Bremsstrahlung emission and plasma characterization driven by moderately relativistic laser-plasma interactions
Sushil Singh, Chris D. Armstrong, Ning Kang, Lei Ren, Huiya Liu, Neng Hua, Dean R. Rusby, Ondřej Klimo, Roberto Versaci, Yan Zhang, Mingying Sun, Baoqiang Zhu, Anle Lei, Xiaoping Ouyang, Livia Lancia, Alejandro Laso Garcia, Andreas Wagner, Thomas Cowan, Jianqiang Zhu, Theodor Schlegel, Stefan Weber, Paul McKenna, David Neely, Vladimir Tikhonchuk, Deepak Kumar
BBremsstrahlung emission and plasmacharacterization driven by moderately relativisticlaser-plasma interactions
Sushil Singh , , , + , Chris D. Armstrong , Ning Kang , Lei Ren ,Huiya Liu , Neng Hua , Dean R. Rusby , Ondˇrej Klimo , ,Roberto Versaci , Yan Zhang , Mingying Sun , Baoqiang Zhu ,Anle Lei , Xiaoping Ouyang , Livia Lancia , Alejandro LasoGarcia , Andreas Wagner , Thomas Cowan , Jianqiang Zhu ,Theodor Schlegel , Stefan Weber , , Paul McKenna , DavidNeely ‡ , Vladimir Tikhonchuk , , Deepak Kumar , ∗ ELI Beamlines, Institute of Physics, Czech Academy of Sciences, 182 21 Prague,Czechia. Department of Radiation and Chemical Physics, Institute of Physics, CzechAcademy of Sciences, 182 21 Prague, Czechia. Laser Plasma Department, Institute of Plasma Physics, Czech Academy of Sciences,182 00 Prague, Czechia. Central Laser Facility, STFC, Rutherford Appleton Laboratory, Didcot OX11 0QX,United Kingdom. National Laboratory on High Power Laser and Physics, Shanghai Institute of Opticsand Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China. Czech Technical University in Prague, FNSPE, Brehova 7, 115 19 Prague, Czechia. LULI - CNRS, Ecole Polytechnique, CEA: Universit Paris-Saclay; UPMC UnivParis 06: Sorbonne Universities, F-91128, Palaiseau cedex, France. Institute for Radiation Physics, Helmholtz-Zentrum Dresden - Rossendorf, 01328Dresden, Germany. School of Science, Xi’an Jiaotong University, Xi’an 710049, China Department of Physics, SUPA, University of Strathclyde, Glasgow G4 0NG, UnitedKingdom Centre Lasers Intenses et Applications, University of Bordeaux-CNRS-CEA, 33405,Talence cedex, FranceE-mail: + [email protected]; ∗ [email protected] September 2020
Abstract.
Relativistic electrons generated by the interaction of petawatt-class shortlaser pulses with solid targets can be used to generate bright X-rays via bremsstrahlung.The efficiency of laser energy transfer into these electrons depends on multipleparameters including the focused intensity and pre-plasma level. This paper reportsexperimental results from the interaction of a high intensity petawatt-class glasslaser pulses with solid targets at a maximum intensity of 10 W/cm . In-situ ‡ deceased a r X i v : . [ phy s i c s . p l a s m - ph ] S e p measurements of specularly reflected light are used to provide an upper bound of laserabsorption and to characterize focused laser intensity, the pre-plasma level and thegeneration mechanism of second harmonic light. The measured spectrum of electronsand bremsstrahlung radiation provide information about the efficiency of laser energytransfer. Submitted to:
New J. Phys.
