ION ACCELERATION IN INTENSE LASER FIELDS ION ACCELERATION IN INTENSE - - PowerPoint PPT Presentation

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

EMMI Workshop, GSI, November 21, 2008 2

Co Co-

• authors

authors

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 3

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 4

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 transport, high absorption efficiency 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

2 8 . 1 3

g/cm 10

MeV i,

ε ρ

−

≅ l

EMMI Workshop, GSI, November 21, 2008 5

Ion acceleration by high Ion acceleration by high-

• energy electrons

energy electrons

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

e- e- e-

p+ p+ p+ p+ p+

E

e- e- e- e- e- e- e- e- e- e- e-

p+ p+ p+ p+ p+ p+ p+

Surface layers : contamination Laser beam Thin target Zone of interaction laser-target Zone of ion acceleration Electric field

O.Klimo et al, PRST-AB, 2008

( )

3 5

i h

T ε ≥ −

/

a h h

E n T ε =

( )

1 75 . 1

2 m 18 2

− + ≅

µ

λ I c m T

e h

EMMI Workshop, GSI, November 21, 2008 6

Circular Circular vs vs linear laser polarization linear laser polarization

Circular laser polarization suppresses the electron heating. It provides favorable conditions for ponderomotive acceleration and ion beam neutralization. Example

• f electron spectra at the laser intensity 1.5×1020 W/cm2 and solid density.

Cold electrons Hot electrons

O.Klimo et al, PRST-AB, 2008

Circular laser polarization and electron radiation losses are two main effects to maintain a low electron temperature

EMMI Workshop, GSI, November 21, 2008 7

Ion acceleration by laser piston Ion acceleration by laser piston – – stationary model stationary model

Ions are accelerated due to the elastic collisions with a moving piston Relation between the piston and ion velocities

( )

2 1 1 2

v v 2v 2v v

f i i f

m ε = − + = −

vf v0 v1 = - v0 + 2 vf

piston

2 (v v )

i i f

p n m = +

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

EMMI Workshop, GSI, November 21, 2008 8

Ion acceleration by the laser piston: Ion acceleration by the laser piston: the piston velocity the piston velocity

2 2 2 2

2 2 1

f i i i f f f

m c β β ε β γ β = = +

Ions are accelerated in the charge separation layer behind the electrons laser

vf=βfc

vi εi

'

Ez ni

'

ne

'

z’ 2n0iγ za

'

a Relation between the piston and ion velocities, ion energy:

charge separation layer

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

inc

1 2 2 ( ) 1

f i f f i e f f f

I n c m Zm c c β γ β γ β β − = + +

EMMI Workshop, GSI, November 21, 2008 9

Structure of the charge separation layer: Structure of the charge separation layer: electrostatic field and ion density distribution electrostatic field and ion density distribution

' 2 ' '2 i

Zen d dz ε Φ = −

The electrostatic field profile in the charge separation layer follows from the Poisson equation (ne = 0)‏ and the ion energy and mass conservation in the piston reference frame:

( )

' ' 2 ' '

v 1 ; 2 v

f i i f i i f i

Ze m c n n ε γ γ Φ + = − =

( )

' 1/ 4 '2 '

2 1

pi i f f i

d dz c ω γ β γ γ = −

The first integral defines the electric field strength: The layer thickness ∆z ~ γfc/ωpi for γf >> 1 εi

'

Ez ni

'

ne

'

z’ 2n0iγ za

'

~c/ωpi

f f pi i z

c m e E β γ ω 2 ≅

EMMI Workshop, GSI, November 21, 2008 10

Structure of the ion charge separation layer Structure of the ion charge separation layer

a) velocity of the accelerated ions in the piston reference frame b) ion γ-factor c) ion density distributions d) spatial distributions of the electrostatic potential and field

EMMI Workshop, GSI, November 21, 2008 11

Structure of the electron sheath: Structure of the electron sheath: laser field and electron density distribution laser field and electron density distribution

