sgattoni, c. benedetti, p. londrillo, l. di lucchio g. turchetti
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Comparison of scaling laws with PIC simulations for proton acceleration with long wavelength pulses
Sgattoni, C. Benedetti, P. Londrillo, L. Di Lucchio Sgattoni, C. Benedetti, P. Londrillo, L. Di Lucchio G. TurchettiG. Turchetti
Università di Bologna INFN Sezione di BolognaUniversità di Bologna INFN Sezione di BolognaINFN Sezione di Bologna INFN Sezione di Bologna
Comparison of RPA scaling with PIC
• Beams for therapyBeams for therapy • Protons from RPA regimeProtons from RPA regime
• Comparison with Aladyn Comparison with Aladyn
Proton sources for therapyProton sources for therapy Proposals for medical use of laser produced beamsProposals for medical use of laser produced beams
ElectronsElectrons for IORT, Thompson for IORT, Thompson X raysX rays for therapy and imaging for therapy and imaging
Protons for therapyProtons for therapy Reduction of cost and sizeReduction of cost and size Side studiesSide studies. Radiobiology of. Radiobiology of small beams. small beams. Treatment Treatment
plansplans
Comparison of RPA scaling with PIC
Bunch mm size
Bunch laser acc.msize
Comparison of RPA scaling with PICShort pulse TiSa lasers
Table top 40 TW laser Amplitudine Pulsar 200
For 200 MeV protons 1 PW laser needed
Main amplifier Front end
Comparison of RPA scaling with PICProposals: e beams for IORT, X rays for imaging and therapyProposals: e beams for IORT, X rays for imaging and therapy Proton facilities approvedProton facilities approved • Saphyr (Fance) Saphyr (Fance) • PMRC (Japan)PMRC (Japan)
• onCOOPtics (Germany)
Activities in ItalyActivities in Italy
• Protons acceleration experiments with laser FLAME at Frascati LNFProtons acceleration experiments with laser FLAME at Frascati LNF• Theory and simulation at Pisa, Milano and BolognaTheory and simulation at Pisa, Milano and Bologna• Coordination therapy initiatives by PROMETHEUS via Alma Mater Coordination therapy initiatives by PROMETHEUS via Alma Mater
foundationfoundation• Expression of interest by CNAO foundationExpression of interest by CNAO foundation
• Italian groups of Milan and Pisa make experiments in EU labsItalian groups of Milan and Pisa make experiments in EU labs
Comparison of RPA scaling with PICFrom Pawelke onCOOPtics: laser radiooncologyFrom Pawelke onCOOPtics: laser radiooncology
Translational researchTranslational research
From in vitro to clinicsFrom in vitro to clinics
In vitro
Tissue
Animal
Clinical translational studies
Clinical application
Ten y
ears
Comparison of RPA scaling with PICCNAO 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
Comparison of RPA scaling with PIC
PLASMONX experimentLaser Flame: 300 TW 7.5 J 25 fs contrast > 108
Main goal: multi GeV electrons, hard X rays
Protons acceleration up to 60 MeV
HILL area
SPARC bunker
HILL
FLAME
Lab. 100TW
tendone
• Site for a laboratory in Bologna Site for a laboratory in Bologna Montecuccolino hall of RB3 reactorMontecuccolino hall of RB3 reactorA cubic building 17 m side A cubic building 17 m side with bunker and travelling crane.with bunker and travelling crane.
Side building 220 mq.Side building 220 mq.
Basement 300 mq for technological systemsBasement 300 mq for technological systemsElectric power 0.8 MW. Electric power 0.8 MW.
Comparison of RPA scaling with PIC
Accelerazione laser: esperimenti virtuali e prospettive Accelerazione laser: esperimenti virtuali e prospettive medicinamedicina
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
1 PW laserFrequency 10 Hz, energy 20 J efficiency 0.05-0.5 % power 0.1-1 W.
Comparison of RPA scaling with PIC
RPA for thick and thin targetsRPA for thick and thin targets
TheThe TNSATNSA is the most investigated regime. The protons acceleration is the most investigated regime. The protons acceleration along along
the laser beam is due to the field ofthe laser beam is due to the field of hot electrons cloud. Top energy hot electrons cloud. Top energy EEpp = k I = k I1/21/2
The pressure radiation dominated acceleration RPA occurs for ap>1.In circular polarization ae>1 is sufficient since electrons remain cold and
EEpp = k I = k I
If the target is thin enough so that the illuminated target rest energy approachesIf the target is thin enough so that the illuminated target rest energy approaches
the laser pulse energy we enter the the laser pulse energy we enter the relativistic mirrorrelativistic mirror or or light saillight sail regime.regime.
Comparison of RPA scaling with PICTNSATNSA We have compared some PIC simulations We have compared some PIC simulations in thein the initial initial
regimeregimedescribed by electrostic described by electrostic Passoni Passoni ’s model’s model. Fits to electric field and . Fits to electric field and
densitydensity......................
Comparison of RPA scaling with PIC
..
..
..
..
..
..
..
..
..
