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Plasmas produits par les impulsions lasers ultra-courtes : de l'ablation à la génération des particules relativistes

V.Tikhonchuk

Centre Lasers Intenses et Applications Université Bordeaux 1 ­ CNRS ­ CEA, France

Journées Plasmas Québec France

Le Garric, Juin 3, 2010

Outline

Propagation of intense laser pulses in gases: generation of THz radiation filament formation and coherent electromagnetic emission from a filament Interaction of ultra-short laser pulses with solids ablation of the matter in non-equilibrium conditions laser light absorption inside transparent materials: void & jet formation ablation of dielectric and metals with sub-ps laser pulses Laser-plasma interaction at relativistic intensities laser beam propagation in under-dense plasmas and electron acceleration in the wake field interaction of relativistic laser pulses with solids: electron & ion acceleration applications of laser accelerated ions for inertial fusion and medicine

Journées Plasma Québec France, Le Garric, June 3, 2010

2

Propagation of intense laser pulses in gases

filament formation and coherent electromagnetic emission from a filament generation of THz radiation from filaments

Journées Plasma Québec France, Le Garric, June 3, 2010

3

Transparent low density gases: paraxial propagation

Propagation of laser pulses can be described in the paraxial approximation for L >> 0 and T >> 1/0 and for unidirectional propagation. The dominant processes are: diffraction/dispersion, ionization and self-focusing Equations are solved within the laser pulse volume

n i i + ib - 2 E = k0 | E |2 - e E n0 z 2k0 2

Plasma response includes the refraction on free electrons and focusing due to the Kerr effect ­ no ion motion Laser pulse affects the media in two ways: atom ionization and electron heating

= Re E ( r , z , t - z / vg ) eik z -i t

r

0 0

ne = col (Te )ne + E ( nat - ne ) t 3 (neTe ) = - J ion col ne + j E 2 t

Journées Plasma Québec France, Le Garric, June 3, 2010 4

Formation of laser filaments

Depending on the focusing conditions, the filaments could be very long: competition between the Kerr focusing and plasma defocusing effects

near threshold filament: 248 nm, 100 fs, 1 mJ

multiple filaments above the threshold: 800 nm, 500 fs, 150 mJ

A.Couairon et al., 2007

Journées Plasma Québec France, Le Garric, June 3, 2010

5

Secondary effects: THz, optical emission & harmonics

Filaments emit electromagnetic radiation in broad band from THz to VUV: effects of the non-stationary ionization and wake field formation

odd harmonics

Emission in the THz domain

broadband optical emission

broadband spectrum of the laser pulse after propagation of 10 m in air: 800 nm, 70 fs, 210 mJ A.Couairon et al., 2007 Journées Plasma Québec France, Le Garric, June 3, 2010 6

Ponderomotive excitation of plasma current

Experiment: laser pulse: Wlas ~ 15 mJ, = 0.8 m, tlas = 50 fs, rep rate = 100 Hz DC E-field: E = 1 ­ 10 kV/cm Efficiency ~ 10-9

Wake plasma wave Quiet plasma ne ~ 1016 cm-3

0 ~ 100 µm

ctL ~ 20 µm

Laser pulse

fp

z

ne

1 THz

p =

c fp

300 m

ctL

A damped plasma wave is excited in the wake of the laser pulse The axial current dominates -2

r r j (r , t ) = e

2 0

r j ( z , t - z / c ) ez

7

Journées Plasma Québec France, Le Garric, June 3, 2010

Spectral content of plasma current: plasma oscillations

Electric current is excited by the ponderomotive force and the radiation pressure. Optimum condition petlas 2 ­ resonance excitation of the plasma wave. Plasma wave is strongly damped due to the electron-neutral collisions: pe ~ e ~ 5×1012 s-1 at the normal pressure

j

e 2 ne + e j = E +S me

z I las ( ) =t- S = - + 2 e c 2me c

Spectrum of the ponderomotively excited plasma current

j ( ) = -

I =

2 e pe ( + 2i e ) I 2 2 2me c 20 2 - pe + i e

(

)

I las sin (tlas / 2 )

