Transcript Introduction - University of Rochester

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” , Russia
2. 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
Acceleration of ions by fast electron current
A space charge created by fast electrons pulls ions from the surface:
three stages - ionization - extraction - acceleration
Thin target
Zone of interaction
laser-target
Laser beam
p+
p+
p+
p+
p+
p+
p+
p+
p+
p+
p+
p+
e-
e-
e-
E
e-
e-
eee-
Zone of ion
acceleration
ee-
e-
eee-
Electric field
Surface layers : contamination
Analytical models of ion acceleration
1D
Quasi-
3D MLT R  rL , R  cs t L
R  rL , R  cs t L FT
Isothermal
R << tL cs
Isothermal
R << tL cs
neutral
R
>>
Rq
1e+1i
Adiabatic
1e+1i
Charged
R
<
Rq
2e+1i
1e+2i
2e+2i
R > t L cs
2e+1i
1e+2i
1e+1i
2e+1i
Adiabatic
2e+2i
Positive ions
1e+1i
2e+1i
1e+2i
2e+2i
R > t L cs
1e+2i
2e+2i
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/e2ne0)1/2
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.
Vix/C
Laser prepulse (MLT density gradient) influence on
ion acceleration
Case2 Vix/C depend on X/λ at 150fs
X/λ
Electric and magnetic fields distributions for
MLT foils
Case2
Case1
a)
15
20
15
10
10
5
5
0
10 20 30 40 50
X/λL
10 20 30 40 50
X/λL
Case4
Case3
c)
25
15
X/λ
20
15
10
10
5
5
10 20 30 40 50
X/λL
-6000 -3000
d)
25
Y/λL
20
0
T=150fs
b)
25
Y/λL
20
0
Y/λL
Ex [MV/μm]
Y/λL
25
0
0
[T]
10 20 30 40 50
X/λL
3000
6000
Dependence of proton maximal energy on plasma
density gradient
Max Ion Energy [KeV]
Max Ion Energy Density [eV/m3]
L/λL
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 beam 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,
10T - green
eh  mec2 ( L 1)
Neh  L / eh
Dependence of maximal electron energy on laser
amplitude
2
 L  1  0.7  I18 L,
I18  IL /1018 W / cm2
m ,
Electric field spatial distributions
Normalized absolute value of electric field during interaction of laser of amplitude a0 = 10, pulse duration 10T and beam
width 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.


1 l l Jl (kR)
(1)
il
E r (, t)  E 0e it sin  eikR cos  
li
H
(kR)e


l
(1)
kR
l 
H l (kR)


c
j (, t) 
H z (, t)
Fr  e2 E  (, t)H z (, t) / mc

4
F  e2 E r (, t)H z (, t) / mc
 / 2
im  rdh e2 E  (, t)H z (, t) / mc

 1.8im
Dependence of ion maximal energy on target shape
Fast ion spectra calculated for the spherical target, and for laser normal incidence
on foil and foil section (square) of the same thickness 4 λ. Laser amplitude a0 = 10, pulse
duration 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 densities
are 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.
 im  Z  eh [ln( pi tef  1  ( pitef ) 2 )]2
 pi  4 Z e neh / mi
2 2
tef  1.5tL
N eh
neh 
S r rdh
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
t= 0,

L
t=30T,
2
t = 50T
V= 0.1c
M1c
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.
Direct acceleration of overdence plasma bunch by laser pulse
(1  R) L
 1,2  1/ 1  1,2 2 , 1,2  1,2 / c
 M 1c 1 1  M 2 c  2 2
c
2
2
 L (1  R)  M1c ( 1 1)  M 2c ( 2 1)  Q
  1
 1
v1  c 2 (1  R)
1  M1c  ( R  1)
2
cm  0.1c
M1,2
Spectrum of scattered light
foil
sphere
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.
Coulomb explosion
 q ,max 
4 ne R p
- the potential of plasma sphere with the radius Rp
3
ek  eq,max
: all electrons can be blow off by laser pulse
1/ 2
ni
 8 e2 ne 0 
n0

  Rp 
a
R

34

;
p

2 
22
3 
 6 10 cm   1 m 
 3me c 
W
I L  1.6 1021 2 , Rp  1 m, n0  6 1022 cm 3
cm
dN i
dvi
1/ 2
1/ 2
v max
400
F ( x)
 2eQ(r0 ) 


m
r
i 0



200
1/ 2
0
1
v1( x)
2
vi / cs
1  2eQ(r0 ) 
vsh  

 *  mi r0 
 0.8 v max
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.
The optimal diameter of laser beam is about 1.5 target diameter for production of
maximal ion energy at minimal geometrical losses.
6.