1. Introduction
High intensity laser pulse interaction with solid targets has many potential applicationsincluding fast ignition [1], ion acceleration [2] and X-ray generation [3–9]. One ofthe most fundamental aspects governing these interactions is laser absorption intorelativistic electrons. The experiment presented in this paper aims to characterize laserabsorption and bremsstrahlung generation on a petawatt-class Nd:glass laser system.When a laser pulse interacts with a solid target at oblique incidence, a significantfraction of light is reflected in the specular direction from the proximity of the criticaldensity surface i.e., the location where the plasma frequency is equal to the laserfrequency. Simultaneously, harmonics of the fundamental laser frequency are generatedby either (a) mode conversion from the resonant electric field at the critical density[10], or (b) by coherent wakefield emission [11], or (c) by reflection from relativisticallyoscillating critical density surface [12, 13]. Due to the different mechanisms of laserabsorption and harmonic generation, monitoring the spectrum and intensity of scatteredlight provides important information about the focused intensity and the laser contrast[14–16]. In particular, the curvature of the critical density surface can be inferredfrom the spatial distribution of the reflected light at the fundamental frequency andcomparing the measurements with hydrodynamic simulations of pre-plasma formationand laser absorption.At the front surface of the target, a significant fraction of the incident laser light isabsorbed and strong electromagnetic fields accelerate electrons to relativistic energies.These electrons traverse the target, and subsequently the most energetic electrons escapethe rear surface while the remaining are trapped by the sheath potential and re-circulate[17]. The escaped electrons can be directly measured by a magnetic spectrometer whilethe electrons which are slowed down by collisions within the target are diagnosed bymeasuring hard X-rays generated by bremsstrahlung [5, 18]. The multi-MeV hard X-raysgenerated in such interactions have been investigated by using photo-nuclear activation[6–8, 19–23]. X-ray measurements in the energy range of hundreds of keV to a fewMeV are also important as they provide a diagnostic of the fundamental laser-plasmainteraction physics, in addition to developing laser based sources for flash radiographyapplications [3–5, 24–27]. Experiments focused on investigating X-rays in this energyrange have revealed the effect of pre-plasma [4] for electron acceleration and concluded (a) -60 -40 -20 0 20
Time (ps) -8 -6 -4 -2 La s e r P o w e r ( A U ) Pedestalt t ASE (b)
Figure 1. (a) Schematic of the experiment showing the main laser pulse, the imagingsystem for the scattering screen, the direction of X-ray pin-hole imaging, electronspectrometer and the scintillator stack. The line of sight of the scintillator stack was18 ◦ above the horizontal plane (i.e. the plane of the incoming laser beam). (b) Powercontrast of the laser beam as measured by a single-shot cross-correlator. that electron re-circulation does not effect the yield of X-rays [25]. The measurementsof X-rays in the range of 100 keV - 1 MeV, described in this paper confirm that targetswith high atomic number (tantalum in this case) and having a thickness of about 2 mmare optimal for maximizing the X-ray flux of photons with energy ∼
2. Experimental Set-up and Diagnostics
The experimental layout at the SG-II upgrade facility [28] is shown in figure 1a.The main laser pulse was generated by a hybrid optical parametric Chirped PulseAmplification (CPA) and Nd:glass amplifier. The beam energy was (300 ±
25) J with apulse duration of ≈ . ≈ µ m diameter containingabout 80% of the incident energy, thus reaching a peak focused intensity of 10 W/cm [28]. The laser intensity contrast was measured using a single-shot cross-correlator witha fiber array and a photo multiplier tube [29] and is shown in figure 1b. The amplifiedspontaneous emission (ASE) contrast was ∼ × − and extended till 850 ps beforethe main pulse which is half the duration of uncompressed chirped pulse of the laser.The pulse has a contrast pedestal in the range of 10 − to 10 − for less than 60 ps beforethe main pulse.The focused beam was incident on tantalum (Ta) targets at an angle of 22 ◦ in theequatorial plane. The thickness of the target was varied in the range from 100 µ mto 4 mm. To increase the hot electron population, the front surface of some tantalumtargets were coated with 10 µ m plastic (parylene) or with glass microspheres of diameter4 − µ m.A number of diagnostics were used to measure fast electrons, X-rays and thespecular reflection of the beam. The accelerated electrons escaping the target werecharacterised with a magnetic electron spectrometer. It was placed at a distance of20 cm from the target at an angle of 28 ◦ from the laser axis. The 1 mm entranceaperture of the spectrometer subtended a solid angle of 20 µ sr. A magnetic field of0 .