1 - (tlas / 2 )2

t exp -i las 2

8

Journées Plasma Québec France, Le Garric, June 3, 2010

Emission of the plasma current

According to the general theory of electromagnetic fields, the radiation field depends on the Fourier spectrum of the plasma current

r r u j r , t u r r 0 3 A(r ,t ) = r u d r r - rr 4

( )

t = t -

r r u r - r cn

uur r 0 eikr r r A ( r ) = j ,k 4 r

ez L r Erad er

Radiated magnetic field in the far-field zone at the distance r from the filament of the length L

ik (1- cos ) L r r 1 e - 1 eikr r r 2 B ( r ) = 0 k j ( ) 0 er × ez 4 - kc cos r

Journées Plasma Québec France, Le Garric, June 3, 2010

9

Angular diagram of emission and efficiency

The radiation is emitted within a hollow cone The cone opening angle depends on the filament length:

Irad ( ) = Im

m = / L

L sin2 (1- cos ) 2 2c (1- cos )

sin2

The emission is a two-step process: Excitation of the plasma wake field

Ep

e 0 pe I las

2 2 m e las

V 200 cm

Radiation of the wake field ­ the emission is suppressed because of the small transverse component Total radiation losses of the laser pulse 2 1 p w ake 0 2

E

Ep / L

D'Amico et al., PRL, 2007

W

=

Transformation efficiency:

E 02 L 10 - 9 W las Wrad Wwake / L 10-2 Wwake

Independent on the filament length 10

Journées Plasma Québec France, Le Garric, June 3, 2010

Interpretation of the emission process

The emission can be interpreted as a transient-Cherenkov emission of a flying dipole · Propagating current has a zero charge = dipole the distance between charges ~ ½p

c

· Propagation velocity = c ( for the Cherenkov emission vg > c) the constructive interference is due to the finite length as in the transition radiation · Emission angle depends on the filament length (for the Cherenkov emission cos = vg/c) · Emission intensity is independent on the filament length (Cherenkov emission is proportional to the length) The wake field emission has certain advantages: easy arrangement ­ no alignment, good directivity, optical control ... and disadvantages: low efficiency, hollow cone

Journées Plasma Québec France, Le Garric, June 3, 2010

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Emission in external parallel DC E-field

The emission can be enhanced by applying the DC electric field parallel to the filament axis. Electrons in plasma column neutralizing the external electric field

Es

Etot = Eind + Epond

1

2 0 pe Es jind ( ) = 2 2 - pe + i e

-

E/Es

14

-

0.8 0.6 0.4 0.2

Quadratic dependence on the DC field strength

12

-

10

-

8

-

6

-

4

-

2

-

0.2 0.4

X

THz wave

Y

Z

Y. Liu et al., ARL, 2008

V

Enhancement ~ 1000 times, efficiency ~ 10-6 Journées Plasma Québec France, Le Garric, June 3, 2010

2 1 + Es2 / E p

12

Emission in the perpendicular external DC E-field

lens V Laser

THz wave

Z

X

Es z

A. Houard et al., PRL, 2008

The perpendicular DC electric field excites the plasma oscillations in the direction perpendicular to the filament axis.

W rad

3 04 0 E s2 L 2 pe c e

Es

x

Enhancement ~ 1000 times Efficiency ~ 10-6 Prop. to the filament length Linear polarization

0.3 0.2

It can be considered as a dipole flying in the direction perpendicular to its axis ­ the emission efficiency is strongly enhanced

c

-

0.1 0.2 0.1 0.2 0.3 0.4 0.6 0.8 1

Journées Plasma Québec France, Le Garric, June 3, 2010

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Interaction of ultra-short laser pulses with solids

laser light absorption inside transparent materials: void & jet formation ablation of dielectric and metals with sub-ps laser pulses ablation of the matter in non-equilibrium conditions

Journées Plasma Québec France, Le Garric, June 3, 2010

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Focusing inside transparent dielectrics: void formation

Laser: 200 fs 800 nm 20 - 120 nJ

microscope

Array of voids: single pulses at 6 µm depth

3D - stage Fs-laser

Laser radiation Objective lens Immersion oil Al2O3 Focal region

100 nm

laser direction

Numerical aperture 1.35 Peak power 0.5 MW Intensity ~ 500 TW/cm2

amorphous shell

void

S.Juodkazis et al., PRL, 2006 E.Gamaly et al., PRB, 2006

Journées Plasma Québec France, Le Garric, June 3, 2010

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Diameter of the void and the laser-affected zone

