## Undulators and free-electron lasersThis new reference is the first fully self-contained and unified monograph on the design and operation of undulators and free-electron lasers. It will be of use to all those working in free-electron laser research as well as for physicists and graduate students who need an introduction to the field. The book includes a convenient overview of early developments and general principles. The different models that are used to describe free-electron laser are presented, sensibly organized according to their range of applicability. Conceptual and mathematical constructs are covered, with an emphasis on obtaining practical results in a simple yet rigorous fashion. Interaction of the undulator with the driving accelerator is treated along with the laser cavity and the design of undulator magnets. A very useful overview of several typical experiments is also included. |

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### Contents

Overview of the general operational principles | 31 |

Motion of an electron in an undulating magnetic field | 45 |

Undulator radiation | 61 |

Copyright | |

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### Common terms and phrases

accelerator according to eqn amplifier amplitude angle angular approximation Aueff axial betatron Boltzmann equation bunch calculated Chapter co-ordinates coefficients coherent component condition corresponding current density detuning parameter dimensionless dispersion equation distribution e-beam E-frame electromagnetic field electromagnetic wave electron beam electron motion electron trajectory emittance emitted energy extraction energy spread equations of motion expression free-electron laser frequency function gain Gaussian beam given by eqn Hamilton equations Hamilton-Jacobi Hamilton-Jacobi equation Hamiltonian harmonic initial input wave integral interaction large-gain linac linear Luchini Madey's theorem magnetic field maximum micropulse mirror modes momentum Motz non-linear number of periods obtained optical klystron optical resonator orbit output particle perturbation phase pulse quantum radiated field regime relativistic Section sinusoidal small-gain solution spontaneous emission storage ring synchronous synchrotron radiation tapered undulator theory transformation transverse ultrarelativistic undulator field undulator length undulator period undulator radiation variables vector potential velocity waveguide wavelength wavenumber zero