BEATSA.L. Bacci, M. Bellaveglia, A. Clozza, G. Di Pirro, M. Ferrario, A. Gallo, T. Levato, E. Pace,

A.R. Rossi, C. Vaccarezza (Resp.)Laboratori Nazionali di Frascati

P. OlivaSezione INFN Cagliari

M. GambacciniSezione INFN FerraraV. Petrillo, L. SerafiniSezione INFN Milano

U. Bottigli, P. Delogu, D. GiuliettiSezione INFN Pisa

1 Introduction

The Thomson scattering X-ray sources show relevant features for several applications due to thecapability of producing intense, quasi-monochromatic, tunable X-ray beams, after collimation, stillwith a reasonably small size apparatus. Applications to medical physics are straightforward, inparticular in mammography where dose control in screening programs is the main relevant issue.The fluence rate is low if compared to those typically achievable by synchrotron sources,but stillcompatible with the requirements of radiography, moreover the facilities based on TS can be inperspective much more compact and less expensive than synchrotrons, well in excess of one orderof magnitude in both items. Hence TS sources represent an appealing alternative to conventionalX-ray tubes.The PLASMONX Thomson source combines a high brightness electron beam (SPARC [5]) and ahigh intensity laser beam (FLAME project [4]) see Fig:1; the source will be able to provide a highflux (up to 1010γ/s) of quasi-monochromatic photons and the mean energy can be varied from 20keV to hundreds keV by changing the electrons energy.The BEATS experiment is an imaging application of the Thomson radiation used on a standardmammographic phantom devoted to improve the contrast between normal and cancerous tissueswhile lowering the absorbed dose. Theoretical and experimental studies on the mammographicimaging suggest that the ideal X-ray source for mammography should produce a low tunableenergy spectrum, with a narrow energy band, in the 17-20 keV energy range [1, 2], and that thetransfer of the radiological potential of monochromatic sources to a clinical diagnosis is advisabletogether with the reduction in size and cost compared with the synchrotron facility. In the 2011the X-ray detection apparatus has been set up for the Thomson source characterization at LNF ; inspring 2012 it will be installed in the SPARC bunker and the first collision experiment is foreseenin fall 2012.

2 The Thomson scattering process

The Thomson scattering(TS) is the electromagnetic process in which each electron absorbs one(linear Thomson scattering) or more (non linear Thomson scattering) photons from (typically) alaser pulse, emitting one photon. If the electrons are ultra relativistic the scattered radiation looksfrequency upshifted and it is emitted forward with respect to the motion of particles, in a smallcone of aperture roughly given by the inverse of their Lorentz relativistic factor. The physics of TSis quite complex in the non linear regime which holds when the density of the incoming photons islarge enough, i.e. when the laser pulse strength a0 = 8.5× 1010(Iλ2)1/2 reaches unity, being I andλ the pulse intensity and the wavelength, respectively. At intensities above the so-called relativistic

Figure 1: CAD drawing of the PlasmonX electron beam transfer lines layout.

intensity Iλ2 = 1018mm2W/cm2 the extremely intense electric field makes the electrons quiveringspeed approaching the light speed, making the magnetic field relevant for dynamics thus generatinga complex particle motion.The computation in the far-field of the scattered photons distributionNg of pulsation ω can be performed in the classical regime provided that the energy of the electronsis far below tens of GeV, as it is our case . A detailed description of the analytical computationof the scattered radiation distribution valid in the case of a planar, flat-top pulse can be foundin [6]; the analytic results show that the spectral distribution of the photons emitted by a singleparticle is almost completely correlated with the scattering angle and it is composed by a sum ofharmonics

d2NγdωΩ

∼=∞∑n−1

V (n, θ, φ)δ(ω − nωf ) (1)

of the fundamental pulsation:

ωF ∼= ωL · 4γ2/(1 + γ2θ̃2 + a20/2) (2)

being γ the Lorentz relativistic factor, ωL the laser pulsation, V (θ, φ) a structure functionwith complex dependance on particle energy, incidence and scattering angles (θe, φe), see [?] Whatis relevant is that in the linear regime (a0 � 1), that is our case, only one harmonic is producedwhile with a weak non linearity (a0 ≈ 1) only a few harmonics are generated.

