Acceleration of a mass limited target by ultra-high intensity laser pulse

A.A.Andreev1, J.Limpouch2, K.Yu.Platonov1 J.Psikal2, Yu.Stolyarov1

1. ILPh “Vavilov State Optical Institute” , Russia2. Czech Technical University in Prague, Czechia

ABSTRACT

Outline

Motivation Numerical models: 2D hydro-code, 1D&2D PIC Theoretical models: quasi-neutral expansion of cold

ions, two sorts of electrons, plane or spherical geometry; charged plasma expansion

Conclusion

“Dynamic Hohlraum & Fast Proton Ignition” scheme for ICF

e-e-

e-

p+

p+

p+

p+

p+

Ee-

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 interactionlaser-target

Zone of ion acceleration

A space charge created by fast electrons pulls ions from the surface: three stages - ionization - extraction - acceleration

Electric field

Acceleration of ions by fast electron current

L s LR r , R c t L s LR r , R c t 1D FT 3D MLT

Quasi-n

eutral

R >> Rq

Isothermal R << tL cs Isothermal R << tL cs

1e+1i 2e+1i 1e+2i2e+2i

1e+1i2e+1i 1e+2i

2e+2i

Adiabatic R > tL cs

Adiabatic R > tL cs

1e+1i 2e+1i 1e+2i 2e+2i 1e+1i 2e+1i 1e+2i 2e+2i

Charged

R < Rq

 

Positive ions  

Positive ions

 

Positive ions with electron admixture

 

 (1)2e + (1)2i → (one)two sorts of electrons (of different temperatures) and (one)two sorts

of ions (of different mass); Rq = (mec2I18/e

2ne0)1/2

Analytical models of ion acceleration

Simulation model of 2.5 PIC calculations

The relativistic, electromagnetic code is used to calculate the interaction of an intense laser pulse with an over-dense plasma. The relativistic equations of motion and the Maxwell equations are solved for the components x, y, px, py, pz and Ex, Ey and Bz

  ∂Pj/∂t = qj(E + vxB), jmj∂r/∂t = Pj, ∂E/∂t = - Jj + c2 rotB, ∂B/∂t = - rotE .

 Particles reaching the simulation box boundaries may be either reflected or frozen at the boundaries. For thick target special conditions is implemented at the boundary in the target interior where fast electrons leaving simulation region are replaced by thermal electrons carrying the return current.

X/λ

Vix

/C

Case2 Vix/C depend on X/λ at 150fs

Laser prepulse (MLT density gradient) influence on ion acceleration

Ex

[MV

/μm

]

X/λ

Case1 Case2

Case3 Case4

T=150fs [T]

Y/λ

L

X/λ L

Y/λ

L

X/λ L

Y/λ

L

X/λ L

Y/λ

L

X/λ L

0 10 20 30 40 50

25

20

15

10

5

0 10 20 30 40 50

25

20

15

10

5

0 10 20 30 40 50

25

20

15

10

5

-6000 -3000 0 3000 6000

0 10 20 30 40 50

25

20

15

10

5

a) b)

c) d)

Electric and magnetic fields distributions for MLT foils

Dependence of proton maximal energy on plasma density gradient

Max

Ion

Ene

rgy

[KeV

]

L/λ L

Max Ion E

nergy Density [eV

/m3]

Dependence of the maximal ion energy on the plasma scale length at 150 fs, where circles are simulation results and the line is the analytical model result. Dependence of the maximal ion energy density on the plasma scale length (see squares).

Electric field spatial distributions for foil and sphere targets

Normalized absolute value of electric field during interaction of laser of amplitude a0 = 10, pulse duration 10T and bea

m width 4 λ with homogeneous plasma foil and sphere of initial size 4 λ and density ne = 4nc. The figures are plotted in

moments 5T after laser maximum reaches the target front side.

Dependence of the different component energy on time

Evolution (time in laser periods) of energy (in normalized units) during interaction of laser of amplitude a0

= 10, pulse duration 5T and beam width

4 λ with plasma sphere of diameter 4 λ and density ne = 4nc.

Electron distribution function

The electron DF: a0 =10, t=35, tL = 5T – blue, 1

0T - green Dependence of maximal electron energy on laser amplitude 2

eh e Lm c ( 1) 2 18 2

L 18 L, m 18 L1 0.7 I , I I /10 W / cm eh L ehN /

Electric field spatial distributions

Normalized absolute value of electric field during interaction of laser of amplitude a0 = 10, pulse duration 10T and beam wid

th 4 λ with homogeneous plasma sphere of diameter 4 λ and density ne = 4nc. The left and right figures are plotted in moments

5T and 30T after laser maximum reaches the sphere front side.

