Transcript laser plasma interaction

Present to International Conference on
Frontier of Science
Charged-particle acceleration
in PW laser-plasma interaction
X. T. He
Institute of Applied Physics and
Computational Mathematics,
Beijing 100088
Outline
1. Introduction
2. Electron acceleration in intense-laser
plasma interaction
3. Proton acceleration by normal incident
intense-laser
4. Influence of laser large oblique incident
angle on energetic proton beam
5. Plasma density effect on ion beam
acceleration
6. Heavy ion acceleration and quark-gluon
plasma research
7. Conclusions and discussions
1. Introduction
1.Introduction
With development of CPA technology, short-pulse and
high-intense laser (PW-1015w) system can provide
intensities 1018-21w/cm2 for each beam. Interaction of the
petawatt (PW) laser with matter may accelerate charged
particles (electrons, protons and heavy ions) to kinetic
energy over GeV.
The acceleration of high-energy charged particle beam
generated from interaction of an intense laser with solid
target has been one of the most active fields of research
in the last few years. It is of important potential
applications in fast ignition and accelerator etc. So far,
proton energy up to tens MeV for per nucleon is gained
by experiments and simulations under conditions on
existing petawatt (PW) laser (1018 -1020 w/cm2) with
normal incident to targets.
1. Introduction
So far only the PW lasers of x100J/0.5ps are used for
experiments. New PW lasers are being constructed :
10kJ/4 beams/1-10ps in Japan, 2x2.6kJ/2 beams/1-10ps
and NIF in US, 1.5kJ/1 beam/1-5ps (and future SG-IV) in
China will be operating in 2-3 years.
In this presentation, charged particle acceleration
mechanisms and the dependence of acceleration on
laser larger oblique angle and higher density target are
discussed and application to QGP research is presented.
It seems to be the traditional PIC code beyond its power,
and a new developed 3D hybrid-Fluid+PIC (HF-PIC) code
must be used to simulate the generation and transport
of electrons, carbon ions, especially protons in solid
target.
2. Electron acceleration in intenselaser plasma interaction
2. Electron wake field acceleration in
intense- laser plasma interaction
(1) Wake-field acceleration:
Laser beam propagates in plasma, a
wake-field is generated by laserdrive plasma wave due to charge
separation. Electrons are
accelerated, like surf in plasma wave.
2. Electron wake-field acceleration in
intense- laser plasma interaction
3x1020w/cm2,
Laser intensity
electron energy >300MeV is
observed (Mangles et al., PRL94(05)
Some electrons are trapped and
accelerated with mono-energy
and within an angular spread of
a few degree in the bubble
(Katsouleas et al., Nature,
515(04)).
2. Electron resonance acceleration
in intense-laser plasma interaction
(2) Resonant acceleration :
Electrons are accelerated
by spontaneous electric
field Es and magnetic field
Bs , both generated in laser-plasma interaction.
Resonance acceleration occurs when resonance
condition ωb = ω- kvz is satisfied, where the
betatron oscillation frequency ωb =[γe/mr0 (Es +
vzBs/c)]1/2 , and ωb/ ω =1-vz/c as relativistic factor
γ »1. Resonance acceleration gives
γ=f(r,t,kB,kE,vg)/(vz-vg), where vz axial velocity for
electron and vg group velocity for laser.
2. Electron resonance acceleration
in intense-laser plasma interaction
Test particle results of resonant acceleration :
Maximal kinetic energy ~140-170 Energy spread about 20% and
MeV for the Gaussian circularly
polarized (CP) laser with intensity divergent angle about 2 degrees.
3.1x1019 w/cm2 and plasma density
ne/nc=0.1.
3. Proton acceleration by normal
incident intense-laser
3. Proton acceleration by normal
incident intense-laser
Electrons driven out of the target front side by PW laser
ponderomotive force set up electrostatic fields that
accelerate protons backward against the PW laser
direction. On the other hand, the electrons in the target
front side can also be accelerated by ponderomotive
force, a thin Debye sheath at the target rear is generated
when electrons penetrate through the target.
3. Proton acceleration by normal
incident intense-laser
When PW laser beam propagates along the target normal
direction or a small angle, the proton emission cone is also
aligned at same as direction or cone. Furthermore, the
electron sheath has a Gaussian profile, and the central region
as well as the edge of the sheath will expel proton normal to
the surface. The Bragg peak proton energy is at the center the
resulting Gaussian proton beam (Zhang and He, IAEA06).
