The comparative analysis of the X-ray tube and source on the basis of parametric X-ray radiation has been carried out. The parametric X-ray radiation intensity of source on the basis of compact linear accelerator with beam energy of 6 MeV and current of 100 ?A is compared with intensity of ordinary X-ray tube. The performance of slow change of parametric X-ray line energy in a wide range from 6 to 130 keV with line width of about 300 eV may provide the good contrast of received image and decreases the radiation dos

Gogolev, A. S.

Potylitsin, A. P.

Electronic archive of Tomsk Polytechnic University

IntroductionXray sources are widely used for fundamental andapplied researches (biology, solidstate physics, microelectronics, medicine etc.). Sources developed on thebasis of electron storage rings with energy ~1 GeV forgeneration of synchrotron radiation (SR) are rather bulky and expensive devices and require significant operating costs as well. Xray tubes are rather cheaper but donot allow obtaining high resolution, for example, inlithography, medical diagnostics [1] and others.Recently beams of parametric Xray radiation(PXR) have been suggested to be used. Its spectralangular density exceeds one of traditional Xray sourcessuch as synchrotron radiation and bremsstrahlung as itwas shown in [2]. In this case there is no need for usingbeams of high energy electrons and narrow spectral linemay be obtained directly at PXR generation. Dispersionrelation [3] connects strictly PXR photon energy withthe its outgoin angle that allows obtaining a beam ofmonochromatic radiation with variable wave length.At present there are Xray radiation sources on thebasis of PXR in (Nihon University Japan) [4] and laboratories LUE (USA) [1], at electron beams with energyof 100 and 56 MeV, respectively. Average current of thelinacs used ~1 mА. Average intensity of a source [4] is~10–1 photon/е–/sr, source [1] ~10–2 photon/е/sr.In this paper the characteristics of Xray radiationsource on the basis of PXR from moderate relativisticelectrons were compared with Xray tube. Source on thebasis of linac with particle energy of 6 MeV may generate PXR with intensity of >10–5 photon/е–/st in narrowspectral range Δω/ω~10–2 and energy range 6...130 keV.Intensity of ordinary Xray tube per 100 kV is about10–6 photon/е–/sr.1. PXR yieldParametric Xray radiation refers to a class of polarization radiation the characteristics of which do notdepend on initial particle mass and are determined only by its energy and charge. Within the kinematic modelPXR mechanism may be considered as a diffraction ofthe virtualphotons field of moving charge particle oncrystal planes [5].By the moment many experiments on studying PXRproperties excited by relativistic electrons have beencarried out. It was shown that PXR of relativistic electrons γ>50 (γ – Lorentzfactor) gives high spectralangular density in a narrow cone with solution ~γ–1 aroundthe direction of mirror reflection [6]. However, in thecase of moderate relativistic particles (γ≤20) openingangle of cone in which the main virtualphotons flux isconcentrated is rather wide. As a result PXR reflectionsstipulated by the reflection of virtualphoton initial fluxfrom crystallographic planes give contributions near thereflection direction from the selected (main) surface.This effect was firstly experimentally observed by theauthors of the work [7] where a beam of electrons withenergies 15,7 and 25,7 MeV was used; correspondingly,cone apex angle amounted to 32 and 19 millirad. Theauthors registered a contribution from satellite planes inthe main peak at the level 1 %.In 2005 the experiment was carried out at the extracted beam of carbon nuclei with energy of2,2 GeV/nucleon (γ=3,36) of Nuclotron LHE JINR(Dubna). The purpose was to detect PXR in silicon crystal (001) from heavy charged particles [8]. The contribution from satellite planes in the main peak amountedto the value η~40 %.The majority of experimental data in studying PXRproperties in crystals is described well by kinematic theory [3] in which photon frequency of PXR is determined by the following dispersion relation:(1)where g is the reciprocal lattice vector for crystal planeswith interplanar spacing d=a/(h2+k2+l2)1/2; a is the latticeconstant; h, k, l are the Miller indices; v is the particle velocity vector; n=k/|k| is the unit vector in the direction ofPXR photon; с is the speed of light; ε(ω) is the target dielectric constant; β=|v|/c, is the Bragg angle (Fig. 1), θ isthe observation angle (counted from beam direction).Angular density of PXR photon yield from thin crystal plate neglecting absorption may be written down ingeneral view [3]:(2)22222 (1 / )( / ),( / ) 1iigdN Z Ld c cccω χαπ β εε ωω= ×Ω − ⋅⎡ ⎤− ⋅× ⎢ ⎥−⎢ ⎥⎣ ⎦∑∑ggk= n vv g eksin( )2 ,1 / 1 cos( )Bcdcβ θπε ε β θω⋅ =⋅ −= −g vn vMathematics and mechanics. Physics53UDC 