ION ACCELERATION IN INTENSE LASER FIELDS ION ACCELERATION IN INTENSE LASER FIELDS T. Schlegel GSI Helmholtzzentrum für Schwerionenforschung GmbH EMMI 2008 Workshop on Plasma Physics with Intense Ion and Laser Beams, GSI 21. - 22.11.2008
Co- -authors authors Co V.Tikhonchuk Centre Lasers Intenses et Applications Université Bordeaux 1, France N. Naumova and G. Mourou Laboratoire d'Optique Appliquée, ENSTA, Palaiseau, France C.Labaune Institute of Lasers and Plasmas and LULI, Ecole Polytechnique, France I. V. Sokolov Space Physics Research Laboratory, University of Michigan, USA EMMI Workshop, GSI, November 21, 2008 2
Outline Outline Ion acceleration with high-intensity lasers: • conditions and required characteristics Ion acceleration by the radiation pressure: the laser • piston model Numerical simulations of the high-intensity ion • acceleration and hole boring Effect of the electron radiation losses on the ion • acceleration Fast Ignition with 'in situ' accelerated deuterons • EMMI Workshop, GSI, November 21, 2008 3
Ion acceleration with intense laser pulses Ion acceleration with intense laser pulses Fast ions can find many applications in fusion, industry and medicine: low ratio current/ energy flux, simple ballistic − ρ ≅ ε 3 1 . 8 2 transport, high absorption efficiency l 10 g/cm i, MeV but one needs an efficient and compact ion accelerator to energies > 100 MeV. Two mechanisms of laser ion acceleration have been considered: TNSA - target normal sheath acceleration: requires an • efficient production of high-energy electrons, high-quality target surface, less restrictions on the laser pulse Ponderomotive acceleration: requires cold electrons, • high-quality laser pulse, less restrictions on the target, could be more efficient EMMI Workshop, GSI, November 21, 2008 4
Ion acceleration by high- -energy electrons energy electrons Ion acceleration by high A cloud of high energy electrons creates an electrostatic field on the density gradient and accelerates ions from the target surface: the TNSA mechanism – broad energy spectrum, Coulomb repulsion of the accelerated bunch. Cold electrons are necessary for charge neutralization of the dense ion bunch Thin target ( ) ε ≥ − = ε 3 5 T E n T / i h a h h 0 Zone of interaction laser-target e- Zone of ion acceleration p+ e- p+ e- p+ e- p+ E e- e- p+ e- p+ e- e- p+ p+ e- e- p+ Electric field p+ e- e- p+ e- p+ Laser beam Surface layers : contamination ( ) ≅ + λ − 2 2 T m c 1 0 . 75 I 1 µ O.Klimo et al, PRST-AB, 2008 h e 18 m EMMI Workshop, GSI, November 21, 2008 5
Circular vs vs linear laser polarization linear laser polarization Circular Circular laser polarization suppresses the electron heating. It provides favorable conditions for ponderomotive acceleration and ion beam neutralization. Example of electron spectra at the laser intensity 1.5×10 20 W/cm 2 and solid density. O.Klimo et al, PRST-AB, 2008 Cold electrons Hot electrons Circular laser polarization and electron radiation losses are two main effects to maintain a low electron temperature EMMI Workshop, GSI, November 21, 2008 6
Ion acceleration by laser piston – – stationary model stationary model Ion acceleration by laser piston Ions are accelerated due to the elastic v 1 = - v 0 + 2 v f collisions with a moving piston Relation between the piston and ion velocities v f ( ) 2 = − + ε = − 1 v v 2v m 2v v 1 0 f i i f 0 2 v 0 Conservation of the momentum flux = + (pressure) in the piston reference frame: p 2 n m (v v ) piston 0 i i 0 f stationary propagation EMMI Workshop, GSI, November 21, 2008 7
Ion acceleration by the laser piston: the piston velocity the piston velocity Ion acceleration by the laser piston: Ions are accelerated in the charge v f = β f c separation layer behind the electrons E z a n e ' ε i ' n i ' Relation between the piston and laser ion velocities, ion energy: 2n 0i γ v i β 2 β = ε = β γ f 2 2 2 2 m c + β i i i f f 2 1 f z a ' 0 z’ charge separation layer − β Conservation of the momentum flux 1 I = γ β + γ β f inc 2 2 n c m ( Zm ) c (pressure) in the piston reference + β 0 i f f i e f f c 1 frame: stationary propagation f EMMI Workshop, GSI, November 21, 2008 8