Electric field E=30GV/cm, laser
intensity 1020w/cm2
Energetic proton in the
rear CH target
3. Proton acceleration by normal
incident intense-laser
Protons by PW laser acceleration was verified by
experiments and simulations, see review papers: Plasma
phys. Controlled Fusion 47, B841(05) by M. Roth et al and
Fusion Science and Tech. 49, 412 (06) by M. Borghesi.
Experimental results are shown in the following plots.
Laser intensities of up to 1020 w/cm2, But the pulse
duration is < 100fs.
4. Influence of laser large oblique
incident angle on energetic
proton beam (simulation)
4. Influence of large oblique incident
angle on energetic proton beam
Model: C+H+2 slab with thickness 5m and linear ramps 1m at both
sides of slab, and initial density ne/ncr ~140 as shown in Figs. [n0C,
n0H , n0e]=[6,1.2, 8.4]x1022cm-3. For laser normal incident (θ=0o), laser
I0=3x1020 w/cm2 with spot 6 m. For oblique incident (θ=60o), slab is
rotated to target thickness 2 m.
Zhou and He, APL
90,031503(07).
4. Influence of large oblique incident
angle on energetic proton beam
For laser normal incident on target, at t=500fs, (a) electrons
accelerated by intense laser penetrate to target rear to form a
collimated electron beam with energy ≤2MeV and an energetic
electron jet with energy >2 MeV and a X-like angular distribution
(divergent angle of 45o). Target normal sheath (TNS) of tens
GV/cm is generated at both front and rear target surfaces. (b), (c)
Proton beam and carbon ion beam at target rear are accelerated
by TNS and both are of Gaussian profiles with maximal
energy~17MeV (protons), ~2.5MeV(carbon ions).
4. Influence of large oblique incident
angle on energetic proton beam
For 60o oblique incident, at t=500fs, energetic electrons are
confined near target front surface and energetic electrons in Xlike angular direction run to target (thickness 2μm) rear to form a
TNS; at target rear, proton beam has a single peak energy
distribution with maximal energy~20MeV and the number of
protons seem to be less than that in normal incident, while at
target front it has an asymmetry profile and double energy peaks
due to target surface electromagnetic fields. Carbon ion beam is
of maximal nergy~2.0MeV and better collimation.
4. Influence of large oblique incident
angle on energetic proton beam
Forθ=60o, angular distribution of
proton energy, detailed the
previous Fig.(e), is shown at four
energy regions :(a) p  2MeV ,
(b) 2   p  12 MeV, (c) 12   p  20 MeV
(d)  p  20MeV , protons emerge
only in the backward direction and
deviate the normal.
Conversion efficiency: for   0  , about 35% from laser to
energetic electrons with temperature >1.0 MeV. For   60 , a
fraction of laser energy is reflected, it leads to only 18%
conversion. Energetic electrons (>2MeV) convert to proton energy

about 14% and 25% for   0 and   60  , respectively.
5. Density effect on proton acceleration
from intense-laser interaction with CH
target ( simulation)
5. Density effect on proton acceleration from
intense-laser interaction with CH target
Model: C+H+2 slab (5eV) with thickness
5m and ramps 1 m , for ρ =3gcm-3,
[n0e , n0H, n0c]=[3.86, 2.57, 1.29]x1023 cm-3
Laser intensity I=3.3x1020 /cm2, = 1 m ,
r0 =3 micron, normal incident. Zhou
and He, Opt. Lett. 32, 2444(07).
Results: at t=50-500fs,
electrons are reflected
many times due to mean
free path much larger than
foil thickness, TNSA
electric filed tens GV/cm.
5. Density effect on proton acceleration from
intense-laser interaction with CH target
3 gcm-3
1/3 gcm-3
Proton acceleration for densities 1/3 gcm-3 (d-f) and 3 gcm-3 (a-c) at
t=400fs. TNSA and shock acceleration for lower density target (d-f)
are more effective than that for higher density target (a-c). However,
for higher density target, TNSA of proton beam becomes more
effective and the collimation is better, though the efficiency of both
mechanisms decreases with density. At rear target surface, TNSA
maximal electric fields |Eρ=1/3 | / |Eρ=3|~4 lead to maximal forward
energy ~28MeV with energy emission cone < |30。| (>5 MeV, red-e) for
density 1/3 gcm-3 and ~6MeV (red-b) with emission cone < |5。| (>1.8
MeV) for density 3gcm-3. Black c and f are backward proton energy.