28 T dispersed the electrons to enable energy resolved detection in the range of 1 − ×
30 cm. The scattering screen covered asolid angle equivalent to f/1 .
67 on the target, which is greater than the f-number of thefocusing parabola f / .
5. The scattering screen was imaged using two cameras to monitorthe light incident on it at the first and second harmonic of the laser pulse. A band passinterference filter centered at 520 nm and with a bandwidth of 40 nm (full width athalf maximum) was used with the camera monitoring the second harmonic and a longpass filter with a cut-on wavelength of 1 µ m was used with the camera monitoring thefirst harmonic. The system was absolutely calibrated using low power continuous wavelasers (at the first and second harmonic) incident on the scattering screen and beingimaged by the cameras.Hard X-rays from 100 keV to 1 MeV were measured using a stack of LYSO(Lu . Y . SiO :Ce) scintillators [32, 33]. Unlike traditional filter stack spectrometerswhich use passive readouts of image plate [34], this diagnostic provides prompt data froman imaging camera. As shown in figure 1a, the hard X-rays generated by bremsstrahlungwere measured at 18 ◦ above the equatorial plane along the laser axis. The stack ofscintillators shown in figure 2a was placed outside the vacuum chamber at a distance of1 . . ×
12 mm was placed to collimate the X-ray beam prior to thescintillators. The aperture subtended a solid angle of 49 µ sr to the source. An exampleof the data collected from the experiment is shown in figure 2b. The scintillator stackincluded ten LYSO crystals and five tungsten filters, each of thickness 2 mm and crosssection 1 . × (a) arb. (b) -2 -1 Photon energy (MeV) -3 -2 -1 E ne r g y depo s i t ed i n sc i n t ill a t o r ( M e V ) (c) Figure 2. (a) A stack of scintillators and tungsten attenuators placed in a plastichousing and behind a lead collimator. (b) Example of raw data in arbitrary units fromimaging the stack of scintillators during a laser shot. (c) Simulated energy depositedin various scintillators in the stack (numbered 1 −
10) as a function of incident photonenergy. -200 0 200-300-200-1000100200300
Figure 3.
X-ray emission in the range of 0 . − . energetic X-rays was simulated using the Monte Carlo code GEANT4 [35–37], and thecorresponding transfer matrix for energy deposited in each scintillator is shown in figure2c. The stack of scintillators and the camera were covered by black aluminum foil toprevent signal contamination from stray light or laser light. Calibration for the relativeefficiency of the individual scintillators in the stack was performed by exposing the stackto a Na radioactive source. The response of the individual scintillators varied within20%.The interaction of the beam with the target was imaged using a grazing incidenceX-ray pinhole camera [38]. The camera imaged the front surface of the target and was
Figure 4.
Intensity distribution of the reflected light on the scattering screen atsecond (top row) and first harmonic (bottom row) of the laser frequency. Each columnrepresents the data collected from a different shot. The target used in each shot isindicated between the rows - 3 mm thick Ta with 10 µ m thick parylene coating, 3 mmthick Ta with 4 − µ m diameter glass microspheres on the front surface, 3 mm thickTa, and 1 mm thick Ta (from left to right). The total energy incident on the scatteringscreen is indicated at the bottom of each image. The dashed white circle in each imagerepresents the angular aperture of the incident off axis parabola if the target at focuswould be an ideal mirror. The white circle appears askew in the images because theshape is compensated for the viewing angle of the cameras. installed in the direction shown in figure 1a. It imaged soft X-rays in the range of0 . − . .
3. The data is shown in figure3, and the full width at half max of the signal is ∼ µ m which is comparable to thefocal spot of the laser.