Structure of the charge separation layer: Structure of the charge separation layer: electrostatic field and ion density distribution electrostatic field and ion density distribution Φ = − ' 2 ' d Zen The electrostatic field profile in the charge separation i ε layer follows from the Poisson equation ( n e = 0) '2 dz 0 and the ion energy and mass conservation in the piston reference frame: ( ) v E z Φ + ε = γ − = γ f ' ' 2 ' Ze m c 1 ; n 2 n n e ' ε i ' i i f i 0 i f n i ' ' v i 2n 0i γ The first integral defines the electric field strength: ω γ ' ( ) d 1/ 4 z a ' ~c/ ω pi = β γ γ − 0 z’ pi '2 i 2 1 f f i ' dz c 2 ≅ ω γ β E m c The layer thickness ∆ z ~ γ f c/ ω pi for γ f >> 1 z i pi f f e EMMI Workshop, GSI, November 21, 2008 9
Structure of the ion charge separation layer Structure of the ion charge separation layer a) velocity of the accelerated ions c) ion density distributions in the piston reference frame d) spatial distributions of the b) ion γ -factor electrostatic potential and field EMMI Workshop, GSI, November 21, 2008 10
Structure of the electron sheath: Structure of the electron sheath: laser field and electron density distribution laser field and electron density distribution Φ = − − 2 ' ' ' Zn n d The electrostatic field profile in the charge separation i e e layer follows from the Poisson equation ε '2 dz 0 The electron energy and the laser amplitude obey the equations: ⎛ ⎞ γ γ γ 2 ' ' ' d n Z a ⎜ ⎟ = γ β − e 0 i e i 2 n e ' ⎜ ⎟ ζ f f 2 γ − − γ − d n ε e ’ '2 2 '2 ⎝ 1 a 1 ⎠ c E z e i 2n 0i γ β − β 2 Z 1 d a n = γ − f a f 0 i 2 a ζ + β f 2 γ − − 1 d n ' 2 2 1 a c/ ω pe c f ' z a 0 e z’ z ω ζ = ' c = ≈ γ β The electron layer thickness c/ ω pe , the laser field a ζ 0 f f EMMI Workshop, GSI, November 21, 2008 11
Structure of the electron sheath Structure of the electron sheath a) particle velocities d) vector potential b) γ -factors e) electrostatic potential c) electron and ion densities f) electrostatic field a) d) e) b) c) f) EMMI Workshop, GSI, November 21, 2008 12
Laser potential in the electron sheath Laser potential in the electron sheath Laser potential on the board of the electron charge separation layer a 0 = ≈ γ β is ~ 20 times larger than one would qualitatively expect a ζ 0 f f and it decreases slower with the plasma density a n e ' ε e ’ E z 2n 0i γ a 0 ' z a 0 z’ A very tight balance between the ponderomotive potential and the electrostatic field makes the electron confinement very unstable EMMI Workshop, GSI, November 21, 2008 13
Efficiency of ion acceleration by the laser piston Efficiency of ion acceleration by the laser piston B I Piston velocity depends on the laser β = = inc where B + intensity and the plasma density f 3 1 B n m c 0 i i Efficiency of laser-ion energy transfer depends on the piston velocity β 2 ε = β γ − = = ≅ λ 2 2 2 f 3 2 m c a I / n m c 0 . 61 I 1 R + β i i f f inc c e 18 µm 1 f EMMI Workshop, GSI, November 21, 2008 14
Ion energy spectrum in an inhomogeneous inhomogeneous plasma plasma Ion energy spectrum in an Ions are mono-energetic in a homogeneous plasma, in an exponential density profile the ions are a power spectrum Deuteron spectra in a plasma with the density increasing from 1 to 100 n c β dN I L 1 4 I = ε = i inc f min inc ( ) ln ε β γ + β β 2 5 4 6 i d 2 m c 1 n c i f f f i max f max EMMI Workshop, GSI, November 21, 2008 15
Time of hole boring and laser fluence Time of hole boring and laser fluence Time of ion acceleration depends on the difference between the photon and piston velocities , 10 GW/cm 2 F 100 = I inc T p is the laser flux needed for accelerate ions from the density increasing from 1 to 100 n c over the length of 100 λ , F 1 is the same for the density range 0.1 to 1 n c over the length of 1000 λ ≈ ∫ L n d m c L n d ∫ ε ∫ = = F L ( )d n n i i i F m cI T i i i i las i inc p n I n inc i i EMMI Workshop, GSI, November 21, 2008 16
1D & 2D PIC simulations of ion acceleration & hole boring 1D & 2D PIC simulations of ion acceleration & hole boring The code accounts for the electron radiation in the laser field and for the electron slowing down due to the radiation emission Laser pulse: a inc = 100 circularly polarized I inc = 4×10 22 W/cm 2 τ = 188 λ /c laser 100 n cr 2D: d/ λ = 20 flat-top with expon. wings Plasma: deuterium 5 n cr exponential profile L p / λ = 60; L/ λ = 20 n 0 / n c = [5-100] z/ λ EMMI Workshop, GSI, November 21, 2008 17
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