Proton energy scaling laws - Generation of above-100-mev proton beams with Z-Petawatt?

Transcription

1 Proton energy scaling laws - Generation of above-100-mev proton beams with Z-Petawatt? Sante Fe, July 28, 2009 Marius Schollmeier Z-Backlighter Facility Sandia National Laboratories Albuquerque, NM Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy s National Nuclear Security Administration under contract DE-AC04-94AL85000.

2 Coworkers Matthias Geissel, Briggs Atherton, Guy Bennett, Mark Kimmel, Patrick Rambo, Jens Schwarz Knut Harres, Frank Nürnberg, Marc Günther, Jörg Schütrumpf, Dieter H.H. Hoffmann, Markus Roth Kirk Flippo, Cort Gautier, Brady Gall, Tom Lockard, Dustin Offermann, Manuel Hegelich, Juan Fernandez Vincent Bagnoud, Abel Blazevic, Klaus Witte Sandrine Gaillard, Thomas Kluge, Tom Cowan Erik Brambrink Hartmut Ruhl, Jörg Schreiber

3 Outline Main topic: Investigation of scaling laws and comparison with results from various laser systems Introduction: Laser ion acceleration by TNSA Scaling law by J. Fuchs et al. Optimized scalings: Energy-enhancement with different laser and different target geometries Summary: Can Z-Petawatt accelerate ions up to 100 MeV and more?

4 Laser ion acceleration: Target Normal Sheath Acceleration (TNSA) μm Intensity I > W/cm 2 I = W/cm 2 ns

5 Laser ion acceleration: Target Normal Sheath Acceleration (TNSA) Laser pulse creates pre-plasma μm Intensity I > W/cm 2 I = W/cm 2 ns

6 Laser ion acceleration: Target Normal Sheath Acceleration (TNSA) Laser pulse creates pre-plasma Main pulse accelerates electrons to MeV-energies μm Intensity I > W/cm 2 I = W/cm 2 ns

7 Laser ion acceleration: Target Normal Sheath Acceleration (TNSA) Laser pulse creates pre-plasma Main pulse accelerates electrons to MeV-energies Electron sheath generates electric field on rear side μm Intensity I > W/cm 2 I = W/cm 2 Ez V/m ns

8 Laser ion acceleration: Target Normal Sheath Acceleration (TNSA) Laser pulse creates pre-plasma Main pulse accelerates electrons to MeV-energies Electron sheath generates electric field on rear side Transverse spread of sheath with speed of light μm Intensity I > W/cm 2 I = W/cm 2 Ez V/m ns

9 Laser ion acceleration: Target Normal Sheath Acceleration (TNSA) Laser pulse creates pre-plasma Main pulse accelerates electrons to MeV-energies Electron sheath generates electric field on rear side Transverse spread of sheath with speed of light Field ionization and ion acceleration in normal direction μm Intensity I > W/cm 2 I = W/cm 2 ns

10 Laser ion acceleration: Target Normal Sheath Acceleration (TNSA) Laser pulse creates pre-plasma Main pulse accelerates electrons to MeV-energies Electron sheath generates electric field on rear side Transverse spread of sheath with speed of light Field ionization and ion acceleration in normal direction μm Intensity I > W/cm 2 extremely rapid acceleration: MeV-energies in 1 ps (ca g) very small volume: ca. (100 µm) 3 high particle number: N > low emittance I = W/cm 2 ns

11 Energy gain in electric field Laser: I = 2 x W/cm 2 tp = 1 ps 10 µm dia. focus --> E = 150 J Target: 10 µm metal foil E(z) = 2k BT e 1 z + 2λ D k B T = m e c 2 ( 1+ ) Iλ MeV λ D =0.56 µm E max V/m acceleration time: very long, about 3 ps!! z 2k BT m p 1 z + 2λ D =0

12 More realistic: Isothermal expansion Mora, PRL 90, (2003): isothermal fluid expansion with charge separation Standard model of TNSA n i t + (v in i ) z =0 v i t + v v i i z = e Φ m p z 2 Φ ε 0 z 2 = e ( n e (z) n i (z) ) ( ) eφ n e = n e,0 exp k B T hot

13 More realistic: Isothermal expansion Mora, PRL 90, (2003): isothermal fluid expansion with charge separation Standard model of TNSA t = 0 fs t = 250 fs t = 500 fs 2kB T hot E max = 2kB T hot E max = eλ D = eλ D 2 ε 0 n e k B T hot