3. Experimental Results
In order to correlate bremsstrahlung generation with laser coupling at the target frontsurface, we measured reflected energy in the specular direction. As seen in figure 4,the reflection at the fundamental harmonic was affected by the choice of target. Foruncoated Ta targets, or for Ta targets covered with 4 − µ m glass microspheres, thereflection at the fundamental harmonic was diffuse and always shifted to the right, whilefor plastic coated Ta targets, the reflection was centered along the specular reflectiondirection. The amount of energy reflected at the fundamental harmonic for plasticcoated targets was of the order of 50 J, which corresponds to about ∼
17% of laserenergy. For other targets, the amount of energy at the fundamental harmonic incidenton the scattering screen was of the order of 30 J. However as can be seen from figure4, most of the reflected radiation missed the scattering screen. We estimate that thetotal amount of reflected laser light could exceed 70 J, which corresponds to a fractionof ∼ −
25% of the incident laser energy. This is consistent with measurements on
Main beamTargetθ φ (a) -0.2 0 0.2-0.3-0.2-0.100.10.2 -4 (b) Figure 5. (a) Geometry of the scattering screen monitoring the specular reflection.(b) The fraction of reflected energy on plane of the scattering screen at first (circles)and second harmonic (squares) of the laser frequency. The reflected energy of bothfrequencies are normalized with laser energy and represented by colorbar in the figure. similar laser system by Gray et al [39], where about 50% of laser energy was scatteredin the first harmonic.In order to quantify the deviation of the reflected light at fundamental and secondharmonics from the specular direction, we define angles θ and φ as shown in figure 5a.The center of the screen is the specular reflection direction and corresponds to θ = 0.The angle φ defines the deviation of the maximum of the scattered radiation with respectto the horizontal plane of laser incidence. Results from the entire experimental campaignare summarized in figure 5b, which shows fraction of reflected energy on the scatteringscreen at first (circles) and second harmonic (squares) of the laser frequency. The resultsindicate that reflected light at first harmonic shifts towards the axis of incoming laserbeam while the light generated at second harmonic is centered on the scattering screen.The deviation from the specular direction at fundamental harmonic is θ ∼ ◦ . Thecircular markers in figure 5b were derived from the maximum of the part of reflectedenergy which was incident on the scattering screen. However, as seen in most cases, themaximum was clearly beyond the scattering screen which corresponds to a deviationfrom specular direction of greater than 17 ◦ . The only two shots for which the reflectionof fundamental harmonic was centered on the scattering screen correspond to targetscoated with 10 µ m parylene.The fundamental harmonic laser light is reflected from the location where theelectron density is equal to n c cos α , where α is the angle the light ray makes withthe local density gradient and n c = m e ε ◦ (cid:0) πceλ (cid:1) , is the plasma critical density. m e is themass of an electron, ε ◦ is the permittivity of free space, c is the speed of light in vacuum, e is the electronic charge and λ is the wavelength of the fundamental harmonic. Theconsistent bias in the direction of reflection of the fundamental harmonic and not in thesecond harmonic leads to the following conclusions: Target surfaceCritical densitysurfaceh r α i Figure 6.
Schematic of reflection of incident rays from a curved critical densitysurface at the focus of a laser beam. The solid red arrows indicate the incident raysof light and the dotted red lines indicate the reflected light from the curved criticaldensity surface. The reflected rays are veered to the right because of the curvature ofcritical density surface. (i) The critical density surface (which is very close to the location where incoming raysare reflected) for the shots with uncoated Ta targets was curved outwards becauseof plasma expansion initiated by the laser pre-pulse while it was relatively flat forthe case of targets coated with plastic. The curved critical density surface for theuncoated target must have expanded at least by a distance h = r/ tan α i , where r isradius of the focal spot and α i is the angle of incidence. This can be explained by asimplified schematic shown in figure 6. For the reflected rays (red dotted rays) to bereflected to the right of specular reflection direction, the rays should be incident oncritical density surface in the right half of the focal spot. Thus for our experimentalparameters of α i = 22 ◦ , and focal spot radius of 22 . µ m, the expected height ofthe critical density surface should be 56 µ m.(ii) The relativistically oscillating mirror mechanism is not the likely model applicablefor our experiment, because had the second harmonic been generated fromrelativistic oscillation of the critical density surface, the second harmonic lightwould have been reflected to the right, similar to the fundamental. Also, as shownbelow, the density scale lengths expected in the experiment are much larger thanthe laser wavelength. Thus, neither relativistically oscillating mirror nor coherentwake field emission can be responsible for generating the second harmonic. Instead,for our experiment it is likely that the second harmonic is generated by the modeconversion of the resonant electric field at the critical density surface [10]. Such amode conversion mechanism is applicable to longer plasma density scale lengths.Thus our experiment is different from similar experiments performed with highcontrast Ti:Sa lasers where the plasma density profile was very steep and a diffuse -30-20-1001020 A ng l e o f de v i a t i on ( deg r ee s ) -80 -60 -40 -20 0 20 40 60 80020406080100120 -1-0.8-0.6-0.4-0.200.20.40.60.81 l og ( n e / n c ) Figure 7.
