R & D Of A High-Average-Power Fabry-Pérot Resonator For Thomson Scattering Experiments

At present,X-rays are widely applied in solid-state physics,in the life sciences,in medical applications and in other disciplines.An X-ray source based on laser-electron interaction,that is,a Thomson scattering X-ray source,can be used to produce high-quality X-rays at a low cost and with a small-sized apparatus.The construction of compact laser-electron sources,each consisting of an electron storage ring and an optical enhancement cavity,has recently attracted the interest of many institutions.The optical enhancement cavity is mainly used to amplify the injected power,circulate the pulses at a high repetition frequency（～tens of megahertz）and produce a beam with a small waist at the interaction point.When introduced into the electron storage ring,the laser pulses produced in the high-average-power cavity scatter off high-energy electrons at a high repetition frequency.Thus,a high X-ray flux of more than 10¹¹ph/s can be obtained.In order to study the physical process inside a high-power resonator,main work has been done as follows.As a first step,we establish a precise transient model of the laser pulse stacking technique considering the CEP（carrier-envelope phase）effect and time detuning.The results of this model in the time and frequency domains match very well.A cavity with a given finesse and no detuning has a narrower linewidth than a detuned cavity with a higher finesse if both cavities have the same gain;consequently,it is easier to lock a laser to the latter cavity.Next,for the first time,we derived the non-paraxial corrections for general astigmatic beams so as to explain the S-shaped cavity mode observed in a non-planar four-mirror cavity.We solved Lax perturbation series of the wave equation for general elliptic Gaussian beams and S-shaped beam modes appear as the beam propagates away from the cavity symmetry point.This feature agrees qualitatively with observations made on a highly divergent non-planar four-mirror cavity.In addition,we study the thermal effect by using Winkler’s deformation model.The cavity gain is very sensitive to the mirror deformation in open loop.A strong feedback and ultra-low expansion mirrors are indispensable to have a high power stored in the cavity.Several significative experiments were performed on the prototype cavity for ThomX.Firstly,we proposed a new frequency stabilization method based on the polarization of a folded cavity and tuning of the cavity mirror reflectivity.Sufficient s-and p-wave phase detuning can be obtained by special design of the cavity mirrors’coatings,which give rise to an error signal that can be used for locking.Compared to the traditional PDH method,this technique is simpler without need for frequency modulation and demodula-tion.Theoretical calculations and experimental results demonstrate the feasibility of the proposed method.Meanwhile,high-power experiments on the prototype S-Box cavity for ThomX were demonstrated.A cavity finesse of approximately 26,000 is measured using four different methods,and the deposition of dust on the cavity mirrors is found to have an enormous effect on the finesse.We achieve a stable power as high as 383 kW with a cavity gain of 10,000.In addition,modal instabilities which limits this power were observed.We believe that this effect originates from cavity modal frequency degeneracy induced by thermal effect.Tsinghua University hosts a compact,low-repetition-frequency X-ray source known as TTX,which is based on a linac system and a terawatt femtosecond laser system.The next step is to upgrade TTX to a high-repetition-frequency X-ray machine called TTX2,consisting of an optical cavity and an electron storage ring.We present the complete design of a prototype optical cavity for TTX2.In summary,a Thomson scattering X-ray source composed of an electron storage ring and an optical cavity can produce a high flux of high-quality X-rays and is very promising as a compact source.