Comparison of scaling laws with PIC simulations for proton acceleration with long wavelength pulses Sgattoni, C. Benedetti, P. Londrillo, L. Di Lucchio

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 Bologna

INFN 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


Bunch mm size

Bunch laser acc.msize


Short pulse TiSa lasers

Table top 40 TW laser Amplitudine Pulsar 200

For 200 MeV protons 1 PW laser needed

Main amplifier Front end


Proposals: 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


From 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

year

s


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


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

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 systems

Electric power 0.8 MW. Electric power 0.8 MW.


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.


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.


TNSATNSA We have compared some PIC simulations We have compared some PIC simulations in thein the initial initial regimeregime

described by electrostic described by electrostic Passoni Passoni ’s model’s model. Fits to electric field and . Fits to electric field and densitydensity..

..

..

..

..

..

..

..

..

..

..


..

..

..

..

..

..

..

..

..

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


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)


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


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


If 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-3-3

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


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 the number of accelerated ions is ions 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 Elaser 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


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 with PIC simuation Comparison with PIC simuation






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)

()

nc

ne


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)


Some 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%


2D effects can be relevant. PIC for RPA protons acceleration on thin target


Applications 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 in

2000 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


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 LS)for 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


Transition between thick RPA and thin RM targets regimes

RM ℓ=5 (red) ℓ=10 (green) ℓ=15 (purple) RPA (red ) ne=10 nc

Documents

Comparison of scaling laws with PIC simulations for proton acceleration with long wavelength pulses Sgattoni, C. Benedetti, P. Londrillo, L. Di Lucchio