Void appears at Elas > 20 nJ No cracks in a pristine crystal at laser energy below 100 nJ Dvoid

Dstop 1000 D (nm)

3 2 1

Dstop

Formation of shock-affected zone can be understood on the basis of energy conservation

Dvoid

6

100

3 YDstop Eabs

100 50 Eabs (nJ)

Crystalline sapphire: Young modulus Y = 375 GPa Silica glass (viosil) Y = 75 GPa Fit to experiments:

Diameter of laser-affected region vs absorbed energy: measured (1) and estimated (2) 3 ­ shock affected zone

Dvoid = lv ( Eabs ,nJ )

1/ 3

lv = 80 nm

A significant part of the incident energy is absorbed ! Absorbed energy is transformed in a work of a void formation

Journées Plasma Québec France, Le Garric, June 3, 2010

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Modelling: sequence of processes in laser affected solid

1 Short time scale: laser energy absorption ~ 1 ps

Tight focussing results in the high intensity ~ 500 TW/cm2 at the focal spot Swift ionisation (fs) and conversion to plasma: electron heating Modifications of optical properties early in pulse time: absorption length ls ~ 1 µm 2 Medium time scale: hydrodynamic expansion ~ 1 ns Energy transfer from electrons to ions: Strong shock wave emergence in a 10 ps time, expansion, and material compression Rarefaction wave propagation backwards: formation of void 3 Long time scale: material cooling ~ 1 µs Phase transitions behind the shock front, pressure release

Journées Plasma Québec France, Le Garric, June 3, 2010

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First step: laser focusing and energy absorption

Description of the laser pulse absorption in solid targets requires the full set of Maxwell's equations in 3D as L 0, 0tioniz < 1 and the effect of reflected wave²

r r r r -1 t D = 0 × B - J e - JE

r r t B = - × E

laser

Plasma response includes the ionization, recombination and the energy deposition

t ne = w E ( nat - ne ) + col ne - -1 ne rec

3 2

r r -1 t ( neTe ) = Je.E -recneTe -Ugapcol ne

laser

Hydrodynamics is separated from laser propagation for the laser pulses shorter than 10 ps Journées Plasma Québec France, Le Garric, June 3, 2010

C.Mézel et al., PoP, 2008

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Dependence of the absorption efficiency on laser energy

Absorption depends strongly on the propagation and focusing conditions Elaser = 50.5 nJ

= 800 nm w0 = 0.3 m = 100 fs

Wmax = 1.1×1011 J/m3

Elaser = 5.6 nJ

Elaser = 22.4 nJ

Wmax = 5×1010 J/m3

Wmax = 1.2×1011 J/m3

C.Mézel et al., PoP, 2008

Journées Plasma Québec France, Le Garric, June 3, 2010

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Second step: hydrodynamic expansion

Blast wave propagation

Electron-to-ion energy exchange time

Wabs > Y

100 GPa

te -i ,energy ~ ( Mat / me ) e -i 10 ps

Plasma temperature

Shock wave formation time

P1, T1

tshock ~ l abs / cs 10 ps

Ti ~ Wabs / nat 10 eV

0

pressure

r

P0, T0

r

temperature

P1= P2

2 1

T1

sw r sw

pressure

temperature

0

r

density

sw

Rarefaction is formed behind the shock

1

T2 sw T0 r

Journées Plasma Québec France, Le Garric, June 3, 2010

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Hydrodynamic evolution depends strongly on the EoS

C.Mézel et al., PoP, 2008 0.2 ps 200 ps SESAME 7252, 600 ps

µm

µm

400 ps

600 ps

Pressure evolution in the exploding cavity with the QEOS: good qualitative behaviour but · the cavity is too big ~ 1 ­ 1.5 µm · weak dependence on the absorbed energy · weak dependence on the Young modulus The tension is not described

Simulations with the SESAME 7252 EoS give also too big cavity: the Grüneisen coefficient G = 0.65 is too big and the sublimation energy is too small