Simulated electron plasma density for laser pre-pulse incident on Tatargets. The electron density was calculated by assuming that the Ta ions arecompletely ionized. Colorbar on the right represents the electron density as a fractionof the critical density n c . Solid lines represent the rays at fundamental harmoniclaunched from the top right corner at an angle of incidence of 22 ◦ . The color of thesolid rays (left colorbar) represents that angle of deviation of the reflected outgoingray, where 0 ◦ corresponds to direction of specular reflection from a mirror. The dashedlines represent the propagation of the rays at the second harmonic which are launchedfrom the critical density surface. The white lines propagate outwards, while the blackrays propagate towards the target before being reflected near the plasma with electrondensity ∼ n c . Distance units in µ m. emission at the second harmonic was attributed to relativistic oscillations of thecritical density surface and originating from the brightest intensities at the centerof laser focus [40].Two dimensional hydrodynamic simulations with cylindrical symmetry wereperformed using the FLASH code [41] to estimate the effect of pre-pulse on the expansionof target material and formation of the critical density surface. The code uses arbitrarymesh refinement of a finite volume Eulerian grid and includes ray tracing model of laserenergy deposition. The code also includes electron and radiation energy transport anduses separate equations for electron, ion and radiation temperatures. The equationsof state and opacities of tantalum, carbon and hydrogen were calculated from theQEOS model [42]. Simulations were performed in the two-dimensional axi-symmetricgeometry. The laser power corresponding to the ASE and the pedestal shown in figure1b was focused on a 50 µ m diameter spot. For the simulations, the incident ASE powerlevel was extended to 850 ps before the main pulse. Laser energy was absorbed viainverse bremsstrahlung, and so the code was only able to simulate ablation and plasmaexpansion up to the time t at 10 ps before the main pulse (see figure 1b), where thefocused intensity was less than 10 W/cm . The last 10 ps before the main pulse cannotbe simulated with a hydrodynamic code, but this has negligible effect on the plasmadensity profile as the velocity of expanding plasma is of the order of 0 . µ m/ps.Simulations were performed for tantalum (plastic coated tantalum) targets, and0predicted a corona electron temperature of ∼
85 eV ( ∼
100 eV) during the ASE,consistent with the laser ablation model [43]. During the ASE (before time t in figure1b), the critical density surface expands to a distance of ∼ µ m ( ∼ µ m) from thetarget surface. Thus, the critical density surface is planar and agrees with the observedspecular reflection from the plastic coated targets. However, it cannot explain theobserved shift in the reflection of fundamental harmonic from uncoated targets. Eventhe two orders of magnitude increase in intensity during the pedestal (between the times t and t ) was insufficient to significantly alter the critical density surface as the durationof pedestal is only ∼
50 ps.The possible explanation of the experimentally observed shift in fundamentalharmonic invokes photo-ionization of the Ta plasma by the main laser pulse. Whilecarbon ions (Z= 6) are fully stripped in the pre-plasma, charge of tantalum ions (Z=73)is ∼
14. Therefore, the main pulse of relativistic intensity may increase the electrondensity in the corona almost instantaneously by a factor of 5. To estimate the effectphoto-ionization might have on the critical density surface, we use the ion density profilefrom the hydrodynamic simulation for Ta target and multiply it with an expectedmaximum ion charge of 73 to get the electron density profile. This can be expectedas the ionization energy of Ta is ≈
