VOLUME 38, NUMBER 1 PHYSI t" AL REVIEW LETTERS 3 JxwvaRv 1977 Measurements of the Frequency Spectrum of Transition Radiation* Michael L. Cherry and Dietrich Muller Enrico Ferjni Institute and DePartment of Physics, University of Chicago, Chicago, Ittinois 60637 (Received 28 June 1976) We report a measurement of the frequency spectrum of x-ray transition radiation. X rays were generated by electrons of 5 and 9 GeV in radiators of multiple polypropylene foils, and detected in the range 4 to 80 keV with a calibrated single-crystal Bragg spec- trometer. The experimental results closely reproduce the features of the theoretically predicted spectrum. In particular, the pronounced interference pattern of multifoil radia- tors and the expected hardening of the radiation with increasing foil thickness are clearly observed. The overall intensity of the radiation is somewhat lower than predicted by cal- culations. The physical characteristics of x-ray transi- two media. " Using procedures that have been tion radiation have mainly been studied in mea- discussed earlier, 4' "we integrate Eq. (1) over surements of the total radiation yield. Various angles and take into account possible reabsorp- radiator-detector configurations' ' have led to tion of x rays inside the radiator. The resulting results which are in fair agreement with the the- frequency spectrum exhibits striking deviations oretical predictions' "(including the expected from that of a single interface: Pronounced max- saturation of the yield at high particle energies). ima and minima occur; and, for sufficiently high However, a precise measurement of the frequen- particle energy, the spectrum saturates, i.e., it cy sPectrum of this radiation is a much more sig- becomes independent of the particle energy. It nificant test of the theory, and, furthermore, should be pointed out that such oscillations do oc- leads to details crucial for the design of transi- cur even in the case of a single foil (N= 1). If tion-radiation detectors for relativistic particles. the ratio l,/l, is large (i.e. , l,/l, & 10), the shape The results of such a measurement are reported of the spectrum is largely determined by the sin- in this Letter. gle-foil interf erence, although the multiple-foil Let us denote the distribution of the transition- interference governs the saturation at high ener- radiation intensity with respect to the emission gies. '" The exact spectral shape and the posi- angle 8, and the frequency &o, as d'S/d8dcu. In tions of maximum intensity are determined by the idealized case of relativistic particles trav- the dimensions of the radiator. ~ Knowledge of ersing a single interface between two different these details is of prime importance for practi- media, this distribution yields, after integration cal applications. over angles, a frequency spectrum that is a mon- In the present experiment, performed at the otonic function of the x-ray energy "In p.ractice, Cornell University synchrotron, we have mea- intensity considerations require a radiator of sured the transition-radiation spectrum, gener- many interfaces. The radiator dimensions and ated by electrons of 5 and 9 GeV in radiators of the x-ray wavelengths may be comparable in the evenly spaced polypropylene foils (CH, ), with rest frame of a relativistic particle. Therefore, dimensions (200-1000 foils, thickness 16 to 82 the coherent addition of the radiation amplitudes ttm, spacing 1.4 mm) that are typical for practi- from the various interfaces leads to interference cal applications. A magnet was used to deflect phenomena which drastically modify the single- the electrons away from the x-ray detector. %e interface radiation pattern" d'S, /d8d~. For a have used a single-crystal Bragg spectrometer. transparent radiator of N foils of thickness ly Thus we avoided an intrinsic difficulty encount- equally spaced by distances l„one obtains ' "" ered in previous experiments"" "where a pro- portional or solid-state detector was used to measure the x-ray energy, such that single-pho- ton events became indistinguishable from events due to several simultaneous photons. One such sin'[N(l, + /Z, l,/Z, )] experiment has, however, been quite success- sin'(l, + /Z, I,/Z, ) ful" because only very short radiators were used. where Z, ,(8, cu) are the "formation zones" of the Both single- and multiple-foil interference phe- VOLUME 38, NUMBER I PHYSICAL REVIEW I.ETTKRS 5 JANUARY 1977 Scin t i I la tor 0 i f fraction ~ I I I I S4 crystal 9 GeV electrons Col lima tor Electron beam Helium Magnet 1000 Foils PXXi WX/8/XXXPXy CO 1. m C3 3 4 mm/16 p. SS CD gl LLJ LIF, peak at 9. 