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laser - compton scattering is an attractive method to generate photons in an energy range from x to @xmath0 rays .
the advantages of of this scheme are ; the required electron energy is lower than those of synchrotron radiation , polarized photons can be produced and easily controlled by the incident laser beam polarization .
thanks to these advantages , this scheme can be applied to a wide area of scientific and industrial fields such as material science , medical science , particle - nuclear physics , and therefore , its characteristics and possible applications have been discussed by many authors @xcite .
one of the issues of the laser - compton scheme is to obtain sufficient photon intensity for various applications .
an optical resonant cavity is an idea to provide high power and high repetition laser pulses by coherently accumulating them in the cavity , which allows us to construct a laser - compton facility without a large scale laser system . for the coherent superposition of laser pulses ,
however , the length of the optical path in the cavity should be multiples of the wavelength with high precision , that reaches o ( 10 ) pm for the finesse of @xmath1 .
therefore , controlling the optical path length is a key issue to realize the laser system with the high finesse optical cavity .
we have developed optical cavities and performed a series of experiment to generate photon beams by laser - compton scattering at the accelerator test facility ( atf ) in kek , japan , by the collaboration of kek , waseda university and hiroshima university with a close information exchange with a group of lal orsay , france .
the initial results were published in @xcite . at the latest experiment
, we successfully kept the optical path length of the cavity with the order of 10 pm and enhanced the laser pulse intensity to 1230 times in the cavity @xcite .    for more power enhancement in the cavity ,
one order higher for example , the required precision will reach o(1 ) pm .
it could be achieved with a sophisticated optical and feedback system , however , is technically challenging to develop such system . as an alternative of precise control of the optical path length by active feedback system , we proposed an idea of self - resonating cavity , in which the optical system composed of a laser amplifier and an optical cavity keeps resonance condition by itself @xcite
.    in this article , we report a status and prospect of our effort to develop optical cavities for laser - compton scattering , including a self - resonating cavity .
a schematic of an optical cavity installed in the atf is shown in figure [ 4mcavity ] .
the cavity is a 4 mirror ring cavity with the optical path length of about 1.68 m. a discussion about various configurations of the 4 mirrors cavities is find in @xcite .
comparing with a simple two mirror cavity , the 4 mirror cavity has advantages of stability against miss - alignment of the mirrors . particularly for an operation with a tight laser beam focusing @xcite .
the main parameters of the atf and laser pulses used in the experiments are summarized in table [ parameters ] .
energy & 1.28 gev + energy spread @xmath2 & @xmath3 + beam intensity & @xmath4/bunch + bunch spacing & 5.6 ns + circumference & 138.6 m + emittance ( @xmath5 ) & @xmath6 + revolution & 2.16 mhz +   + wavelength & 1064 nm + repetition frequency & 357 mhz + pulse width & 11 ps ( fwhm ) + power & 10 w ( 28nj / pulse ) +    [ parameters ]        a unique feature of the cavity is that the 4 mirrors of the cavity are arranged in a way to make a twisted optical path for the circulating laser pulses .
it causes a geometric phase for a laser wave state in the cavity , and as a result , the cavity only resonates with left- or right- circularly polarized state separately at different optical path length .
this feature is useful for generating circularly polarized photon via laser - compton scattering and also applicable to a feedback control scheme with a simple setup @xcite .
we conducted the laser - compton experiments at the kek atf , an electron storage ring which was constructed to develop technique for an ultra - low emittance electron beam required for future linear colliders @xcite .
figure [ storage ] shows the stored power in the cavity during the operation in the atf ring .
the average power was observed to be 2.6 kw .
since the input power to the cavity was 2.1 w , the stored power was enhanced by a factor of 1230 . from the fluctuation of the stored power , 38 w ,
the precision of the optical path control was calculated to be @xmath7 pm .
we also succeeded to generate @xmath0 rays at the rate of @xmath8 with their average energy of 24 mev    it must be mentioned , while not discussed in this article , another 4 mirror optical cavity was installed by the french group in the atf and successfully demonstrated photon generation of @xmath9 photons per second with an average power in the cavity of 35 kw @xcite .
