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Partially Coherent X-Ray Oscilex Radiation from a FEL-Modulated Positron Bunch during Its Planar Channeling in a Crystalline Undulator

Hayk L. Gevorgyan, Lekdar A. Gevorgian

TL;DR

The paper addresses zero-angle radiation from a microbunched positron beam channeled in a crystalline undulator (CU) embedded in a dispersive medium, revealing a soft Oscilex component arising from medium polarization in addition to conventional undulator radiation. It develops a comprehensive framework combining undulator theory in a dispersive medium with form-factor-based partial coherence to derive spectral line shapes and photon numbers for both channeling- and CU-driven Oscilex radiation, for Gaussian bunch distributions. The study provides analytic expressions for spontaneous and partially coherent Oscilex photons, and demonstrates, with LCLS- and SASE XFEL-based parameters in a diamond CU, that Oscilex photon yields can exceed the number of positrons by 1–2 orders of magnitude and that coherence gains can reach $10^3$–$10^4$, suggesting the generation of powerful, directed, monochromatic X-ray beams. The results have potential practical impact in beam-based X-ray sources and indicate similar Oscilex effects may occur in axial electron channeling as well.

Abstract

The radiation emitted at zero angle by a microbunched positron bunch undergoing planar channeling in a crystalline undulator (CU) is studied. The bunch energy is assumed to be far above the threshold for radiation generation in the dispersive CU medium. Besides the usual ``hard'' undulator radiation produced by channeling oscillations (channeling undulator radiation) and by the CU bending (crystalline undulator radiation), a ``soft'' medium-polarization component also appears at zero angle due to the oscillations that excite atomic electrons. We refer to this soft component as Oscilex (oscillationally-excited) radiation. Since the two types of oscillations have different frequencies, they yield two distinct frequency components of both undulator and Oscilex radiation. The Oscilex frequencies are set by the plasma frequency and the characteristic oscillation frequency and are, to high accuracy, independent of the positron energy. The CU period is chosen so that the radiation wavelength is not shorter than the microbunch length, ensuring coherent emission from microbunches and partially coherent Oscilex emission from the full bunch. Analytical expressions are obtained for the spectral line shapes and the number of photons of spontaneous Oscilex radiation. For partially coherent emission, Gaussian distributions are used for both the bunch and microbunches. Gain factors for the two Oscilex components, including longitudinal form-factors, and the total number of partially coherent photons are derived. A positron bunch with LCLS parameters, modulated by SASE XFEL, channeling between (1 1 0) planes of a periodically bent diamond crystal is analyzed. The number of spontaneously emitted Oscilex photons exceeds the number of positrons by $1\text{÷}2$ orders of magnitude, and the gain factors reach $10^3 \text{÷} 10^4$.

Partially Coherent X-Ray Oscilex Radiation from a FEL-Modulated Positron Bunch during Its Planar Channeling in a Crystalline Undulator

TL;DR

The paper addresses zero-angle radiation from a microbunched positron beam channeled in a crystalline undulator (CU) embedded in a dispersive medium, revealing a soft Oscilex component arising from medium polarization in addition to conventional undulator radiation. It develops a comprehensive framework combining undulator theory in a dispersive medium with form-factor-based partial coherence to derive spectral line shapes and photon numbers for both channeling- and CU-driven Oscilex radiation, for Gaussian bunch distributions. The study provides analytic expressions for spontaneous and partially coherent Oscilex photons, and demonstrates, with LCLS- and SASE XFEL-based parameters in a diamond CU, that Oscilex photon yields can exceed the number of positrons by 1–2 orders of magnitude and that coherence gains can reach –, suggesting the generation of powerful, directed, monochromatic X-ray beams. The results have potential practical impact in beam-based X-ray sources and indicate similar Oscilex effects may occur in axial electron channeling as well.

Abstract

The radiation emitted at zero angle by a microbunched positron bunch undergoing planar channeling in a crystalline undulator (CU) is studied. The bunch energy is assumed to be far above the threshold for radiation generation in the dispersive CU medium. Besides the usual ``hard'' undulator radiation produced by channeling oscillations (channeling undulator radiation) and by the CU bending (crystalline undulator radiation), a ``soft'' medium-polarization component also appears at zero angle due to the oscillations that excite atomic electrons. We refer to this soft component as Oscilex (oscillationally-excited) radiation. Since the two types of oscillations have different frequencies, they yield two distinct frequency components of both undulator and Oscilex radiation. The Oscilex frequencies are set by the plasma frequency and the characteristic oscillation frequency and are, to high accuracy, independent of the positron energy. The CU period is chosen so that the radiation wavelength is not shorter than the microbunch length, ensuring coherent emission from microbunches and partially coherent Oscilex emission from the full bunch. Analytical expressions are obtained for the spectral line shapes and the number of photons of spontaneous Oscilex radiation. For partially coherent emission, Gaussian distributions are used for both the bunch and microbunches. Gain factors for the two Oscilex components, including longitudinal form-factors, and the total number of partially coherent photons are derived. A positron bunch with LCLS parameters, modulated by SASE XFEL, channeling between (1 1 0) planes of a periodically bent diamond crystal is analyzed. The number of spontaneously emitted Oscilex photons exceeds the number of positrons by orders of magnitude, and the gain factors reach .

Paper Structure

This paper contains 9 sections, 31 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Theory of Undulator Radiation
  3. Oscilex Radiation
  4. Partially Coherent Radiation and Form-Factors of a Bunch
  5. Partially Coherent X-ray Radiation from a Microbunched Bunch in a CU
  6. Partially Coherent Oscilex Radiation due to Channeling Oscillations
  7. Partially Coherent Oscilex Radiation due to CU Oscillations
  8. Numerical Results
  9. Conclusion

Figures (1)

  • Figure 1: Scheme of the experiment to obtain a powerful, super-monochromatic, and directed X-ray photon beam. A schematic diagram of a single-pass Free Electron Laser (FEL) operating in the Self-Amplified Spontaneous Emission (SASE) mode is used [https://arxiv.org/pdf/hep-ph/0106314] with the addition of a Crystalline Undulator (CU) and the Oscilex radiation generated within it. In the original figure, the bunch density modulation (microbunching), which develops in parallel with the SASE XFEL radiation power, was shown in the lower part.