' ' 2 ' '2 i e

Zn n d e dz ε − Φ = −

The electrostatic field profile in the charge separation layer follows from the Poisson equation The electron energy and the laser amplitude obey the equations:

c z ω ζ ' =

2 ' ' ' 2 '2 2 '2

2 1 1

e i e i f f c e i

d n Z d n a γ γ γ γ β ζ γ γ ⎛ ⎞ ⎜ ⎟ = − ⎜ ⎟ − − − ⎝ ⎠

The electron layer thickness c/ωpe, the laser field

f f

aζ γ β

= ≈

a

Ez ne

'

z’ 2n0iγ za

'

εe’

c/ωpe

a a Z n n d a d

f f e a f c i f

β β γ β γ ζ + − − − − = 1 1 1 2

2 2 ' 2 2

EMMI Workshop, GSI, November 21, 2008 12

Structure of the electron sheath Structure of the electron sheath

a) particle velocities b) γ-factors c) electron and ion densities d) vector potential e) electrostatic potential f) electrostatic field

a)‏ b)‏ c)‏ d)‏ f)‏ e)‏

EMMI Workshop, GSI, November 21, 2008 13

Laser potential in the electron sheath Laser potential in the electron sheath

Laser potential on the board of the electron charge separation layer a0 is ~ 20 times larger than one would qualitatively expect and it decreases slower with the plasma density

f f

aζ γ β

= ≈

a

Ez ne

'

z’ 2n0iγ za

'

εe’

a0

A very tight balance between the ponderomotive potential and the electrostatic field makes the electron confinement very unstable

EMMI Workshop, GSI, November 21, 2008 14

Efficiency of ion acceleration by the laser piston Efficiency of ion acceleration by the laser piston

inc 3

where 1

f i i

I B B B n m c β = = +

Piston velocity depends on the laser intensity and the plasma density Efficiency of laser-ion energy transfer depends

• n the piston

velocity

2 1 1

f f

R β β − = +

2 2 2

2

i i f f

m c ε β γ =

µm 18 3 inc

61 . / λ I c m n I a

e c

≅ =

EMMI Workshop, GSI, November 21, 2008 15

Ion energy spectrum in an Ion energy spectrum in an inhomogeneous inhomogeneous plasma plasma

( )

inc 2 5 4 6

1 2 1

i i f f f

dN I L d m c ε β γ β = +

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 100nc

min inc max max

4 ln

f i i f

I n c β ε β =

EMMI Workshop, GSI, November 21, 2008 16

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/cm2

F100 = IincTp is the laser flux needed for accelerate ions from the density increasing from 1 to 100nc over the length of 100λ, F1 is the same for the density range 0.1 to 1nc over the length of 1000λ

( )d

i i i i

F L n n ε ≈ ∫

inc

d

i i p i

m c L n T I n =

∫

las inc

d

i i i

L n F m cI n =

∫

EMMI Workshop, GSI, November 21, 2008 17

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: ainc = 100 circularly polarized I inc= 4×1022 W/cm2 τ = 188 λ/c 2D: d/λ = 20 flat-top with expon. wings Plasma: deuterium exponential profile Lp/λ = 60; L/λ = 20 n0/nc = [5-100]

100ncr 5ncr

laser

z/λ

EMMI Workshop, GSI, November 21, 2008 18

1D PIC simulation 1D PIC simulation – – electron & ion phase plots electron & ion phase plots

t = 30 λ/c beginning of acceleration

• Electrons maintain the

acceleration field: they are driven by the ponderomotive force of the laser field in the forward direction, while the charge separation field accelerates them backwards.

• Ions driven by the charge

separation field are accelerated and move forward.