3 The electron beam

The electron beam generation system must be able to produce and transport electron bunchescharacterized by an energy Ebeam ≈ 30MeV , (corresponding to γ = 60), reaching the focal spotwith a transverse size comparable with the laser focal spot size (σx, y ≈ 810µm) and minimizingthe hourglass effect [7], in order to allow the optimization of the geometrical overlapping withthe laser pulse on the whole interaction duration. These considerations imply severe constraintson the longitudinal energy spread and on the transverse emittance of the electron beam at theinteraction point: the SPARC-LAB Thomson source is meant to produce high brightness electronbeam able to accomplish to the experiment requirements, the electron beam transfer lines providethe beam transport from the phoinjector up to the interaction point preserving the 6D-phase space

characteristics and providing the required final strong focusing for the interaction with the laserpulse. In Fig. 2 the transverse beam rms size evolution is reported for the reference working pointsetup starting from the photoinjector down to the IP as obtained from the simulations performedwith the Tstep code tracking 15 kparticles, for a beam energy of 30 meV, and a quite high valuefor the starting normalized emittance �nx,y ≈ 2.7µm.

Figure 2: Rms beams sizes evolution along the transfer line (left), and detail of longitudinal ”tun-ability” of the beam waist at the interaction point.

4 The source simulation

The properties of the photons emitted by the whole electron bunch can be simulated by summingup the intensity contributions of each electron (i.e .in the incoherent regime). To do that we haveemployed the Thomson scattering simulation tool (TS)2 code developed by P. Tomassini et al [3].The code works as follows: the secular trajectory of each particle of the bunch is first computed byneglecting transverse ponderomotive effects (this approximation is fully consistent with the laserpulse and electron bunch parameters considered in this paper, see Tomassini et al. [6]. Since theanalytical outcome sketched in Eq. 1 and 2 are valid only for the case of planar long flat-top laserpulse, the code decomposes the pulse in a sequence of single cycles of the laser pulse, each cyclehaving its own phase shift and intensity. While the particle is moving along its secular path, itinteracts with different cycles of the pulse and the coherent summation of the radiation emitted ineach cycle gives rise to the radiation emitted during the entire interaction.

5 The TS laser pulse parameter optimization

The laser used in this experiment is the FLAME laser at LNF: a Ti-sapphire laser able to deliverpulses with energy up to 6J, whose duration can vary from a few ps down to 20 fs, with a repetitionrate of 10Hz [16]. In our case to fit the electron bunch length the laser pulse willbe only partiallycompressed to attain few ps duration. A well optimized laser is meant to generate the highestX-ray flux while keeping the relative energy spread of the radiation below 20% FWHM for thefundamental harmonic. An additional requirement is that high order harmonics should be as lowas possible in order to prevent their enhancement after filtration.Free parameters are:

• pulse focusing size w0 (waist size),

• pulse duration T,

• acceptance angle θM of the scattered radiation.

Two, competitive phenomena play the major role: at very small focusing size the diffraction makesthe laser pulse to spread transversally in a longitudinal size 2ZR = 2πw

20/λ smaller than the

electron bunch length σL, making the queue of the bunch to interact with a poorly intense laserpulse; on the opposite side, a too large focusing size reduces the pulse intensity and thus thescattered radiation yield. Further the pulse duration T is linked to the non linear phenomena thatappear at high pulse intensity while the diffraction effect imposes an upper limit to T.The requirements for the maximum energy spread and high order harmonics maximum intensityimpose strong constrain on the maximum collecting (or acceptance) angle θM , Since the energy ofa scattered photon is almost completely correlated with the scattering angle, see 2, in a linear orweakly non linear regime it comes out that by collecting the radiation within a cone of half apertureθM = 1/γ an overall energy spread exceeding 50% is obtained. As result of the optimizationprocess described in detail in [8] a laser pulse of waist size w0 = 15µm, duration T = 6ps, intensityI = 2.3× 1017W/cm2 and amplitude a0 = 0.33 has been chosen to collide with the electron bunch.The backscattered radiation will be collected within a cone of aperture θM = 8mrad, yieldinga flux of 1.5 × 108photons/shot with an energy spread of 20% FWHM. In Fig. 3 the spectral-angular (integrated in the azimuthal angle φ) distribution of the collected radiation is shown.Thefundamental at energy about 20 keV and the second harmonics are clearly visible while the thirdharmonic is much less intense. Note the dependence of the energy on the scattering angle.

