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FEL Gain Enhancement in an Optical Klystron

Anahit H. Shamamian, Hayk L. Gevorgyan, Lekdar A. Gevorgian

TL;DR

The paper analyzes FEL gain enhancement in an optical klystron formed by two identical undulators separated by a gap $sL$. By deriving the zero-angle spontaneous line shape $F(x,s)$ and the total radiation field, it shows that line narrowing scales with $(1+s)$ and that the FEL gain is proportional to the derivative $-\partial F(z,s)/\partial z$, with the optimum gap favoring constructive interference. Using $SASE$ XFEL and $LCLS$ parameters, the authors compute gains in the X-ray and water-window regimes, finding $G \approx 2.5$ for X-rays and up to $G \approx 90$ in the water window, indicating substantially enhanced monochromaticity despite a reduced spontaneous photon yield. The results suggest that optical klystrons can be a practical approach to improving FEL monochromaticity and performance across regimes by tuning the inter-undulator gap.

Abstract

A system comprising two identical helical or planar undulators separated by a gap -- viz., an optical klystron (OK) -- is investigated. A formula for the frequency distribution of spontaneous radiation at zero angle is derived. It is shown that the spontaneous radiation line shape gradually narrows with increasing distance (up to an optimal value) between the undulators due to the constructive interference of the radiation fields formed in each of them, while the number of radiated photons decreases. The free-electron laser (FEL) gain coefficient also gradually increases, since it is proportional to the derivative of the spontaneous radiation line shape. Using the undulator parameters of the SASE XFEL and the bunch parameters of the LCLS, the total gain coefficient in the X-ray range is on the order of 2.5 and, for a different electron energy, reaches approximately 90 in the water window frequency range.

FEL Gain Enhancement in an Optical Klystron

TL;DR

The paper analyzes FEL gain enhancement in an optical klystron formed by two identical undulators separated by a gap . By deriving the zero-angle spontaneous line shape and the total radiation field, it shows that line narrowing scales with and that the FEL gain is proportional to the derivative , with the optimum gap favoring constructive interference. Using XFEL and parameters, the authors compute gains in the X-ray and water-window regimes, finding for X-rays and up to in the water window, indicating substantially enhanced monochromaticity despite a reduced spontaneous photon yield. The results suggest that optical klystrons can be a practical approach to improving FEL monochromaticity and performance across regimes by tuning the inter-undulator gap.

Abstract

A system comprising two identical helical or planar undulators separated by a gap -- viz., an optical klystron (OK) -- is investigated. A formula for the frequency distribution of spontaneous radiation at zero angle is derived. It is shown that the spontaneous radiation line shape gradually narrows with increasing distance (up to an optimal value) between the undulators due to the constructive interference of the radiation fields formed in each of them, while the number of radiated photons decreases. The free-electron laser (FEL) gain coefficient also gradually increases, since it is proportional to the derivative of the spontaneous radiation line shape. Using the undulator parameters of the SASE XFEL and the bunch parameters of the LCLS, the total gain coefficient in the X-ray range is on the order of 2.5 and, for a different electron energy, reaches approximately 90 in the water window frequency range.
Paper Structure (6 sections, 20 equations, 1 figure)

This paper contains 6 sections, 20 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Total Radiation Field and Radiation Line Shape in OK
  3. Probability of Spontaneous Radiation and the Number of Radiated Photons
  4. Gain of Stimulated Radiation Formed in the Optical Klystron
  5. Gain in the X‑Ray and Water‑Window Regimes
  6. Conclusion

Figures (1)

  • Figure 1: Line shape $F(z,s)$ (top) and total gain coefficient $G_{h,p} (z,s) \propto - \tfrac{\partial F(z,s)}{\partial z}$ in units $K$ (bottom) as functions of the dimensionless frequency $z$, for different gap values between two undulators: $s=0$ (black dotted), $s=0.3$ (orange dashed), $s=0.5$ (blue dot-dashed), and $s=0.7$ (red). The results apply to both helical (h) and planar (p) undulators (see Eqs. \ref{['Line shape']} and \ref{['Gain']}).