We develop the basic scaling laws for the design of a proof of principle two-beam accelerator based on a solid-state active medium (TBA-AM). The essence of the paradigm is to rely on a low-charge trigger bunch which will generate a weak intensity Cherenkov wake in a dielectric extraction structure. The wake consists of a discrete spectrum of eigenfrequencies, one of which is amplified by the active dielectric material. The exponential growth of the wake, behind the trigger bunch, continues as long as virtually all the energy from the medium is depleted. At this point, the electromagnetic field reaches saturation and thus its maximum value. Beyond this peak gradient, a trailing bunch may be placed and thus accelerated. Evidently, the major difference between the proposed paradigm and the existing ones is the energy source: in existing schemes the energy is stored in the driving bunch, whereas in ours, the required energy is stored in the active medium. Special attention is paid to three quantities which characterize the interacting mode: its initial amplitude generated by the trigger bunch, its exponential growth, and its saturation level. The latter indicates that accelerating gradients in excess of $1\mathrm{GV}/\mathrm{m}$ are feasible in a less than 10 cm long structure.

中文翻译：

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基于切伦科夫尾波的两束加速器，由光学活性介质放大

我们为基于固态活性介质（TBA-AM）的原理证明两束加速器的设计开发了基本的缩放定律。该范式的本质是依靠低电荷触发器束，该触发器束将在介电提取结构中产生弱强度的契伦科夫尾波。尾波由离散的本征频谱组成，其中一个被有源电介质材料放大。只要几乎所有来自介质的能量都耗尽，在触发束后面的尾流就将继续呈指数增长。此时，电磁场达到饱和，因此达到最大值。超过此峰值梯度，可以放置尾随束并因此而加速。显然，拟议范式与现有范式的主要区别在于能源：在现有方案中，能量存储在驱动束中，而在我们的方案中，所需的能量存储在活动介质中。要特别注意表征交互模式的三个量：由触发束产生的初始振幅，其指数增长和饱和度。后者表明加速梯度超过$\mathrm{1个}\mathrm{GV}/\mathrm{米}$ 在不到10厘米长的结构中是可行的。