X-ray free-electron lasers can generate intense and coherent radiation at wavelengths down to the sub-ångström region^1,2,3,4,5, and have become indispensable tools for applications in structural biology and chemistry, among other disciplines⁶. Several X-ray free-electron laser facilities are in operation^2,3,4,5; however, their requirement for large, high-cost, state-of-the-art radio-frequency accelerators has led to great interest in the development of compact and economical accelerators. Laser wakefield accelerators can sustain accelerating gradients more than three orders of magnitude higher than those of radio-frequency accelerators^7,8,9,10, and are regarded as an attractive option for driving compact X-ray free-electron lasers¹¹. However, the realization of such devices remains a challenge owing to the relatively poor quality of electron beams that are based on a laser wakefield accelerator. Here we present an experimental demonstration of undulator radiation amplification in the exponential-gain regime by using electron beams based on a laser wakefield accelerator. The amplified undulator radiation, which is typically centred at 27 nanometres and has a maximum photon number of around 10¹⁰ per shot, yields a maximum radiation energy of about 150 nanojoules. In the third of three undulators in the device, the maximum gain of the radiation power is approximately 100-fold, confirming a successful operation in the exponential-gain regime. Our results constitute a proof-of-principle demonstration of free-electron lasing using a laser wakefield accelerator, and pave the way towards the development of compact X-ray free-electron lasers based on this technology with broad applications.

X 射线自由电子激光器可以在低至亚埃区域^{1、2、3、4、5}的波长下产生强烈的相干辐射，并已成为结构生物学和化学等学科中应用不可或缺的工具⁶。几个 X 射线自由电子激光设备正在运行^2,3,4,5；然而，他们对大型、高成本、最先进的射频加速器的需求引起了人们对开发紧凑且经济的加速器的极大兴趣。激光尾场加速器可以维持比射频加速器高三个数量级以上的加速梯度^7,8,9,10，并且被认为是驱动紧凑型 X 射线自由电子激光器的有吸引力的选择¹¹ . 然而，由于基于激光尾场加速器的电子束质量相对较差，这种设备的实现仍然是一个挑战。在这里，我们通过使用基于激光尾场加速器的电子束，展示了指数增益状态下波荡器辐射放大的实验演示。放大的波荡器辐射，通常以 27 纳米为中心，最大光子数约为 10 ¹⁰每次发射，产生的最大辐射能量约为 150 纳焦耳。在设备中三个波荡器的第三个中，辐射功率的最大增益约为 100 倍，证实了在指数增益状态下的成功操作。我们的研究结果构成了使用激光尾场加速器进行自由电子激射的原理验证演示，并为基于该技术开发具有广泛应用的紧凑型 X 射线自由电子激光器铺平了道路。