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Small-signal gain for parabolic profile beams in free-electron lasers

机译：自由电子激光器中抛物线形光束的小信号增益

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Abstract: Three new types of free electron lasers (FELs) that are being examined in new ranges of parameter design space are: compact systems, XUV systems, and high power devices. Shorter wiggler wavelengths, shorter or longer lasers, higher currents, and higher quality electron beams are a few of the trends in the FEL community. The primary predictor of FEL oscillation is the small signal gain. We present 3-D small-signal calculations for more realistic parabolic-profile electron beams in the limit of moderately wide to wide electron beams. This limit complements the thin electron beam limit and needs be included in any analytical approximation that encompasses all 3-D effects. The system of equations for the optical modes are of Hamiltonian form and are solved as the analytical eigenmodes of the stationary quantum mechanical harmonic oscillator. We show the complete solution to the initial value problem in the special case of a cold, resonant electron beam, including the damped modes heretofore neglected. From this we derive the asymptotic solution as a superposition of Hermite $LB@square symmetry$RB or Laguerre (circular symmetry) modes. We give expressions for the mode size, the spatial growth rate, and injection fraction for the dominant mode.!4
机译：摘要：在参数设计空间的新范围内正在研究的三种新型自由电子激光器（FEL）是：紧凑型系统，XUV系统和高功率器件。较短的摇摆器波长，较短或较长的激光，较高的电流和较高质量的电子束是FEL界的一些趋势。 FEL振荡的主要预测指标是小信号增益。我们提出了3D小信号计算，用于在中等宽度至宽电子束范围内更真实的抛物线轮廓电子束。此限制补充了细电子束限制，需要包含在所有3D效应的任何分析近似中。光学模式的方程组是哈密顿形式，并作为固定量子力学谐波振荡器的解析本征模式求解。我们展示了在冷共振电子束的特殊情况下初始值问题的完整解决方案，包括迄今忽略的阻尼模式。由此，我们得出渐近解为Hermite $ LB @ square symmetry $ RB或Laguerre（圆对称）模式的叠加。我们给出了主要模式的模式大小，空间增长率和注入分数的表达式!! 4

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