Analytical formula of free electron laser exponential gain for a non-resonant electron beam
Analytical formula of free electron laser exponential gain for a non-resonant electron beam
复制标题
非共振电子束自由电子激光指数增益解析公式
DOI：
10.1088/1674-1137/39/4/048101
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发表时间：
2015
影响因子：
3.6
通讯作者：
Jia Qi-Ka
中科院分区：
文献类型：
--
作者：
Jia Qi-Ka
研究了非谐振情况下的自由电子激光（FEL）增益公式，并明确给出了一些新的严格解析公式。对于单能非谐振电子束，以比文献中简单得多的形式得到了FEL特征三次方程解的精确表达式，并明确给出了增益长度作为失谐参数的函数。然后可以很容易地计算出不同失谐参数从低到高的增益。还给出了非谐振情况下指数增益计算的简化近似公式。对于电子束具有能量分布的情况，分别明确给出了矩形能量分布和洛伦兹分布的特征三次方程的解。此外，该显式表达式还可用于求解包含空间电荷影响的特征三次方程。分析了从低增益到高增益的转变。演示了增益带宽和最大增益失谐参数的变化。分析了小信号增益公式和指数增益公式的适用范围。
The free electron laser (FEL) gain formulas for a non-resonant case are studied, and some new rigorous analytical formulas are given explicitly. For the mono-energetic and non-resonant electron beam, the exact expression of the solution of the FEL characteristic cubic equation is obtained with a form much more simple than that in the literatures, and the gain length as the function of the detuning parameter is explicitly given. Then the gain for different detuning parameters and from low to high can be easily calculated. A simplified approximation formula is also given for the exponential gain calculation in the non-resonant case. For the case of the electron beam with an energy spread, the solution of the characteristic cubic equation is given explicitly for rectangular energy distribution and Lorentz distribution, respectively. Moreover the explicit expression also can be used for the solution of the characteristic cubic equation including the impact of the space charge. The transition from the low gain to the high gain is analyzed. The variations of the gain bandwidth and of the detuning parameter for the maximum gain are demonstrated. The applicable ranges of the small signal gain formula and the exponential gain formula are analyzed.