Simulations with a modified EoS with the realistic Grüneisen coefficient G = 0.05 and a higher sublimation energy Hsub = 28 kJ/cm3 reproduce correctly the cavity size

Journées Plasma Québec France, Le Garric, June 3, 2010

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Focusing near the rear boundary: jet formation

Laser focusing near the boundary may produce an ejection of a cold material

Absorption and shock formation Cavity formation and expansion Cavity collapse & jet formation

500ps

1 m

5 ns

13.2 ns

LASER

Shock wave formation

Cavity expansion

Jet formation

Numerical simulations: = 800 nm

w0 = 0.3 µm

las = 100 fs

Elas = 50.5 nJ 22

Journées Plasma Québec France, Le Garric, June 3, 2010

Jet formation: from 10 µJ to 100 J

Laser: 10 µJ w0 = 4.65 mm las = 28 fs = 800 nm target jet Laser E100 J = 300 ps 600 µm

Electron density distribution

jet radius 4.5 µm jet speed 90 m/s

0.5 (cm) 0.4 0.3 0.2 0.1

bow shock

5 bars

2 mm

mm Jet speed: 500 km/s, M = 10 ­ 15

reverse shock

10 bars

9 ns

Clear similarity between the processes in very different energy scales: possibility of rescaling up to astrophysical conditions

0.1 0.2 0.3 0.4 0.5 0.6 (cm) Journées Plasma Québec France, Le Garric, June 3, 2010

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Focusing at the surface: electron heating & fast ablation

laser Two-temperature EoS describes the ablation if the hydrodynamic time is shorter than the e-i temperature relaxation

Gold: phase diagram Gold: melting time

Fast electron heating affects the ablation process of metals if the laser pulse duration las and the pressure relaxation time lt/cs are shorter than e-i temperature equilibration time ei

B.Chimier, PhD thesis, 2008

In dielectrics: the melting temperature depends on the density and temperature of electrons in the conduction band

Experiment: LP3, 2009

SiO2: electron melting temperature ne

SiO2: effect of the pulse duration

Journées Plasma Québec France, Le Garric, June 3, 2010

24

Laser-plasma interaction at relativistic intensities

laser beam propagation in under-dense plasmas and electron acceleration in the wake field interaction of relativistic laser pulses with solids: electron & ion acceleration applications of laser accelerated ions for inertial fusion and medicine

Journées Plasma Québec France, Le Garric, June 3, 2010

25

Relativistic laser pulse self-focusing in low density plasma

Competition between the relativistic self-focusing of the laser pulse and the ionization defocusing enables the pulse guiding for many Rayleigh lengths

ne / (r)

(r)

ne (r ) = 1 - 2 (r )nc ne P > Pc = 16.2 GW nc

z=0 vg z = 2.75ZR vg

I(r)

zR

z = z - vgt Journées Plasma Québec France, Le Garric, June 3, 2010

S.Kalmykov, U. Texas, Austin, 2009

26

Relativistic laser wake & electron acceleration

Strong wake field formation: electrons can be accelerated to relativistic energies on a distance of a few mm Ions do not move, calculation box moves along with the laser pulse = z - vgt Bubble regime of electron acceleration: plasma: ne = 2.5×1017 cm-3 energy: 5.7 GeV, Imax 1020 W/cm2 Ne ~ 108 Q ~ 10 ­ 100 pC spread 8.4%

Wmax = 4 mec2 2 = 02 / pe2

Experiment PIC

Divergence = 6 mrad

J. Faure et al. Nature (2004) S.Kalmykov, U. Texas, Austin, 2009

Journées Plasma Québec France, Le Garric, June 3, 2010

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Control of the electron energy and spectrum

Combination of two counter propagating laser pulses facilitates the injection in the acceleration phase and enables controling the energy and charge of the electron beam Applications: compact accelerators, sources of X-radiation: betatron, FEL

Zinj=225 m Zinj=-175 m

pump injection

late injection

300 250 35

pump injection

E/E

Epeak

30 25

Peak Energy (MeV)

200 150

E/E (%)

20 15 100 50 spectrometer resolution E/E ~ 5 % 0 -200 -100 0 100 200 300 400 10 5 0 500

early injection

-zinj (µm)