the cavity equipped an automated mirror alignment system with pound - drever - hall stabilizing technique , while the cavity described in this article adopted relatively simple mechanical configuration and the polarization based feedback system .
the average photon yield depended on the electron beam conditions during the experiments , which eventually gave us a similar number of photons per second .
the photon yields normalized by the electron intensity for both experiments were consistent with the laser power and the french cavity showed approximately 400 photons per laser - election pulse interaction , which is the world record at the time of the publication @xcite .
the obtained photon yields of @xmath10 , described in the previous section , are still not sufficient for realistic applications , thus we need to increase intensity of both electron and laser beams . in terms of the laser power in the optical cavities ,
the required precision of the optical path control will reach order of picometers or less . to avoid
the technical difficulty , an idea of the self - resonating cavity was proposed @xcite .
a configuration of the self - resonating cavity is illustrated in figure [ self - setup ] , which forms an optical loop with a laser amplifier and an optical cavity . at the beginning , a laser wave which satisfies
the resonance condition , @xmath11 , circulates in the optical loop and acts as a seed of the laser oscillation .
when the gain of the amplifier becomes sufficient to compensate over all power loss in the loop , the laser oscillation starts spontaneously with a wavelength which satisfies the resonance condition .
the length of the cavity , @xmath12 , and therefore the resonance wavelength , fluctuates due to environmental disturbances , however , the system , in principle , keeps the laser oscillation with a new wavelength chosen by the cavity .
we demonstrated the idea with a two mirror fabry perrot cavity@xcite .
the reflectivity of the mirrors are 99.999% and the intrinsic finesse of the cavity was independently measured to be @xmath13 .        as the first trial , we operated the system with continuous wave laser with the wavelength around 1047 nm .
we observed a highly stable operation with the power fluctuation of @xmath14% for more than two hours .
figure [ drop ] shows a demonstration of the stability of the self - resonating cavity . during a stable operation of the cavity
, we hit the body of the cavity with a hammer .
a sharp drop of the stored power was observed , but was automatically restored in about 40 ms , which was consistent with a damping time of the mechanical vibration of the body of the cavity .    .
what shown in b ) is a magnification of the behavior at the power recovery .
see text for the description of a sharp drop the power and its recovery . ]    the effective finesse , which is a measure of the performance of the cavity including the stability of self - resonating mechanism , was measured to be @xmath15 . the stored power in the cavity , which was calculated from the transmitted power with the transmittance of the mirror , was @xmath16 kw , showing a power enhancement factor of approximately 187,000 .
toward application of this idea to the laser - compton scattering , the mode locked pulsed oscillation is necessary .
it requires a mechanism to make pulses in the system such as a nonlinear polarization rotation optics .
in addition , mode locked oscillation requires a relation between the entire optical path and the cavity length as @xmath17 , where @xmath18 and @xmath12 are the optical path length of the entire loop and the length of the cavity embedded in the optical loop .
we succeeded a proof of the principle experiment of a mode locked oscillation with low finesse ( about 220 ) cavity as shown in figure [ self - modelock ] .
the details of the mode locked operation can be found in @xcite and the r&d toward a stable and high power storage is now in progress .
a series of experiments has been performed at the atf electron ring in kek and demonstrated photon generation by laser - compton scattering .    a new cavity based on the self - resonating mechanism has been developed and we successfully demonstrated a stable operation with continuous wave .
an effort is in progress toward realization of stable mode lock operation for the laser - compton experiment .
the authors would like to thank the members of the atf group and collaborators of lal orsay , france . this research has been supported by quantum beam technology program of japanese mext and also supported by jsps kakenhi grant numbers 23226020 , 24654076 and 25246039
we have been developing optical resonant cavities for laser - compton scattering experiment at the accelerator test facility in kek . 
 the main subject of the r&d is to increase laser pulse energy by coherently accumulating the pulses in an optical resonant cavity . 
 we report previous results , current status and future prospects , including a new idea of an optical resonant cavity .    laser - compton scattering , optical resonant cavity , self - resonating cavity