishingly small amplitude of the undulator field transform into fast and slow cyclotron waves. The instability increments are found in the case when the electromagnetic wave is synchronized with the longitudinal or transverse beam waves both separately and at the same time. It is shown that for low beam current the increment is all the higher the larger the number of electron waves participating in the interaction with the signal wave.

Generation of a given linear polarized radiation in a plane undulator

The distribution of the undulator magnetic field providing generation of monochromatic radiation with a relatively large angle between the electron velocity vector and the undulator axis is found. The possible trajectories of the particle motion are investigated.

Increasing the acceleration gradient of the transverse-field accelerator using a dielectric medium

A gas-loaded undulator is proposed as a method for the coupling of intense optical radiation and charged particles to achieve high-gradient acceleration of 100 MeV/m or more. The theory of the gas-loaded inverse free electron laser (IFEL) is the same as that of the vacuum IFEL, with the exceptions that the phase-matching condition between the optical field and the charged particle is changed, and that multiple scattering of the electrons by the gas molecules has been introduced. The new phase matching condition allows reasonable undulator magnetic fields while still maintaining good acceleration gradients for extremely relativistic beams. Synchrotron radiation losses can then be kept to acceptable values. A Monte Carlo simulation of the interaction has been done which includes elastic scattering, radiation losses, laser and electron beam characteristics, and gas and helix parameters. As with the conventional IFEL, tapering the undulator with an increasing magnetic field is found to affect both the maximum energy and population of the accelerated particles.

Oscillator evolution in free-electron lasers

In a free-electron laser oscillator, both the amplitude and frequency of the optical field are free to evolve. We use a Lagrangian formalism to describe the dynamics of the interacting electron beam and optical wave in a single pass. The character of the evolution over many passes is controlled by the design of the undulating magnetic field in the free-electron laser interaction region. Several laser magnet designs are presented under the same formalism and compared: the undulator, the tapered undulator, the optical klystron, and transverse gradient ("gain-expansion") undulator. For each of these designs we numerically calculate the gain as a function of optical amplitude and frequency. These "gain surfaces" are used to infer a variety of properties of oscillator evolution and clearly demonstrate the relative merits of each magnet design.

Theory of free electron laser instability in a relativistic annular electron beam

A self-consistent theory of the free electron laser instability is developed for a hollow electron beam propagating through an undulator (multiple mirror) magnetic field. The stability analysis is carried out within the framework of the linearized Vlasov–Maxwell equations. It is assumed that the beam is thin, with radial thickness much smaller than the mean beam radius, and that ν/γb≪1, where ν is Budker’s parameter and γbmc2 is the characteristic energy of the electron beam. The dispersion relation describing the free electron laser instability in a hollow relativistic electron beam is obtained for an equilibrium distribution function in which all electrons have the same value of transverse energy and the same value of canonical angular momentum, and a Lorentzian distribution in axial momentum. It is shown that the influence of finite radial geometry plays a critical role in determining the detailed stability behavior. Moreover, the growth rate and bandwidth of the instability can be expressed in terms of Budker’s parameter ν, instead of the plasma frequency as in the case of a uniform density beam. Furthermore, it is found that free electron laser stability properties exhibit a sensitive dependence on axial momentum spread.