14 Energy gain in isothermal model peak electric field moves with ions -> stronger acceleration still about 650 fs needed for protons to reach 100 MeV --> plasma has to stay at temperature for this time basic model, but good enough for comparison with experimental data

15 thick targets and a 10 µm FWHM laser spot size. b, Numbertemperature of protons inta p. Circles and squares are experimental data for the This in around transition, 10 MeV as ahowever, function of laser remains intensityto multiplied be laser-pulse-duration by the ranges shown. The line is given by the fluid m gth squared. The last parameter Comparison chosen as it governs the with 20-µm-thick hot electron experiments: targets, a 10 µm FWHMScaling laser spot size and lawa 0.5 ps eture robustness T p. Circles and and squares highare beam experimental quality, data for inthe two duration. References are as follows: LOA 12, JanUSP 20, RAL PW 46, N rate lse-duration the ranges rear-surface shown. The mechanism line given by the that fluid model RAL assuming VULCAN 16,17, Osaka 47, CUOS 48, MPQ 21, Tokyo 49, ASTRA 18. LULI thick roven targets, in aseveral 10 µm FWHM facilities laser spot andsize that and ahas 0.5 ps laser pulse data presented in this article (see Fig. 2).. two References criteria. are as follows: LOA 12, JanUSP 20, RAL PW 46, Nova PW 2, LCAN 16,17 J., Osaka Fuchs 47, CUOS et al., 48, MPQ Nature 21, Tokyo Physics 49, ASTRA2, LULI(2006) represents and thej. Fuchs et al., Phys. Plasmas sented 14, in this article (see (2007) Fig. 2). : Isothermal expansion with stopping time MODELLING ts reported here, we have measured the from laser-irradiated solid aluminium (I L )+3 τ L + t min for IL [ , [ W/cm 2, τ acc = 1.3 τ L + t min for I L W/cm 2. ye one maximum parameter (cutoff) at a energy time, either that can laser be gained by the rated (E), laser ions pulse based duration the simple (τ self-similar, isothermal, fluid laser ) or target l (for example, equation (10) of ref. 28) is given by ductor targets (for example, gold) give lts to those using aluminium. Insulator, show unsatisfactory filamentary proton E max = 2T hot [ln(t p + (t 2 p +1)1/2 )] 2, (1) t p targets = ω pi t acc are /(2exp all 1 that ) 1/2 is are the studied normalized here. acceleration time, lized using the ion (of charge number Z i and mass m i ; taneously all the obtained scalings with otons Z i = 1, m i = m p ) plasma frequency ω pi =[(Z i rmal, time-limited Validity conditions: Similar lasers with tp e0)/(m i ε 0 )] 1/2, with fluid e the model electron 28 using charge, a ε the electric = [300 fs, 1 ps], with similar ttivity, ffective and acceleration Tcontrasts of about 10-6 hot and n e0 time the temperature (or limit, metallic time) and density targets of the with hot d > 10 µm ns t acc that 1.3τ drive laser thematches rear-surface wellexpansion. with all the This model updates us ined. models of freely expanding plasma 29 with a steady electron rature observed (andboth thusin unlimited experiments acceleration) and into the case of a nximated burst ofby energetic a quasithermal electrons. distribution As our simple model cannot ato account maximum the progressive energy. Typical transferspectra of energy from the fast ns to the ions and the decrease of the accelerating charge ental conditions reported here can be The maximum (cutoff) energy that can be g accelerated ions based on the simple self-similar, iso model (for example, equation (10) of ref. 28) is given E max = 2T hot [ln(t p + (t 2 p +1)1/2 )] 2, where t p = ω pi t acc /(2exp 1 ) 1/2 is the normalized acce normalized using the ion (of charge number Z i for protons Z i = 1, m i = m p ) plasma frequency e 2 n e0 )/(m i ε 0 )] 1/2, with e the electron charge, permittivity, and T hot and n e0 the temperature and den electrons that drive the rear-surface expansion. This m previous models of freely expanding plasma 29 with a s temperature (and thus unlimited acceleration) to sudden burst of energetic electrons. As our simple take into account the progressive transfer of energy electrons to the ions and the decrease of the accele separation field, we use the crude approximation of

16 Comparison with experiments: Scaling law Parameters: tp = 500 fs focus dia. = 6 µm 25 µm target E max (MeV) scaling law LULI 100TW, Fuchs, Nature Phys. 2, 48 (2006) VULCAN PW, Robson, Nature Phys. 3, 58 (2007) NOVA PW, Snavely, Phys. Rev. Lett. 85, 2945 (2000) Emax = 100 MeV: I = 6 x W/cm 2 I = 2 x W/cm I L (W/cm 2 ) E = 84 J or 168 J (50% foc.) E = 280 J or 560 J (50% foc.)