Figure 3: Spectral-angular(integrated in the azimuthal angle φ) distribution of the collected radiationfor the optimized parameters w0 = 15µm and duration T = 6ps θM = 8mrad

6 X-ray imaging simulation

The X-ray spectrum produced by the simulation code (TS)2 is used to generate images of a breastequivalent phantom, in order to evaluate image quality. A set of Monte Carlo simulations havebeen performed to explore the image quality of a mammographic phantom upon the parametervariation [8]; the code described in [9] has been used to generate the images: in the spectraldistribution of the Thomson source , Fig. ?? a central area with the mean energy Emean = 20.6keVand standard deviation of 1.7 keV has been selected, the fluence is supposed to be uniform overthe phantom. The object to be imaged is a phantom made of 50% adipose and 50% glandular

tissue. For elemental composition and density of adipose and glandular tissue values from ICRUReport 44 [10] are used. The thickness of the phantom is 5 cm.Tumor-like masses of thickness1, 2, 5 and 10 mm are simulated. Tumor-like masses are supposed to have the same chemicalcomposition of glandular tissue and a higher density (1.044g/cm3) [11]. The considered detectoris a digital flat panel detector based on amorphous selenium (a-Se). The absorber is a directconverting a-Se of 0.25 mm of thickness, with a density of 4.28g/cm3. These parameters aretypical for mammographica-Se flat detectors. Other detector layers and structures are supposedto be negligible in the detection process [11]. Noise is considered to follow Poisson statistics. Thepixel pitch is 100µm. The image quality is evaluated in terms of dose efficiency or quality factorQ [11], defined as the ratio of the squared signal-to-noise ratio (SNR) to the mean glandular dose(MGD) [?,?]. Hence:

Q =SNR2

MGD(3)

The dose efficiency Q is expressed in arbitrary units in order to compare the imaging perfor-mances of different spectral distributions and the influence of detector resolution and blurring andthe effect of any visual system are neglected [11]. In Fig. 4 the dose efficiency calculated for theTS source is reported as a function of detail thickness. For comparison Q values are also reportedfor monochromatic sources at optimal energy and for the X-ray tube.

Figure 4: Dose efficiency of Thomson scattering source, as a function of detail thickness. Forcomparison Q is also reported for the optimal monochromatic energy and for the X-ray tube fordigital mammography.

It can be seen that Q values forTS source are 5÷6% smaller than maximum Q values obtainedby monochromatic beams. On the other hand X-ray tube shows dose efficiencies that are about40% smaller than optimal values. The percent reduction of Q values (with respect to peak Q valuesfor the same detail) for the TS source and for the X-ray tube depends on the discrepancy betweenthe mean energy of the beams and the optimal energy to image the detail. The mean energy of theTS source (20.6 keV) is very close to the optimal energies to image the details (between 20.3 and20.7keV) while the mean energy of the X-ray tube is only 17.7 keV. The different performances ofthe TS source and the X-ray tube are also due to the different energy spreads of the two beams:the TS source presents an energy spread of 1.7 keV, while the spectrum of the polychromatic beamdiffers significantly from zero in the range 10 ÷ 30keV .

7 The Experimental apparatus

In 2011 the BEATS apparatus has been set up and installed, a picture of the X-ray beamline isshown in Fig. 5.

Figure 5: X-ray beamline, (a) detail of the apparatus for collimation, monitoring and characteri-zation; (b) a view of the complete x-ray beamline

The first stage of the X-ray beamline is for x-rays monitoring and characterization, in par-ticular this system consists of:

• first wide collimation and lead shutter for beam stopping;

• a rotating collimator holder that allows to reduce the angular divergence of the beam,equipped with six different collimator corresponding to angular acceptance varying fromabout 9 mrad to 1 mrad;

• a free-air ionization chamber, used as a x-ray beam monitoring;

• two additional filter/collimator holders with six available position each, for beam filtrationor further collimation;

• a removable device based on a silicon PIN diode for X-ray flux measurement.

In Fig. 5 is also shown the table that will provide the support for imaging detectors andsample. An additional table will be placed downstream the beam to permit the study of imagingtechniques such as free-propagation phase contrast that require longer propagation distances.

7.1 X-ray beam monitor

The monitoring of the production of x-ray pulses, in order to verify the correct operation and thepulse-to-pulse intensity repeatability, is provided by a ionization chamber that collects the chargeproduced in air by radiation, without affecting the beam. This device was designed and assembledby Ferrara research unit and has been tested for stability and linearity at Larix Laboratories ofFerrara University, at University of Pisa and at the ELETTRA synchrotron facility (SYRMEPbeamline) both with polychromatic and monochromatic beams and continuous and pulsed irradia-tion. A picture of the chamber and of the electrometer used for acquisition is shown in Fig.6. The

minimum number of photons per pulse that produce a readable signal is about 106 photons withan average energy of 20 keV.

Figure 6: Xray fluence measurement system in detail.