• Almost complete neutrality is

maintained in front of the piston

• Some electrons escape the

piston: they are losing their energy by generating high energy photons, and reverse their motion.

pz,e/mec z/λ

laser

γ

pz,i/mic z/λ electrons ions Electron radiation losses assure the quality of the piston

EMMI Workshop, GSI, November 21, 2008 19

1D PIC simulations with/without radiation reaction 1D PIC simulations with/without radiation reaction

Laser pulse: a = 100, circular polarization, t = 200T, plasma: n = 10nc,mi = 2mp.

• High quality ion

beam

• 14% of the laser

pulse energy of 28 laser cycles is converted into a high frequency radiation!

t/T=50 t/T=100

• 100 -50 0 50

100

• 100 -50 0 50

100

• 100 -50 0 50

100

z /λ w/o RF t/T=50 t/T=50 t/T=50 t/T=100 t/T=100 t/T=100

2% 8% 10% 10%

• 100 -50 0 50

100

z /λ

Pz,i /mic Pz,e /mec

with RF

electrons ions

EMMI Workshop, GSI, November 21, 2008 20

Radiation Reaction: Compton Radiation Reaction: Compton-

• Thomson Cooling

Thomson Cooling

a) charge separation & E-field creation b) escaped e- moves backwards, scatters

• n the incoming field

& returns back

c c E E c

γ

EMMI Workshop, GSI, November 21, 2008 21

Electron radiation slowing down Electron radiation slowing down

Thomson scattering is strongly amplified in the relativistic laser field due to high order harmonic generation: γe << a γe >> a

4 2 2 rad 3 max

3 , a c e P a N ε π ω ≅ ≅

2 2 2 2 rad 2 max

3 ,

e e

a c e P a N γ ε π ω γ ≅ ≅

Radiation is enhanced if the electron propagates toward the laser beam with a high energy, γe >> a >> 1. The photons with the frequencies ωph ~ ω a γe

2 are emitted in a

narrow cone θ ~ a/γe << 1. The electron radiation stopping length reads

m 5 3 ~ 40 1 1

4 2 2 2 2 rad

µ λ γ ω − ≅ ≅

c i e e e

n n a r a r c l

for ni/nc = 40 and a = 100.

EMMI Workshop, GSI, November 21, 2008 22

1D PIC simulation 1D PIC simulation – – ion energy distribution ion energy distribution

t = 250 λ/c end of acceleration Laser fluence: 20 GJ/cm2 Ions: 5.4 GJ/cm2 (27%)‏ Electrons: ~1% High energy photons: ~ 10%

analytical simulation

z/λ The ions are gaining the main part of laser energy, the electrons remain cold due to the radiation losses

pz /mi c

EMMI Workshop, GSI, November 21, 2008 23

2D PIC simulation 2D PIC simulation – – channel formation channel formation

z/λ

y/λ y/λ

t = 90λ/c t = 190λ/c Flat-top laser intensity profile Ion density distribution demonstrates efficient hole boring in the plasma, a clean and a stable channel Filamentation is strongly suppressed due to radiation losses Velocity of hole boring is in agreement with the 1D model ions ions

EMMI Workshop, GSI, November 21, 2008 24

Angular distribution of ions vs energy at the final instant at |y/λ| < 10 shows a narrow peak in forward direction Energy distribution in the central part (a cone of 6o) agrees well with 1D PIC simulations and analytical model laser

2D PIC simulation 2D PIC simulation – – ion energy ion energy distribution and angular spread distribution and angular spread

EMMI Workshop, GSI, November 21, 2008 25

Conclusions Conclusions

Laser acceleration of ions to high energies by the ponderomotive pressure could be efficient at high intensities: high contrast and circular polarization are needed A model of a laser piston predicts the ion energy spectrum as function of the laser and plasma parameters. Efficient ion charge neutralization by cold electrons Numerical simulations are in a good agreement with the model at high plasma densities: suppression of laser beam filamentation in the channel, stabilizing effect of electron radiation losses on the channel formation More extended 1D & 2D simulations are under way: electron radiation losses, stability of ion acceleration, ion beam divergence