Journées Plasma Québec France, Le Garric, June 3, 2010

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Electron acceleration in solid density targets

Acceleration of electrons is also efficient at the surface of solid targets The number of electrons is much larger but the energies smaller Applications: electron fast ignition, ion acceleration targe t laser

h

e

Th U p = mec2

electron phase plot

(

2 1+ 1 a0 -1 ; a0 0.6 I182 2

)

5×1019 W/cm2

electron energy spectrum L.Gremillet, 2009

Henig et al. PRL, 2009

Journées Plasma Québec France, Le Garric, June 3, 2010

29

TNSA mechanism of ion acceleration

Target normal sheath acceleration from a narrow layer at the rear side of the target; exponential energy spectrum Two step process: · efficient production of high energy electrons (> 30%) · ion are pulled out by the sheath electric field from the rear surface

laser target

electron sheath

eeee

-

ions

plasma

Debye

cs = ZTe / mi

E = Th / ecs t

dN i / dv = ni 0t exp(-v / cs )

Journées Plasma Québec France, Le Garric, June 3, 2010 30

Expansion of two ion species: spatial separation

The ion species separation happens naturally in a homogeneous multi-species targets: Heavy ion rarefaction wave Gurevich, JETP, 1973; Srivastava, Phys. Plasmas, 1988 The species with different ratio Z/mi are differentially accelerated

C+/H+ = 10:1

vh max

vl min

N peak < Ntail

p2t = 20 p2t = 40

xk1

xk2

vk2

Tikhonchuk, Pl. Phys. Conf. Fus., 2005

Journées Plasma Québec France, Le Garric, June 3, 2010

31

Experiment on ion acceleration from water droplets

Formation of peaks and holes in the ion energy spectrum has been seen in the experiment: liquid water droplets are the unique targets with two ion species and without surface contamination. The idea of light ions accelerated in the heavy ion front was verified with H2O and D2O targets

400 p ro to n s p+

1019 W/cm2 40 fs

ions in 256 nsr @ 5% bandwidth

200

100

p ro to n s

50

p+

400 200

p ro to n s

p+

Ø 20 µm

100

d+

50

d e u te ro n s

Two times difference in the deuteron and proton energies they are accelerated to the same velocity

0 .2

0 .4

0 .6

0 .8

1

2

e n e rg y (M e V )

Brantov, Phys. Plasmas, 2006

Journées Plasma Québec France, Le Garric, June 3, 2010

32

Ion acceleration in small-size targets: experiment

Laser interaction with small size targets D < 200 µm shows enhancement of hot electrons density and temperature. More energetic ions are produced. Lateral hot electron recirculation explains this effect

2×1019 W/cm2 400 fs 2 max energy of protons

# of hot electrons

hot electron temperature

hot electron temperature

(b)

Buffechoux et al. Phys. Rev. Lett, 2010

Journées Plasma Québec France, Le Garric, June 3, 2010

33

Radiation pressure acceleration (RPA) of ions

Radiation pressure acceleration at the front side and in the volume of target: · direct ion acceleration · neutralized ion bunch · more ions could be accelerated · heavy ions can be accelerated · could be more efficient · mild restrictions on the target Necessary conditions: · cold electrons (circ polarization) · high quality laser pulse (very high contrast > 1012) · higher intensities > 1021 W/cm2

target electron sheath laser ions

empty channel

sheath

Journées Plasma Québec France, Le Garric, June 3, 2010

34

Polarization control of the electron heating

Crossing of electron orbits is the dominant mechanism of electron heating at the relativistic laser intensities. The electron heating is greatly reduced in the circular polarization wave Experiment with the DLC foils at the intensity 5×1019 W/cm2 demonstrates cold electrons at circular polarization.

