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Sgattoni, C. Benedetti, P. Londrillo, L. Di Lucchio G. Turchetti

Comparison of scaling laws with PIC simulations for proton acceleration with long wavelength pulses. Sgattoni, C. Benedetti, P. Londrillo, L. Di Lucchio G. Turchetti Università di Bologna INFN Sezione di Bologna INFN Sezione di Bologna. Comparison of RPA scaling with PIC.

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Sgattoni, C. Benedetti, P. Londrillo, L. Di Lucchio G. Turchetti

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  1. Comparison of scaling laws with PIC simulations for proton acceleration with long wavelength pulses Sgattoni, C. Benedetti, P. Londrillo, L. Di Lucchio G. Turchetti Università di Bologna INFN Sezione di Bologna INFN Sezione di Bologna

  2. Comparison of RPA scaling with PIC • Beams for therapy • Protons from RPA regime • Comparison with Aladyn

  3. Comparison of RPA scaling with PIC Bunch mm size Bunch laser acc. mm size Proton sources for therapy Proposals for medical use of laser produced beams Electrons for IORT, Thompson X rays for therapy and imaging Protons for therapyReduction of cost and size Side studies. Radiobiology of small beams. Treatment plans

  4. Comparison of RPA scaling with PIC Short pulse TiSa lasers Table top 40 TW laser AmplitudinePulsar 200 For 200 MeV protons 1 PW laser needed Main amplifier Front end

  5. Comparison of RPA scaling with PIC Proposals: e beams for IORT, X rays for imaging and therapy Proton facilities approved • Saphyr (Fance) • PMRC (Japan) • onCOOPtics (Germany) Activities in Italy • Protons acceleration experiments with laser FLAME at Frascati LNF • Theory and simulation at Pisa, Milano and Bologna • Coordination therapy initiatives by PROMETHEUS via Alma Mater foundation • Expression of interest by CNAO foundation • Italian groups of Milan and Pisa make experiments in EU labs

  6. Comparison of RPA scaling with PIC In vitro From Pawelke onCOOPtics: laser radiooncology Translational research From in vitro to clinics Tissue Animal Clinical translational studies Tenyears Clinical application

  7. Comparison of RPA scaling with PIC CNAO Centro Nazionale Adroterapia Oncologica sede a Pavia Sinchrotron for C ions 400 MeV/u (4.8 GeV) Protons 200 MeV Treatment 2000 patients/year from 2010 Center for proton therapy in Trento

  8. HILL area HILL FLAME tendone Lab. 100TW SPARC bunker Comparison of RPA scaling with PIC PLASMONX experiment Laser Flame: 300 TW 7.5 J 25 fs contrast > 108 Main goal: multi GeV electrons, hard X rays Protons acceleration up to 60 MeV

  9. Site for a laboratory in Bologna Montecuccolino hall of RB3 reactor A cubic building 17 m side with bunker and travelling crane. Side building 220 mq. Basement 300 mq for technological systems Electric power 0.8 MW. Comparison of RPA scaling with PIC

  10. Accelerazione laser: esperimenti virtuali e prospettive medicina 1 PW laser Frequency 10 Hz, energy 20 J efficiency 0.05-0.5 % power 0.1-1 W. Commercial cyclotron Diameter 4 m Weight 20 tons Energy 250 MeV W= 100 W Current 3 1012 protons/sec Emittance few mm mrad Cost 10-15 Meuro Cost of center 50-60 Meuro

  11. Comparison of RPA scaling with PIC RPA for thick and thin targets TheTNSA is the most investigated regime. The protons acceleration along the laser beam is due to the field ofhot electrons cloud. Top energy Ep = k I1/2 The pressureradiation dominated acceleration RPAoccurs for ap>1. In circular polarization ae>1 is sufficient since electrons remain cold and Ep = k I If the target is thin enough so that the illuminated target rest energy approaches the laser pulse energy we enter the relativistic mirror or light sailregime.

  12. Comparison of RPA scaling with PIC TNSA We have compared some PIC simulationsin theinitial regime described by electrostic Passoni ’s model. Fits to electric field and density. . . . . . . . . . .

  13. Comparison of RPA scaling with PIC Comparison of the scaling law for the protons top energy with PIC Ep (MeV)= 1.8 a The solution of Poisson-Maxwell equation D F = 4 p e n0 e eF/T ~ a log 1+tan2 Having fixed by fitting h=2 ℓ the yop energy if given by Ep(MeV) = a . . . . . . . . . h-x eF ℓ 2 mec2 e F(0) 2 me c2

  14. Comparison of RPA scaling with PIC RPA a thick target the top energy is given by Macchi’s scaling Eion (MeV)= = a2 OK with PIC If we choose the illuminated area as S= 20 l2 a= 0.6 = 0.6 As a consequence the top energy for protons is given by Eion (MeV)= 1.8 mpv2/2 Z nc 2 mec2 A ne 1/2 1/2 Elaser 1 5 Elaser (J) t(ps) t S/l2(m) 1018 nc Elaser (J) ne t(ps)

  15. Comparison of RPA scaling with PIC Number of accelerated ions. It is assumed that all ions in a cylinder of volume V= S dskin is accelerated, where dskin= -1 nc = The number of accelerated protons for S= 20 l2 is Np~ = 10 f = 3 109l(m) f The magnitude is correct but f(x) in PIC is almost constant. Above estimate f(x) = x(x-1) -1/2~ x1/2 . -1/2 l ne p l2rcl 2p nc l ne nc rcl