17 Lasers with longer pulses and larger foci Parameters: tp = 1 ps focus dia. = 10 µm target: 10 µm same scaling law Result: longer pulses and thinner targets result in higher proton energy: E max k B T ln ( ne τ acc ) E max (MeV) scaling laws Z-100 TW at SNL (2008) LULI 100TW, Fuchs, Nature Phys. 2, 48 (2006) VULCAN PW, Robson, Nature Phys. 3, 58 (2007) NOVA PW, Snavely, Phys. Rev. Lett. 85, 2945 (2000) TRIDENT, Flippo, RSI 79, 10E534 (2008) PHELIX, Germany (2009) I L (W/cm 2 )

18 Lasers with longer pulses and larger foci Parameters: tp = 1 ps focus dia. = 10 µm target: 10 µm same scaling law Result: longer pulses and thinner targets result in higher proton energy: E max k B T ln ( ne τ acc ) E max (MeV) scaling laws Z-100 TW at SNL (2008) LULI 100TW, Fuchs, Nature Phys. 2, 48 (2006) VULCAN PW, Robson, Nature Phys. 3, 58 (2007) NOVA PW, Snavely, Phys. Rev. Lett. 85, 2945 (2000) TRIDENT, Flippo, RSI 79, 10E534 (2008) PHELIX, Germany (2009) I L (W/cm 2 ) What if the target geometry is changed?

19 Change of target geometry gets even better results Experiments at Trident (K. Flippo, S. Gaillard, et al., MG, MS): copper Flat Top Cones (FTC) Trident Shot 21170, 81 Joules and 670 fs: I ~ 4 x W/cm 2 > 65 MeV protons, highest energy protons in the world from laser-ion acceleration Copper Flat-Top Cone Target Image preliminary data! Kα shows deep penetration of laser and electrons RCF images show a proton beam of > 65 MeV flat foil: 50 MeV, FTC: 65 MeV energy increase: 30%

20 Change of target geometry gets even better results Scaling law fits, if fabs = 0.5 is fixed and kt doubled (more efficient electron heating due to cone-shaped front side, backed up by K-alpha imager data) E max (MeV) FTC data scaling laws Z-100 TW at SNL (2008) LULI 100TW, Fuchs, Nature Phys. 2, 48 (2006) VULCAN PW, Robson, Nature Phys. 3, 58 (2007) NOVA PW, Snavely, Phys. Rev. Lett. 85, 2945 (2000) TRIDENT, Flippo, RSI 79, 10E534 (2008) PHELIX, Germany (2009) I L (W/cm 2 )