5×1019 W/cm2

Circular polarization cold electrons

Linear polarization hot electrons

Henig et al. Phys. Rev. Lett, 2009

1.5×1020 W/cm2

Klimo et al. PRST AB, 2008

Journées Plasma Québec France, Le Garric, June 3, 2010

35

Ion acceleration by the laser piston: the piston velocity

Conservation of the momentum (pressure) in the piston reference frame: stationary propagation

I las 1 - f 2 = 2 0 2 f2 c 2 f c 1+ f

piston velocity vf = fc

f =

I las I las + c 3

laser

ion energy and the efficiency of ion acceleration are defined by the piston velocity

charge separation layer

i = 2mi c 2 f2 2 1 - R = 1 + f f

Naumova, PRL, 102, 2009, Robinson, PPCF, 51, 2009

2 f

Journées Plasma Québec France, Le Garric, June 3, 2010

36

Example of 1D PIC simulation: circular polarization

Lower intensity: a0 = 20, I0 = 1.6×1021 W/cm2 n0 = 20 nc Estimates: 1 ­ R = 0.129 f = 0.07 Tb= 93T0 eEz /meoc = 37 pi /mic = 0.14 i = 18 MeV

electrons 0.2%

ions12.8%

electric field oscillations Agreement of num. results with theory No electrons escape the piston Small energy spread of accelerated ions Small radiation losses Electron heating behind the front pe >> pi

Schlegel, Phys. Plasmas, 2009

Journées Plasma Québec France, Le Garric, June 3, 2010

37

2D PIC simulation ­ channel formation

a0 = 100 circular polarization 4×1022 W/cm2 exponential profile L/0 = 20 n0/nc = 5 ­ 100

t = 90/c ions

y/

Laser pulse with a flat-top intensity profile demonstrates: · efficient hole boring in the plasma

· · · · · clean and a stable channel filamentation and SRS are suppressed strong radiation pressure small ion angular divergence, less than 10° velocity of hole boring is defined by 1D model

t = 190/c ions

laser

y/

Naumova, Phys. Rev. Lett., 2009

z/

38

Journées Plasma Québec France, Le Garric, June 3, 2010

Radiation acceleration of ultra-thin films

Light sail regime corresponds to acceleration of the whole foil under the laser radiation pressure;

ions

The regime of acceleration change when the piston comes out of the rear side of the target las > D/vf Then the whole target is accelerated by the laser pressure: very thin films and high laser intensities t = 8 0 t = 28 0

ions

I = 3×1020 W/cm2, D = 200 nm i ~ 150 MeV

Journées Plasma Québec France, Le Garric, June 3, 2010

Klimo, PRST-AB, 2008

39

Fast ignition with laser accelerated ions

Required parameters: beam energy 10 kJ, beam radius at the deposition point 20 µm, pulse duration < 10 ps Protons (deuterons) ion energy 10 ­ 20 MeV Carbons: ion energy 400 ­ 500 MeV (30 ­ 40 MeV/n)

Drive + cone + TNSA ions

Direct drive fast ignition + RPA ions

TNSA problems: source protection, control of ion energy spectrum, angular divergence, low surface number of ions, necessity of focusing, high laser power Practical limit is less than 1017 ions par cm2

2 P = Ilas Rsource las

Double laser pulse: hole boring and ignition

V.T. Tikhonchuk et al., NF, 2010

1021 W/cm2 × ( 300µm) = 1018 W

2

Journées Plasma Québec France, Le Garric, June 3, 2010

40

Fast ion radiography

1 Ionization beam 2 Proton generation beam 3 Interaction beam

300 ps FWHM t = 1 ns

t = 100 ps

L. Lancia et al., PRL, 2010

Journées Plasma Québec France, Le Garric, June 3, 2010

41

Medical applications

Laser produced ions are the attractive sources for the positron emission tomography. Production of the isotopes C11 O15 and F18 in pn reactions requires 20 ­ 30 MeV protons: 10 J, 1 Hz for production of samples with the activity of 200 ­ 300 MBq For the cancer therapy the ions with energies of 250 ­ 350 MeV are required with a well controlled spectrum and high reproducibility

PMRC, Japan. 2009

Journées Plasma Québec France, Le Garric, June 3, 2010

42

Conclusions

Laser produced plasma as a source of electromagnetic radiation: efficiency, flexibility, high power Laser induced material ablation and explosion: material processing and access to the proprieties at high pressure/temperature/density regimes Similarity of the processes at low and high laser pulse energies Laser produced plasma as a source of high energy charged particles: competition with conventional accelerators (small size) and wide range applications

Journées Plasma Québec France, Le Garric, June 3, 2010

43

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