537.533.7COMPARISON OF XRAY SOURCES ON THE BASIS OF BREMSSTRAHLUNG AND PARAMETRIC RADIATIONSA.S. Gogolev, A.P. PotylitsinTomsk Polytechnic UniversityEmail: alextpuftf@tpu.ruThe comparative analysis of the Xray tube and source on the basis of parametric Xray radiation has been carried out. The parametricxray radiation intensity of source on the basis of compact linear accelerator with beam energy of 6 MeV and current of 100 μA is compared with intensity of ordinary Xray tube. The performance of slow change of parametric Xray line energy in a wide range from 6 to130 keV with line width of about 300 eV may provide the good contrast of received image and decreases the radiation dose.where Z is the charge of incident particle; α is the finestructure constant; L is the crystal thickness; eki is theunit polarization vector; kg=k+g, χg is the expansion coefficients of dielectric polarizability; ? is the Planckconstant; Ω is the solid angle.Fig. 1. Sheme of PXR generation. Nondash coordinate systemis laboratory coordinate system, dashed is detector coordinate system In Fig. 1 nВ is the Bragg direction of PXR reflection,determined by the formula:where is the unit vector in beam direction.Formula (1) and (2) were used in the simulation basis of PXR generation process; crystal thickness in allcases equaled to 100 μm. Code which allows taking intoaccount influence of such factors as radiation absorption, beam size, divergence, multiple scattering, energylosses and final aperture of detector by MonteCarlomethod was developed. In Fig. 2 the results of simulationin the ideal case for different Lorentz factors from a certain crystal family of silicon crystal planes are shown.According to kinematic model the PXR main radiation flux in moderate relativistic case is concentrated ina rather wide cone (Fig. 2). Therefore, at a fixed observation angle a detector there may be detected some PXRlines corresponding to various reflections. It is also seenfrom despersion relation (1) that at fixed observationangles and beam incidence PXR quantum energy fromdifferent planes may be close in value if the condition ofkinematic grouping is fulfilled:gi.v≈gj.v, i≠j. (3)To take into account correctly the contributionfrom different crystal planes the summation is carriedout by a set of vectors g in expression (2).2. Source of monochromatic radiation with tunable wave length on the basis of PXR It is possible to show that in a case when moderaterelativistic charged particle moves along the axis of type<111> and observation angle is in range θ<90( PXR reflections which give contribution >1 % relative to thestrongest in the observation direction satisfy the kinematic grouping conditions (3).Line position on energy scale in this case is determined by observation angle and does not practically depend on azimuth angle.Enhancement in this geometry at γ=3 for siliconamounts to 40 % relative to the strongest reflection (111)with observation angle of 35° from beam axis that corresponds to angular distribution maximum. Amplification is of the same order that in Bragg geometry [8]however, satellite peaks are lost except the following diffraction orders. For tungsten the angular distributionmaximum is around angle of 55° with beam axis andenhancement is 82 %. Satellite peaks are absent as wellas for silicon, Fig. 4.Increasing Lorentz factor the effect of kinematicenhancement decreases owing to narrowing the radiation cone of single reflections. For crystals with facecentered cubic lattice and diamond type lattice enhancement does not exceed 7 % at γ=12. Whereas for crystals with volumecentered cubic lattice enhancement issignificant ~80 % at γ=12, Fig. 5.0B 0 22( ) ,⋅= − g nn n ggBulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 254Fig. 2. The simulation results of PXR angular distribution of reflection (111) from Si crystal (Bragg angle θВ=20° for different Lorentzfactors:  ⎯ – 6; – – –  – 12; ······· – 20 (neglecting absorption). Curve –■–  is the dependence of PXR photon energy on observation angle (right scale)Fig. 6 shows the PXR spectrum generated by electrons with energy of 5,6 MeV at the output from tungsten and silicon crystal (111) in Bragg geometry, for thecomparition. According to the simulation results andthe experiment [8] PXR spectrum is rather complicated. Orientation at which the angle between normal tocrystal surface and beam direction is ψ=π/2–θВ, anglebetween directions <110> and axis ОY equals to zerowas selected for certainty. It is supposed that detectorwith dimension of 300 eV is placed in the reflection maximum (111) which makes angle θy'≈γ –1 rad with Braggdirection.Calculations of intensity for ideal conditions are given in Fig. 7. In real situation a part of a beam is reflected from target surface layer owing to beam oblique incidence in the sheme of Bragg and Laue. For incidenceangle equal to 