Ep (MeV) = 1.8 a
Comparison of the scaling law for the protons top energy with PIC
The solution of Poisson-Maxwell equation
= 4 e n0 e e/T
~ a log 1+tan2
Having fixed by fitting h=2 ℓ the yopenergy if given by
Ep(MeV) = a
e
mec2
h-x
ℓ 2
e (0)
2 me c2
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= 202
a= 0.6 = 0.6
As a consequence the top energy for protons is given by
Eion (MeV) = 1.8
mpv2/2
2 mec2
Z nc
A ne
Elaser 1
S/2() 1018
1/2 5 Elaser (J) (ps)
1/2
nc
ne
Elaser (J)
(ps)
Comparison of RPA scaling with PIC Number of accelerated ionsNumber of accelerated ions.. It is assumed that all ions in a cylinder of It is assumed that all ions in a cylinder of
volume volume V= S dV= S dskinskin is accelerated, where is accelerated, where
ddskinskin= -1 n= -1 nc c ==
The number of accelerated protons for S= 20The number of accelerated protons for S= 2022 is is
NNpp ~~ = = 10 10 f = 3 10 f = 3 1099 (() f) f
The magnitude is correct but f(x) in PIC is almostThe magnitude is correct but f(x) in PIC is almost
constant. Above estimate f(x) = x(x-1) constant. Above estimate f(x) = x(x-1) -1/2-1/2 ~ x~ x1/21/2
..
ne
nc
-1/2
rcl
ne
nc
rcl
RPA regime [T. Esirkepov, 2004] Circular polarization
Quasi monochromatic spectrum High efficiency
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
Comparison of RPA scaling with PICThe relativistic mirrorThe relativistic mirror of surface density of surface density is described by the equationsis described by the equations
Introducing the scaled variables t’=t/Introducing the scaled variables t’=t/x’=x/(cx’=x/(c), w=t’-x’-1 and ), w=t’-x’-1 and =2I=2I00//cc22
dd = = f(w) = 1- f(w) = 1-
Introducing the integrating factor C=(1+Introducing the integrating factor C=(1+)(1-)(1-) ) -1-1 (1- (1-2) 2) -3/2-3/2 the first integral is the first integral is. . H(w,b) =H(w,b) = ∫ f(w’) dw’ - ∫ f(w’) dw’ -
Initial conditions x(0)=Initial conditions x(0)=(0)=0 give H=-1 and highest speed (0)=0 give H=-1 and highest speed ** at and of pulse at and of pulse
≡ ≡ ∫∫ f(w) dw f(w) dw - = - - = -==
2I0
2
2+2
dt’
=
dx’
dt’
-1
w
1/2
-1
1
d
dt c2f
t-x/c -1
dx
dt= c
Comparison of RPA scaling with PIC Protons energy Protons energy
EEionion = m = mionion c c22
Alternative expression for EAlternative expression for Eion ion and and
EEion ion = = = = = =
Efficiency Efficiency
==
Elaser
Nioni
1 +
2 Elaser
Nioni mion c2
2 Elaser
E0mirror
1 +
2
2+2
Comparison of RPA scaling with PICIf the foil thickness d is too small it becomes transparent. If a >>1 theIf the foil thickness d is too small it becomes transparent. If a >>1 theno transparency condition is given by no transparency condition is given by MacchiMacchi
= = > a > a
..Example: Example: =10 =10 =1 ps E=1 ps Elaserlaser < 100 J a < 14 n < 100 J a < 14 ncc=10=101919 cmcm--
33
nnee/n/ncc d ( d () ) d dskin skin ( ( ) E) E00mir mir (J)(J) N Np p EEpp(MeV)(MeV)
22 25 25 16 16 1.6 1.6 150 10150 1012 12 1.3 3451.3 345
10 10 5516 16 0.53 0.53 150 10150 1012 12 1.3 1.3 345 345
60 60 1 1 19 19 0.210.21180 1.2 10180 1.2 1012 12 1.1 1.1 270 270
ne d
nc
Table
Comparison of RPA scaling with PIC For a thin target of thickness For a thin target of thickness ℓ and area S=20 ℓ and area S=20 2 2 the number of accelerated ions the number of accelerated ions
is is
NNpp= n= nee S S ℓℓ = n = ncc 20 20 2 2 = 20 = 20
Reflectivity is insured if Reflectivity is insured if > a namely if N> a namely if Npp ≥ ≥ N Npp**
. NNpp
* * = 20 = 20 aa = 6.6 10= 6.6 1099 (() a) a
Notice Notice NNpp* * grows as Egrows as Elaserlaser
½ ½. The ions energy . The ions energy grows as grows as EElaserlaser ½ ½. .