70 keV. The resulting increase in electron densitymoves the surface of reflection to 22 µ m, as can be seen in figure 7. The effect of sucha density profile on the reflection of incoming rays and the direction of propagationof second harmonic is also shown in figure 7. For imitating the propagation of lightwithin the Rayleigh length near the focus, individual rays at fundamental harmonicwere launched from the top right corner at an angle of 22 ◦ within a diameter of 45 µ m,corresponding to the focal spot in the experiment. As seen in figure 7, most of therays are reflected away from the specular direction towards the incoming laser axis(i.e., corresponding to a negative angle of deviation) as observed in the experiment.Generation of the second harmonic is described according to the theoretical model byErokhin et al [10]. As shown in figure 7 with dashed lines, these rays propagate suchthat they preserve the transverse component of the momentum of the incoming raysat fundamental frequency. The second harmonic rays are less refracted compared tothe fundamental frequency and show a more diffuse pattern similar to the experimentalobservation. The plasma density profile and the ray propagation as shown in figure 7provide only a qualitative illustration that photo ionization of tantalum can provide asignificantly curved critical density surface which can explain the measured deviationof the reflected light in the experiment. A consistent calculation of the density profileby including photo-ionization of tantalum and the corresponding light propagation andgeneration of second harmonic is beyond the scope of the paper.The energy measured at the second harmonic depends on the target material. Thereflected energy in the range of 0 . − . et al [44]. The measured conversion efficiency of (cid:46) .
1% to the1
Electron Kinetic Energy (MeV) N u m be r o f e l e c t r on s ( / M e V / s r) T e =2.0 MeVT e =2.7 MeV Figure 8.
Experimental measurements of escaped electrons energy distribution froma single shot for Ta target of thickness of 0 . second harmonic was significantly less than the conversion efficiency of ∼
10% reportedfor Ti:Sa lasers with similar focused intensity [16]. The conversion efficiency of laserenergy reported here into second harmonic is a lower bound because some radiation fallsbeyond the scattering screen. The measured conversion efficiency provides an estimationfor the electron density profile near the critical density. According to the theoreticalmodel [10], the conversion efficiency Q ω depends on three parameters: the angle ofincidence α i , the ratio of the density scale length to the laser wavelength ρ = 2 πL n /λ ,and on the dimensionless laser amplitude a = eE /m e ωc , as follows Q ω ∼ a ρ sin α i Q res , (1)where Q res ∼ ρ / sin α i e − ρ sin α i / is the efficiency of resonance absorption of thelaser near the critical density. The function Q res for our experimental parametersstrongly depends on plasma density scale length, it decreases from ∼ − to ∼ − for ρ increasing from 100 to 200. Similarly, assuming a ∼ − . − . The measuredefficiency of 10 − is within this range. We thus conclude that the plasma density scalelength in the experiment is in the range of 20 − µ m. The energy spectrum of escaped electrons was measured directly by a magneticspectrometer installed at a distance of 20 cm from the Ta target (see figure 1a). Figure 8shows the measured electron spectrum for 100 µ m and 2 mm thick targets. The electrontemperature estimated from the slope of the distribution is (2 ± .
2) and (2 . ± . . µ m thick target, a total number of electrons with energy greaterthan 1 MeV escaping the target is of the order of 10 , which corresponds to a charge2 S i gna l s t r eng t h ( A U ) (a) Photon energy (MeV) -8 -7 -6 -5 P ho t on s / M e V / p r i m a r y (b) Scintillator number S i gna l ( A U ) (c) Figure 9. (a) Average brightness across the data from scintillator stack. The tenpeaks correspond to the ten scintillators, with the peak on the left corresponding tolow energy photons. (b) Expected photon spectra from the experiment generated byMonte Carlo simulations. (c) Comparison of the predicted response of the scintillatorstack to the measurement. of about 20 nC. The total energy carried by these electrons is ∼ .