45° at electron energy of 5,6 MeV estimates of reflected particles fractions from tungsten givesMathematics and mechanics. Physics55Fig. 3. PXR angular distribution, γ=3: a) silicon (111); b) tungsten (111). Crystal is perpendicular to a beam – larger crystal face is parallel to crystal planes (111)Fig. 4. Rated PXR spectra in new geometry, γ=3Fig. 5. Rated spectra of PXR in new geometry, γ=12, observation angle in both cases is 35°the value 22 % maximum falls on a layer of 57 μm [9].So, decreasing Bragg angle a part of reflected beam increases. Thus, PXR yield is significantly suppressed in aspectral hard part in Bragg sheme; in Laue sheme suppression due to reflection is in soft part. In new shemathe reflection effect may be minimized using crystal cutalong planes (111).Fig. 7. Intensity of PXR line from Si and W targets for Bragg andLaue cases and new geometry, indices В, L and N, respectively. Electron energy is 5,6 MeVThus, if PXR line intensity exceeds 10–5 photon/е–/sr(Fig. 7) then Xray source intensity on the basis of linear accelerator with average current 100 μA and collimator solid angle equal to 10–6 sr exceeds 6,25·103 photon/s.3. Characteristics of Xray radiation sources on the basisof Xray tube and compact electron accelerator In comparison with bremsstrahlung which possessescontinuous spectrum PXR is monochromatic that in itsturn gives the possibility to increase contrast at considerably decreased radiation dose. Normalized spectra of PXRgenerated by electrons with energy of 6 MeV in tungstencrystal and Xray tube radiation per 100 kV with tungstenanode is given in Fig. 8 [10]. PXR lines for various observation angles are given in the Figure. In calculation it wassupposed that detector resolution is 300 eV and aperture is10–6 sr. In the given geometry PXR spectrum does not posses satellite lines as in the cases of Bragg and Laue.Fig. 8. Normalized spectra of PXR (solid lines) excited by electrons with energy of 5,6 MeV in tungsten crystal andbremsstrahlung (dash line) of tungsten from electronswith energy 100 keVBulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 256Fig. 6. PXR spectra from electrons with energy of 5,6 MeV at the output from crystal W and Si (111) for Bragg case. Angle θD=2θВ isthe angle between beam direction and Bragg direction (θD≈θ) W WSi SiIt is seen from comparison that source intensity onthe basis of PXR from electron beam with energy of5,6 MeV and current of 100 μA of the same order that instandard Xray tube per 100 kV with tungsten anodecurrent of which is of mA order. Radiation dose is integral under spectrum is rather higher from Xray tubeIn the work [11] the source of monochromatic Xrayradiation on the basis of Xray tube using two crystalsmonochromator was suggested. It is clear that monochromator use results in partial radiation loss. It isnecessary to increase current in compensation. Theauthors of the work [11] need a beam power of Xraytube beam up to 2...4 kW to overlap energy range from 3to 40 keV to obtain intensity of 104 photon/s. The design beam power of the monochromatic Xray radiationsource on the basis of PXR of the same intensity equalsto 0,6 kW and overlapped range is 6...130 keV.Estimate of PXR line width from tungsten crystalwith thickness of 100 μm accounting multiple scatteringamounts to the value FWHM=280 eV from electron beam with energy of 5,6 MeV and aperture of forming collimator equal to 10–6 sr with area of input window 1 cm2.Conclusion The monochromatic Xray source on the basis ofcompact electron accelerator with energy of 5,6 MeVand beam current of the order 100 μA using parametricXray radiation in comparison with Xray tube was examined. Such source intensity with tungsten crystal isabout 104 photon/s in energy range from 6 to 130 keVwith line width of 280 eV.It is seen from source characteristics comparisonthat the source on the basis of parametric Xray radiation possesses a number of advantages: firstly, monochromaticity and capacity of tunning of a PXRpeak energy allows increasing the resolution of studied object; secondly, radiation dose to the object decreases by an order of magnitude; thirdly, radiationintensity of the same order that the Xray tube possesses at rather decreased power input. For example,to obtain Xray radiation in the range from 6 to 130keV for applying in medicine by Xray tube the beampower up to13 kW is required while beam power ofthe source on the basis of parametric Xray radiationis about 1 kW.The work is fulfilled at partial support of RFBR grants060281016Бел_а, 050850244а.65max2,37 10 17,7.1,34 10BRPXRYY⋅= =⋅Mathematics and mechanics. Physics57REFERENCES1. Sones B., Danon Y., Block R.C. 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Comparison of X-ray sources on the basis of bremsstrahlung and parametric radiations

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