2r zF e E ( , t)H ( , t) / m c

2r z / 2

F e E ( , t)H ( , t) / m c

2im dh z imr e E ( , t)H ( , t) / m c 1.8

li t ikR cos l (1) ill

r 0 l(1)l l

J (kR)1E ( , t) E e sin e li H (kR)e

kR H (kR)

z

cj ( , t) H ( , t)

4

Dependence of ion maximal energy on target shape

Fast ion spectra calculated for the spherical target, and for laser normal incidenceon foil and foil section (square) of the same thickness 4 λ. Laser amplitude a0 = 10, pulse dura

tion 5T and 10T, beam width 4 λ with plasma sphere of diameter 4 λ and density ne = 4nc.

Dependence of ion maximal energy on laser field amplitude

Fast ion distribution maxima (peak) and maximum ion energy versus normalized laser amplitude.

Target is plasma sphere of diameter 4 λ and density ne = 4 nc, pulse duration 5T. Initial electron densitiesare 4, 4, 12, 36nc

and initial temperature 10, 10, 50 200 keV for a = 3, 10, 30 and 100 respectively. Peak

energies are recorded at 40T and maximum energies at 50T.2 2[ ( 1 ( ) )]im eh pi ef pi efZ ln t t

2 24 /pi eh iZ e n m eh

ehr dh

Nn

S r1.5ef Lt t

Dependence of ion energy on laser beam radius

Dependence of ion energy (normalized on ion energy for foil target) on radius

of laser beam (normalized on target radius)

Ion density dependence on time

21

L

M c

t= 0, t=30T, t = 50T V= 0.1c

Ion density distributions calculated for the different time moments. Laser amplitude a0 = 10, pulse duration 5T, beam width 4 λ

interacts with plasma sphere of diameter 4 λ and density ne = 4nc.

1 1 1 2 2 2

(1 ) LRM c M c

c

2 21 1 2 2(1 ) ( 1) ( 1)L R M c M c Q

21,2 1,2 1,2 1,21/ 1 , / c 1,2M

1 1 2 (1 )v c R

1 21 1 ( 1)M c R

Direct acceleration of overdence plasma bunch by laser pulse

0.1cm c

Spectrum of scattered light

sphere foil

Electron and ion distributions obtain dipole momentum during acceleration. It produces low frequency e.m. radiation in transversal direction. The generated light is shifted into the red side because target movement. Diffraction produces first laser harmonics at target rear.

    - the potential of plasma sphere with the radius Rp

  : all electrons can be blow off by laser pulse 

,max

4

3e p

q

n R

,maxek qe

1/ 2 1/ 220 0

2 22 3

21 22 302

834 ;

3 6 10 1

1.6 10 , 1 , 6 10

pep

e

L p

Re n na R

m c cm m

WI R m n cm

cm

Coulomb explosion

1 20

200

400

F x( )

v1 x( )

in

i

i

dN

dv1/ 2

0max

i 0

2eQ(r )v

m r

/i sv c

1/ 2

0sh max

i 0

2eQ(r )1v 0.8 v

* m r

Dependence of maximal ion energy on laser intensity for MLT target

Conclusions

1. The calculation of the mass limited targets (MLT) under the short pulse action is described by the isothermal automodel solutions of the hydrodynamics equations. The long laser pulse corresponds to the adiabatic solutions.

2. The presence of the hot and the cold groups of electrons in adiabatic and isothermal models results in the gap at the ion distribution function. In the plane case (foil target, FT) the gap is observed for Th/Tc 9.9, and in the MLT one – only for Th/Tc 34.

3. It is found that maximal ion energy can be significantly enhanced by choosing of mass limited target instead of foil of the same thickness.

4. During laser pulse interaction it produces electron bunches, which propagate MLT and generate dipole radiation in transverse direction beside ordinary EM scattering.

5. Diffracted light additionally accelerates electrons at MLT rear and produce short electron bunches, which correlate with light structure. It instead changes the spectrum of reflected light and help in production of subfemtosecond light pulses.

6. The optimal diameter of laser beam is about 1.5 target diameter for production of maximal ion

energy at minimal geometrical losses.