The total energy of ions grows as EThe total energy of ions grows as E laser laser for for >>1. >>1. For NFor Npp=N=Npp* minimum thickness and highest energy.* minimum thickness and highest energy.
ne ℓ
rc
l
nc
rc
Comparison of RPA scaling with PIC
Values of Values of crcr and E and Ecrcr for n for nee/n/ncc=10, =10, =10 =10 = 1 ps= 1 ps
d(d()) 5 10 15 5 10 15
EE00mirrormirror(J) 150 300 450 (J) 150 300 450 linear in linear in dd
cr cr 0.03 0.06 0.091 0.03 0.06 0.091 linear linear EElaser laser (J)(J) 2.25 9 20. 2.25 9 20. quadraticquadratic EEcr cr (MeV)(MeV) 0.4 1.6 3.8 0.4 1.6 3.8 quadraticquadratic
cr
1+cr
nc
938
E0mirror (J)
ps=
ne
1.8
Transition between thick and thin targets Transition between thick and thin targets The crossing between the two regimes occurs for The crossing between the two regimes occurs for = = crcr
Comparison of RPA scaling with PICComparison with PIC simuation Comparison with PIC simuation
Comparison of RPA scaling with PICComparison with PIC simuation Comparison with PIC simuation
Comparison of RPA scaling with PICComparison with PIC simuation Comparison with PIC simuation
Comparison of RPA scaling with PIC
Comparison of scaling laws for protons energyComparison of scaling laws for protons energy
TNSATNSA E Ep p (Mev) (Mev) ~ 1.8 ~ 1.8 a a linear polarizationlinear polarization
HBHB EEp p (MeV)(MeV) ~ ~ aa22 N Npp= 3 10= 3 109 9 (() f) f
LSLS EEp p (MeV)(MeV) ~ 470 ~ 470 NNpp= 6.6 10= 6.6 109 9 (() a) a. . circular polarizationcircular polarization
= = 1.11.1 a a EE00mirror mirror (J)(J) = m= mppcc22 N Np p = = (() a) a
nc
ne
2
(ps)
()
ncne
Comparison of RPA scaling with PIC
Comparison of scaling laws for protons energy in terms of laser Comparison of scaling laws for protons energy in terms of laser powerpower
TNSATNSA E Ep p (Mev) (Mev) ~ 3.4 P ~ 3.4 P 1/21/2 linear polarizationlinear polarization
HBHB EEp p (MeV)(MeV) ~ 1.8 P ~ 1.8 P circular polarizationcircular polarization RSRS EEp p (MeV)(MeV) ~ 470 ~ 470 NNpp ~ 0.9 10~ 0.9 1010 10 PP1/2 1/2 (())
P = P = power in TW power in TW = 1.5 P = 1.5 P1/21/2
ne
2
(ps)
()
nc
Elaser(J)
(ps)
Comparison of RPA scaling with PICSome estimates from scalingsSome estimates from scalings
FLAMEFLAME P= 300 TW E=7.5 J P= 300 TW E=7.5 J = 0.8 = 0.8
TNSA TNSA EEpp ~ ~ 60 MeV 60 MeV a=a=3333
RPA RPA EEp p ~~ 54 MeV n 54 MeV ne e = 10 n= 10 nc c a=23a=23
RM RM EEpp ~~ 167 MeV N 167 MeV Npp=1.2 10=1.2 101111 = 0.8= 0.8=45%=45%
CO2 CO2 P= 10 TW E=10 J P= 10 TW E=10 J = 10 = 10
RPA RPA EEp p ~~ 18 MeV n 18 MeV ne e = n= nc c a= a= 4.24.2
RM RM EEpp ~~ 65 MeV N 65 MeV Npp= 3 10= 3 101111 = 0.45= 0.45=30%=30%
Comparison of RPA scaling with PIC2D effects can be relevant. PIC for RPA protons acceleration on thin target
Comparison of RPA scaling with PICApplications to Applications to therapytherapy low dose N low dose Npp=10=108 8 high energy high energy
EEpp>100 MeV>100 MeV
1 Gy = 1 mJ / 1 g1 Gy = 1 mJ / 1 g
Adavanced tumor 50 g dose 60 Gy J delivered inAdavanced tumor 50 g dose 60 Gy J delivered in2000 shots at 10 Hz (3.5 m session). 2000 shots at 10 Hz (3.5 m session).
Per shot 1.5 mJ or 10Per shot 1.5 mJ or 1088 protons at 100 MeV protons at 100 MeV
Protons number not a major problem also with sharp energy selectionProtons number not a major problem also with sharp energy selection
Applications to Applications to inertial fusioninertial fusion high dose high efficiency high dose high efficiency
Comparison of RPA scaling with PIC
ConclusionsConclusions
●● Comparison of energy scaling with 1D PIC Comparison of energy scaling with 1D PIC =10=10
fair for TNSA, god for HB, excellent fot LSfair for TNSA, god for HB, excellent fot LS
● ● RPA protons number scales as RPA protons number scales as / r/ rcl cl ( ( x x P P1/21/2 for for LS)LS)
● ● Top energy scales as P in HB and early LSTop energy scales as P in HB and early LS as Pas P1/2 1/2 for asymptotic LSfor asymptotic LS
Comparison of RPA scaling with PICTransition between thick RPA and thin RM targets regimes
RM ℓ=5 (red) ℓ=10 (green) ℓ=15 (purple) RPA (red ) ne=10 nc