7.2 PIN diode system for flux measurement

The current produced in a PIN diode by an x-ray beam is proportional to the rate of energyreleased in the photodiode active area by the radiation. The rate of energy released in a siliconslab depends on the incident photon energies and the flux. Owen et al. [?] demonstrate that it ispossible to measure the flux of a monochromatic x-ray beam impinging on the diode, multiplyingthe photon induced current by a coefficient calculated from the energy absorbed in the silicon layer.For our measurements a PIN diode HAMAMATSU mod. S3584-09 operating in photo-voltaic mode(i.e. without applying a reverse polarization) is used. The sensitive area of this detector is 28 x28 mm2. The diode is mounted in a metallic box with an entrance window made of an aluminum-coated polymide film to avoid photocurrent production by visible light. The x-ray absorption ofthe entrance window is negligible in the energy range of interest. A picture of the system is shownin Fig. 7

Figure 7: Silicon PIN diode system for x-ray flux measurement.

The photocurrent produced is measured by an electro-meter Keithley mod. 6517B (KeithleyInstruments Inc., Ohio, US).

Table 1: Diode calibration coefficients K, measured at synchrotron facility and evaluated fromtheoretical model.

E (keV) K (ph/C) KT (ph/C) Ratio16 2.99±0.09 × 1015 3.04 × 1015 1.0218 3.43±0.10 × 1015 3.56 × 1015 1.0420 4.14±0.12 × 1015 4.18 × 1015 1.0122 4.79±0.14 × 1015 4.91 × 1015 1.0324 5.50±0.16 × 1015 5.73 × 1015 1.04

If Q is the charge created by the interaction of a flux ϕ of x-rays with an energy hν (¡ 35keV) on a silicon diode, the photocurrent produced is I = ϕQ, and the photoconversionratio Kcan be expressed as:

K =ϕ

I=

�

e[1 − exp(−µpet])], (4)

where � is the average energy to create an electron-hole pair, e is the electron charge andµpe is the photoelectric linear attenuation coefficient of silicon. This photoconversion factor K canbe evaluated theoretically or measured, for this reason the system was previously tested at theELETTRA synchrotron facility (Trieste, Italy) with monochromatic x-rays in the energy rangebetween 16 and 24 keV. Diode response has been calibrated comparing its signal to the air-dosesignal provided by two suitable free-air ionization chambers. The coefficients K to convert thecurrent produced in the diode to the flux are shown in Table 1 in comparison with the onespredicted by the theoretical model KT , showing good agreement.

The minimum number of photons per pulse that produce a readable signal is about 103-104

photons with an average energy of 20 keV. PIN diode have proved to work properly at high x-ray fluxes (up to 1012 ph/s) but in continuous irradiation condition. High instantaneous fluxesof a pulsed source, in the case of BEATS experiment < 1020 ph/s, could produce in the diode acharge density extremely high, leading to recombination and partial collection of charge, so to anunderestimation of the real number of interacting photons. Sources with an instantaneous x-rayflux as high as needed in order to perform test on our devices are not available, and a preliminarytest on a pulsed laser (800 nm) showed the possibility to be in such a regime of partial collection.For this reason is ongoing the measure of diode response coupled to a slow scintillator (CsI) inorder to increase the time of charge production in the diode and decrease the istantaneous chargedensity.

7.3 System for energy distribution evaluation

The use of traditional spectroscopic techniques based on single photon detection, either with pho-tomultiplier coupled to scintillator or solid state device, is very difficult because of the extremelyhigh instantaneous flux produced by the source. In fact with this kind of detectors it is not feasibleto operate with sub-picosecond data acquisition time. In order to evaluate the energy distributionof the x-rays produced a technique based on the analysis of the diode photocurrent produced bybeam filtered with suitable k-edge materials has been implemented [13]. Using filters of Mo, NbZr and Al with thicknesses properly selected it is possible to obtain a measure of the energy distri-bution in an energy range from 16 to 22 keV. The technique was also tested measuring the energydistribution of an x-ray beam having a spectrum similar to the BEATS expected one by using atungsten anode x-ray tube properly filtered and powered. In Table 2 is shown a comparison of thenormalized energy distribution measured with a traditional HPGe detector ϕ(E) and the one mea-sured with k-edge technique ϕk−edge(E). It is possible to notice that the two energy distribution

Table 2: Energy distribution of the x-ray tube measured ϕ(E) and obtained from PIN diode currentϕPD(E) (normalized data).

E (keV) ϕ(E) (norm.) ϕk−edge(E) (norm.)20 0.425 0.451

are in good agreement (maximum discrepancy about 7%).

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