21 $ A fit of this equation to the data is shown as the red line in fig The FWHM of the fit is 8 log 2 σ = Figure 6.1: Scaling of maximum energy with laser intensity, for a 25 µm thick metal foil. Shown are data from LULIThis value is within the error bars of the FWHM determined by the fit to the energy-resolved sourc 100 TW ( ) [15], VULCAN-PW ( ) [16], the NOVA Petawatt ( ) [21] and data obtained in this thesis, µm. Both data sets strongly indicate that thedivergence hot electron has. indeed a Gaussian transverse compared to the 92.8 scaling explained in section assuming an electron anglesheath of α = 30 and the observed angle of beam spread is a result of the Gaussian distribution. Target geometry II: Curved foils get [194]. Nonetheless it is not clear whether or not the efficiency and beam quality of beams generated by these mechanisms is equal or better than TNSA-beams. Additionally, the experimental realization might only become realizable with the next generation of high-energy, high-intensity laser systems. 100!m concave targetsthere lead to other slight focusing are some options to increase the efficiency of TNSA with the existing generation of laser systems. In order to increase thedensity hot electron temperature, a confinement of the pre-plasma at the front side and the -> enhancement of electron region of ion-acceleration at the rear side is proposed. The cone-shaped targets have been proven to enhance on symmetry axis the conversion efficiency from laser energy to hot electron temperature. Further investigations for more efficient should be done with these cones, in order to get a better scaling with the cone dimensions 100!m and to find -> electric field TNSA increase the optimum geometrical shape. Additionally, at the tip of the cone, a Gaussian shaped foil could be placed. -> more efficient TheTNSA Gaussian shaped foil could lead to a reduction of the proton opening angle and, due to the confinement of the expanding plasma for early times, the adiabatic cooling due to the expansionfoils would with be slower, increasing Gaussian shaped about 100 µm width the maximum energy as well. An 4.14: energy-enhancement of the protons has The been10 already observed 2D-PIC Figure Gaussian shaped target foils. µm produced thin Cu foilin has a SNL. Gaussian-shaped impression and height have been for simulations in refs. [302, 303]. Up to %µ higher maximum energy The couldphotographs be obtained by a strongly m width and height. were taken curved by a light microscope. The drawin Experimental campaign planned this year. foil [302]. right side shows the configuration for the experiment. These findings lead to the conclusion that Gaussian-shaped target foils could be used to collimate TNSAThe FWHM of the Gaussian foils should be on the order of 100 µm. Following these suggestions, were made by NanoLabz [282] by order of Sandia National Laboratories for the experimental campa Petawatt in december The targets were made of 10 µm thick Cu foil, with a Gaussian shaped de as illustrated in figure 4.14 (right image). Various depressions with varying depths from 0 µm (flat foil) 100 µm (left images) were made. Unfortunately, due to technical difficulties during the manufacture, th did not arrive in time and could therefore not be used in the experiment. Our group decided that the e targets should be used in a separate beam time dedicated especially to this experiment at the end of later. Therefore, only test-experiments will be presented in this section. Energy increase seen in 2D-PIC: 20% Figure 6.2: Comparison of the proton distribution for a flat foil (left image) at t = 2 ps and a Gaussian shaped foil (center and right images). The curved target surface leads to a collimation of the beam Beam optimization by target g 6.1. Further optimization and control Experiment by M. Roth et al.: ~30% (article in preparation)

22 Summary: Can we get there? Requirements: - I ~1.3 x W/cm 2 - pulse duration: ~ 1 ps - 10 µm -> 25 µm targets - focal spot: 10 µm diameter 100 Z-Petawatt --> 100 J in focus or 1.5 J/µm 2 (> 200 J laser energy) Comparison to simulations: - J. Davis & G.M. Petrov, Phys. Plasmas 16, (2009): similar value: ~2 J/µm 2 (with a 80 fs pulse) E max (MeV) 10 1 scaling laws Z-100 TW at SNL (2008) LULI 100TW, Fuchs, Nature Phys. 2, 48 (2006) VULCAN PW, Robson, Nature Phys. 3, 58 (2007) NOVA PW, Snavely, Phys. Rev. Lett. 85, 2945 (2000) TRIDENT, Flippo, RSI 79, 10E534 (2008) PHELIX, Germany (2009) - T. Esirkepov et al., Phys. Rev. Lett. 96, (2006): 100 MeV for 10 µm focus, 200 fs pulse, 100 J, 6x10 20 W/cm I L (W/cm 2 )

23 Summary: Can we get there? Requirements: - I ~1.3 x W/cm 2 - pulse duration: ~ 1 ps - 10 µm -> 25 µm targets - focal spot: 10 µm diameter --> 100 J in focus or 1.5 J/µm 2 (> 200 J laser energy) Comparison to simulations: - J. Davis & G.M. Petrov, Phys. Plasmas 16, (2009): similar value: ~2 J/µm 2 (with a 80 fs pulse) - T. Esirkepov et al., Phys. Rev. Lett. 96, (2006): 100 MeV for 10 µm focus, 200 fs pulse, 100 J, 6x10 20 W/cm 2

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25 Outlook Different acceleration schemes: Enhanced TNSA / Laser break-out afterburner requires ultra-high contrast (10-12 and better) and ultra-thin foils first TNSA, then volumetric heating of bulk when foil becomes transparent First results: Ep = 40 MeV with I = 7 x W/cm 2 (A. Henig et al., PRL 103, (2009)) Include circular polarization: Radiation pressure acceleration requires ultra-high contrast (10-12 and better) and ultra-thin foils experimentally difficult to realize (B-Integral, Plasma mirrors) extremely high intensities are needed for 100 MeV: > W/cm 2 (A.P.L. Robinson, PPCF 51, (2009)) benefit: whole foil is accelerated, quasi-monoenergetic ions