### Abstract

(QFEL) have performed an averaging and the application of periodic boundary conditions to the coupled Maxwell – Schrödinger equations over short, resonant wavelength intervals of the interaction. Here, an extended, one-dimensional model of the QFEL interaction is presented in the absence of any such averaging or application of periodic boundary conditions, the absence of the latter allowing electron diffusion processes to be modeled throughout the pulse. The model is used to investigate how both the steady-state (CW) and pulsed regimes of QFEL operation are affected. In the steady-state regime it is found that the electrons are confined to evolve as a 2-level system, similar to the previous QFEL models. In the pulsed regime Coherent Spontaneous Emission (CSE) due to the shape of the electron pulse current distribution is shown to be present in the QFEL regime for the first time. However, unlike the classical case, CSE in the QFEL is damped by the effects of quantum diffusion of the electron wavefunction. Electron recoil from the QFEL interaction can also cause a diffusive drift between the recoiled and non-recoiled parts of the electron pulse wavefunction, effectively removing the recoiled part from the primary

electron-radiation interaction.

Original language | English |
---|---|

Pages (from-to) | 33429-33438 |

Number of pages | 10 |

Journal | Optics Express |

Volume | 25 |

Issue number | 26 |

DOIs | |

Publication status | Published - 25 Dec 2017 |

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### Keywords

- free-electron lasers (FELs)
- coherent optical effects
- electron wavefunction
- electron-radiation interaction

### Cite this

*Optics Express*,

*25*(26), 33429-33438. https://doi.org/10.1364/OE.25.033429

}

*Optics Express*, vol. 25, no. 26, pp. 33429-33438. https://doi.org/10.1364/OE.25.033429

**An extended model of the quantum free-electron laser.** / Brown, M. S.; Henderson, J. R.; Campbell, L. T.; McNeil, B. W. J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An extended model of the quantum free-electron laser

AU - Brown, M. S.

AU - Henderson, J. R.

AU - Campbell, L. T.

AU - McNeil, B. W. J.

PY - 2017/12/25

Y1 - 2017/12/25

N2 - Previous models of the quantum regime of operation of the Free Electron Laser(QFEL) have performed an averaging and the application of periodic boundary conditions to the coupled Maxwell – Schrödinger equations over short, resonant wavelength intervals of the interaction. Here, an extended, one-dimensional model of the QFEL interaction is presented in the absence of any such averaging or application of periodic boundary conditions, the absence of the latter allowing electron diffusion processes to be modeled throughout the pulse. The model is used to investigate how both the steady-state (CW) and pulsed regimes of QFEL operation are affected. In the steady-state regime it is found that the electrons are confined to evolve as a 2-level system, similar to the previous QFEL models. In the pulsed regime Coherent Spontaneous Emission (CSE) due to the shape of the electron pulse current distribution is shown to be present in the QFEL regime for the first time. However, unlike the classical case, CSE in the QFEL is damped by the effects of quantum diffusion of the electron wavefunction. Electron recoil from the QFEL interaction can also cause a diffusive drift between the recoiled and non-recoiled parts of the electron pulse wavefunction, effectively removing the recoiled part from the primaryelectron-radiation interaction.

AB - Previous models of the quantum regime of operation of the Free Electron Laser(QFEL) have performed an averaging and the application of periodic boundary conditions to the coupled Maxwell – Schrödinger equations over short, resonant wavelength intervals of the interaction. Here, an extended, one-dimensional model of the QFEL interaction is presented in the absence of any such averaging or application of periodic boundary conditions, the absence of the latter allowing electron diffusion processes to be modeled throughout the pulse. The model is used to investigate how both the steady-state (CW) and pulsed regimes of QFEL operation are affected. In the steady-state regime it is found that the electrons are confined to evolve as a 2-level system, similar to the previous QFEL models. In the pulsed regime Coherent Spontaneous Emission (CSE) due to the shape of the electron pulse current distribution is shown to be present in the QFEL regime for the first time. However, unlike the classical case, CSE in the QFEL is damped by the effects of quantum diffusion of the electron wavefunction. Electron recoil from the QFEL interaction can also cause a diffusive drift between the recoiled and non-recoiled parts of the electron pulse wavefunction, effectively removing the recoiled part from the primaryelectron-radiation interaction.

KW - free-electron lasers (FELs)

KW - coherent optical effects

KW - electron wavefunction

KW - electron-radiation interaction

U2 - 10.1364/OE.25.033429

DO - 10.1364/OE.25.033429

M3 - Article

VL - 25

SP - 33429

EP - 33438

JO - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 26

ER -