1 keV I I I I I I I I I I I I I I I I I I I I I I I I I I II I I I I I I I I I I I I I I I I I I I I I I I I I I It Sl s2 g :2- Scinti I lators Radiator Allfl COIOCldence scintillator A 0 p ply I I / ~ '% (Xe/CO~i Pb shielding FIG. 1. Diagram of the experimental setup. I l l I l 0 5 10 15 20 25 X-Ray Energy(keV) nomena were observed in this case. FIG. 2. Measured pulse-height distributions in the Figure 1 shows our experimental arrangement. proportional counter. The solid points show transition The x-rays reached the spectrometer through a radiation from 1000 CH& foils, while the open symbols obtained with background radiator. Note the good 0.5-cm wide collimator, 6 m from the radiator. are a agreement between the distributions outside the x-ray The spectrometer consisted of a LiF or an organ- peak. ic PET (polyethylene terephthalate) crystal, cov- ering the energy range 4 to 30 keV, and a xenon proportional counter, the signal of which was low differential yield, special efforts were re- pulse-height analyzed. The whole apparatus was quired to shield the apparatus from background. kept in a helium-filled enclosure to reduce x- The absolute ref lectivity of the crystals has ray absorption. Frequent tests were performed been calibrated with laboratory x-ray machines. throughout the runs to check the alignment be- The effective resolution varied between - 1 eV at tween spectrometer and beam. In order to nor- 4 keV and -40 eV at 29 keV. Details of these cal- malize the measured x-ray intensity to the elec- ibration measurements will be described in a tron flux, we assumed that transition-radiation separate publication. photons follow closely (i.e. , 8 =mc'/E) the tra- In Fig. 3 me show the results of our measure- jectory of their parent electrons in the absence ments for three radiators with different foil thick- of a magnetic field. This assumption was veri- nesses, normalized as photons per interface and fied by steering the beam across the spectrom- per electron. The number of foils in each radia- eter slit. With the magnet turned off, the flux tor is chosen such that the total mass (and hence of parent electrons was determined with scintil- the total photoelectric absorption) is approxi- lators by measuring the rate S1 S2 S3 2 (see Fig. mately the same in each case. Our data points 1), where A is a scintillator with an opening are corrected for the efficiency of the crystal through the center matching exactly the dimen- and the xenon counter, and for the transmission sions of the spectrometer slit. of the absorbing material (mainly helium) be- Figure 2 shows two superimposed pulse-height tween the radiator and the spectrometer. Typi- distributions, measured with the LiF crystal set cal errors are indicated. They are essentially for 9-keV x rays. One distribution mas generat- due to small changes in the electron beam and, ed with a radiator in place, while for the other mainly at low intensities, uncertainties in the the radiator was replaced by a solid block of background subtraction. For comparison with polyethylene of the same total mass. This back- the experimental results, the curves in Fig. 3 ground test has been performed for every run. show the shape of the expected distributions, cal- The distinct peak at 9 keV due to transition radi- culated as discussed above. Our data points re- ation is excellently resolved from background, produce the calculated spectral shapes excellent- and at 18 keV even a small second-order peak ly. The maxima and minima due to interference can be noticed. The width of the x-ray peaks is effects are mell resolved and appear exactly at determined by the resolution of the proportional the calculated frequencies. However, our over- counter. Because of the high resolution of the all intensity is somewhat lower than expected. crystal itself, more than 10' electrons are need- In order to fit the experimental data better, the ed for each 9-keV x-ray count. In view of this calculated spectra in Fig. 3 are scaled down by VQLUME 38, +UMBER 1 PHYSICAL REVIEW LETTERS $ JANUARY 1977 I I I I I I I I I I II IIlljllnllllli i plasmapressionn frequency of the foil material). This ex- Thickness= 4 82~m ~9 GeY 200 Foils assumes the radiator to be transparent at Io,„, and it also assumes that l,/l, » 1, i.e. , that the spectrum is determined primarily by sin- gle-foil interference. For the 82- and 50-pm ixIO— radiators, we measure the last maximum at 23 and 15 keg, respectively (see Fig. 3), while OId' =29 and 18 keV. This small but significant shift I I I I I I ( I I I I I I I I I t I I I I I I I I III II IIIIII' in frequency is caused by multifoil interference CD 4 —Thick effects.