05 J, indicating aconversion efficiency from laser energy to escaped electrons of the order of 10 − .The electron temperature measured from laser interaction with a 100 µ m thicktarget is a factor of two higher than the ponderomotive scaling [46], assuming thedimensionless laser field amplitude a = 2 −
3, but similar to measurements on otherhigh energy Nd:glass laser systems [47–49] and also predicted by simulations [50]. Thisis explained by contribution of the direct laser acceleration and stochastic heating in aplasma extended to 10 laser wavelengths or more [49].The number of electrons detected from 2 mm thick targets is reduced by a factorof about 50 and the maximum cutoff energy of electrons is decreased by about 6 MeV.This is consistent with the expected energy lost by fast electrons while traversing 2mm thick tantalum targets [51]. The lower energy electrons are scattered more withinthe target compared to the high energy electrons. Thus, a higher fraction of highenergy electrons are able to escape the thick target and reach the electron spectrometercompared to the low energy ones. This results in an apparent increase in hot electrontemperature measured by the spectrometer for thick targets, but it is only an artifact ofelectron scattering in thicker targets and not a result of higher electron temperatures atthe laser focus. The electron spectrometer data thus shows that electron temperatureabout 2 MeV and energies up to 20 MeV were generated in the laser plasma interaction.
X-ray measurements from targets of two different thicknesses are shown in figure 9a. Thespectrum from the 100 µ m thick Ta target is dominated by low energy photons of energy100 −
200 keV, as evident from the significantly lower signal in the second scintillatorcompared to the first. These photons are generated by a low energy, non-relativisticcomponent of electrons in plasma. Their bremsstrahlung emissivity depends inversely3on the electron energy [52] and the target thickness is comparable to their stopping range[51]. The emissivity of relativistic electrons is much smaller and the corresponding highenergy photons deposit their energy in all the scintillators in the stack (see also figure2c), but the energy resolution as defined by the first few layers is insufficient to deducetheir energy distribution. The higher intensity of the data collected from 2 mm thicktargets and the relatively gradual decay along the scintillators (see figure 9a) impliesthat the photon spectrum from the 2 mm thick Ta target is dominated by harder photonsand also has a higher flux.These observations are supported with dedicated Monte Carlo simulations forexpected photon spectra shown in figure 9b. The simulations were performed with theFLUKA code [53–55] and used the electron spectra shown in figure 8 as an input. Theelectrons were injected along the direction of laser propagation and had an opening coneangle of ± ◦ [25, 26]. The temperature of the photon distribution for energies greaterthan 1 MeV was T γ ∼ . ∼ −
4. Conclusion
In summary, this paper presents results from an experiment in which a short pulse froma Nd:glass laser was focused on Ta target of thickness ranging from 100 µ m to 4 mmat an intensity of 10 W/cm . Measurements of the optical emission in the specularreflection direction provide information about a pre-plasma density profile which extendsto several tens of µ m because of the photo-ionization of expanding tantalum plasma. Theamount of energy specularly reflected in the fundamental harmonic is as high as 25%.Efficiency of the laser energy conversion into second harmonic confirms the estimatedpre-plasma scale length of 20 − µ m. EFERENCES µ mand 2 mm thick Ta targets. The measured electron temperature of 2 MeV anddependence of the bremsstrahlung photon yield on the target thickness are in closeagreement with results from Monte Carlo simulations. These results are important fordevelopment of new efficient photon sources and for designing hot electron diagnosticmethods in relativistic laser plasma interactions. Previous experiments reported up to atwo-fold enhancement in X-rays from targets coated with plastic [4]. However, we onlymeasured about a 25% increase, which is within the uncertainty limit due to shot-to-shotfluctuation. Acknowledgments
This research was sponsored by the Czech Science Foundation (project No. 18-09560S)and by the project High Field Initiative (CZ . . . . .
015 0030000449) from theEuropean Regional Development Fund (HIFI). The results of the project LQ1606 werealso obtained with the financial support of the Ministry of Education, Youth andSports as part of targeted support from the National Programme of Sustainability II.The work was also supported by the project Advanced research using high intensitylaser produced photons and particles (CZ . . . . .
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