  16. Comparison of RPA scaling with PIC The RPA regime for a thin target The theory was developed by Macchi, Pegoraro, Bulanov. The analytical results are in good agreement with 1D PIC simulations RPA regime [T. Esirkepov, 2004] Circular polarization Quasi monochromatic spectrum High efficiency Dq <1o

  17. Comparison of RPA scaling with PIC d b 1-b dx 2I0 t-x/c = c b = f -1 (1-b2)3/2 t mc2 1+b dt dt The relativistic mirrorof surface density mis described by the equations Introducing the scaled variables t’=t/t, x’=x/(ct), w=t’-x’-1 and c=2I0t/mc2 db = c f(w) = 1-b Introducing the integrating factor C=(1+b)(1-b) -1 (1-b2) -3/2 the first integral is . H(w,b) = c∫ f(w’) dw’ - Initial conditions x(0)=b(0)=0 give H=-1 and highest speed b* at and of pulse a≡ c∫ f(w) dw a - = -1 g*-1= dx’ 1-b (1-b2)3/2 dt’ 1+b dt’ 1/2 w 1+b 1-b -1 a2 1 1+b* -1 1-b* 2+2a

  18. Comparison of RPA scaling with PIC a2 Protons energy Eion = mion c2 Alternative expression for Eion and a Eion = a = = Efficiency h= 2+2a 2 Elaser 2 Elaser Elaser a E0mirror Nioni mion c2 1 + a Nioni a 1 + a

  19. Comparison of RPA scaling with PIC If the foil thickness d is too small it becomes transparent. If a >>1 the no transparency condition is given by Macchi z = p > a . Example: l=10 mt=1 ps Elaser < 100 J a < 14 nc=1019cm-3 ne/nc d (m) z dskin ( m) E0mir (J) Np a Ep(MeV) 225 16 1.6 150 1012 1.3 345 10 516 0.53 150 1012 1.3 345 60 1 19 0.21180 1.2 1012 1.1 270 ne d nc l Table

  20. Comparison of RPA scaling with PIC ne ℓ l For a thin target of thickness ℓ and area S=20 l 2 the number of accelerated ions is Np= ne S ℓ = nc 20 l2 = 20 z Reflectivity is insured if z > a namely if Np≥ Np* . Np* = 20 a= 6.6 109l(m) a Notice Np* grows as Elaser ½. The ions energy grows as Elaser ½. The total energy of ions grows as Elaser for a>>1. For Np=Np* minimum thickness and highest energy. nc l rc l rcl

  21. Comparison of RPA scaling with PIC Transition between thick and thin targets The crossing between the two regimes occurs for a = acr Values of acr and Ecr for ne/nc=10, l=10 m, t= 1 ps d(m) 5 10 15 E0mirror(J) 150 300 450 linear in d • acr 0.03 0.06 0.091 linear • Elaser (J) 2.25 9 20. quadratic • Ecr (MeV) 0.4 1.6 3.8 quadratic acr 1.8 E0mirror (J) nc = 1+acr 938 t(ps) ne

  22. Comparison of RPA scaling with PIC Comparison with PIC simuation

  23. Comparison of RPA scaling with PIC Comparison with PIC simuation

  24. Comparison of RPA scaling with PIC Comparison with PIC simuation

  25. Comparison of RPA scaling with PIC Comparison of scaling laws for protons energy TNSA Ep (Mev) ~ 1.8 a linear polarization HBEp (MeV)~ a2 Np= 3 109 l(m) f LSEp (MeV)~ 470 Np= 6.6 109 l(m) a . circular polarization a = 1.1 a E0mirror (J)= mpc2 Np = l(m) a nc nc ne ne a2 1+a t (ps) l(m)

  26. Comparison of RPA scaling with PIC Comparison of scaling laws for protons energy in terms of laser power TNSA Ep (Mev) ~ 3.4 P 1/2linear polarization HBEp (MeV)~ 1.8 P circular polarization RSEp (MeV)~ 470 Np~ 0.9 1010 P1/2 l(m) P = power in TW a = 1.5 P1/2 nc ne a2 1+a t (ps) Elaser(J) l(m) t(ps)

  27. Comparison of RPA scaling with PIC Some estimates from scalings FLAMEP= 300 TW E=7.5 J l = 0.8 m TNSA Ep~ 60 MeV a=33 RPA Ep ~ 54 MeV ne = 10 nc a=23 RM Ep~ 167 MeV Np=1.2 1011a = 0.8 h =45% CO2 P= 10 TW E=10 J l = 10 m RPA Ep ~ 18 MeV ne = nc a= 4.2 RM Ep~ 65 MeV Np= 3 1011a = 0.45 h =30%

  28. Comparison of RPA scaling with PIC 2D effects can be relevant. PIC for RPA protons acceleration on thin target

  29. Comparison of RPA scaling with PIC Applications to therapy low dose Np=108 high energy Ep>100 MeV 1 Gy = 1 mJ / 1 g Adavanced tumor 50 g dose 60 Gy J delivered in 2000 shots at 10 Hz (3.5 m session). Per shot 1.5 mJ or 108 protons at 100 MeV Protons number not a major problem also with sharp energy selection Applications to inertial fusion high dose high efficiency

  30. Comparison of RPA scaling with PIC Conclusions ●Comparison of energy scaling with 1D PIC l=10m fair for TNSA, god for HB, excellent fot LS ● RPA protons number scales as l / rcl ( x P1/2for LS) ● Top energy scales as P in HB and early LS as P1/2 for asymptotic LS

  31. Comparison of RPA scaling with PIC Transition between thick RPA and thin RM targets regimes RM ℓ=5 (red) ℓ=10 (green) ℓ=15 (purple) RPA (red ) ne=10 nc

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