Abstract A quantum mechanical treatment is presented to describe slow–wave free–electron lasers (FELs) operating in the low–gain regime. Here, we address the quantum effect of electrons on the FEL operation where each electron is represented as a Gaussian wave packet with an arbitrary width. It is shown that this quantum effect should be described in two different regimes. The first regime is realized when the initial width of the electron wave packet σ z 0 is comparable to (larger or smaller than) the radiation wavelength λ L . In this regime, the gain degrades significantly as σ z 0 increases and approaches λ L . The latter regime is realized when σ z 0 is quite smaller than λ L (i.e., approximately when σ z 0 λ L / 3 ) where the behavior of the gain is opposite to that in the first regime since it decreases with decreasing σ z 0 . Therefore, it is predicted that there is an optimum initial width of the electron wave packet at which the gain is maximum.

中文翻译：

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在低增益区工作的慢波自由电子激光器的量子效应

摘要 提出了一种量子力学处理方法来描述在低增益范围内运行的慢波自由电子激光器 (FEL)。在这里，我们解决了电子对 FEL 操作的量子效应，其中每个电子都表示为具有任意宽度的高斯波包。结果表明，这种量子效应应该用两种不同的方式来描述。当电子波包的初始宽度σ z 0 与辐射波长λ L 相当（大于或小于）时，实现了第一种状态。在这种情况下，随着σ z 0 增加并接近λ L ，增益显着降低。当 σ z 0 远小于 λ L 时（即大约当 σ z 0 λ L / 3 时）实现后一种状态，其中增益的行为与第一种状态相反，因为它随着 σ z 0 的减小而减小. 所以，