5. Density effect on proton acceleration from
intense-laser interaction with CH target
Proton acceleration for densities 1/3 gcm-3 (d-f) and 3 gcm-3 (a-c).
Till t=500fs, conversion efficiency of laser energy to proton is about
5.6% for lower density and only 0.3% for higher density, as shown in
plots. Experimental results for Al and CH targets have ranged
between 2-7% (Fusion Sci. & Tech. 49, 412(06)). The proton number
about 8.8x1012 (1MeV) and the carbon ion number about 4.7x1012
(1MeV) for lower density are roughly estimated.
5. Density effect on proton acceleration from
intense-laser interaction with CH target ( thin
target and acceleration within tens of femtosecond)
Model: C+H+2 slab (5eV)-left figure,
 =0.2(I), 1(II) and 3(III) gcm-3,
Laser intensity I=2x1020 /cm2, λ=1µm
r0 =3 μm, normal incident.
Zhou et al., JAP 101,103302(07)
Results: for t=5-100fs, trajectories of
several typical electrons for density (II)
show that electrons experience multireflection, stochastic heat and collision.
TNS fields of tens GV/cm at both front
and rear of target are observed.
5. Density effect on proton acceleration from
intense-laser interaction with CH target
ρ=0.2gcm-3
ρ=1.0gcm-3
ρ=3.0gcm-3
Plots show snapshots of density profiles of electrons, protons and
carbon ions at 75fs. An ion hole driven by laser ponderomotive is formed
on the front surface, the hole boring velocities [5.1, 2.3, 1.3]x10-2c are
greater than the sound velocity~0.5x10-4c, the collisionless shock wave is
formed. The ions are backward into left vacuum and forward into the
target by the shock. At the rear target, ions are accelerated by TNSA and
shock wave, the latter produces the mono-energy~1MeV.
5. Density effect on proton acceleration from
intense-laser interaction with CH target
ρ=0.2gcm-3
ρ=1.0gcm-3
ρ=3.0gcm-3
Figs. show at t=75fs proton velocity and angular distributions. The
proton energies reach ~15, 6 and 3 MeV from lower to higher density at
rear target respectively, and the higher density is favorable to proton
collimation as shown in Fig. (i). TNSA dominates at lower density, while
shock wave acceleration may intensify TNSA at higher density > 3gcm-3.
5. Density effect on proton acceleration from
intense-laser interaction with CH target
P
C+
C+
P
ρ=0.2gcm-3

ρ=1.0gcm-3
ρ=3.0gcm-3
At t=75fs, vz / c distribution.
C+ and P strongly respond to
laser and space-charged
fields at both sides of target,
though C+ has a longer
response time due to its
heavier mass.
The thermal energy (eV) of P
accelerated by shock decreases
with density increase, and is
quite small at rear target. The
divergent angle by TNSA also
decreases. While C+ by shock
has a higher thermal energy than
by TNSA at t=75fs.
6. Heavy ion acceleration and
quark-gluon plasma
Finding quark and gluon and understanding QGP in
laboratory are an essential mission in high energy
physics and high energy astrophysics
Heavy ion beam colliding in the frame of center of
mass has achieved QGP information.
In the past 2-3 years, gold nuclei are accelerated by
RHIC and collide in the frame of center of mass
and the QGP like ideal fluid state was observed.
The QGP state rapidly reaches thermo-equilibrium
like equilibrium plasma and can be explained by
the fluid equations.
6. Heavy ion acceleration and
quark-gluon plasma
T μν
Motion equation for QGP：
0
μ
x
ε (ε  P)

0
Equation for energy density :
τ
τ
For ideal massless QG gas,
ε
π2 4
T
Pressure: P   g t ot
3
90
g tot  [ g g 
7
g q  g q ], g g  8 2, gtot  37
8
The Solution: ε(τ)  ε(τ)   τ 0 
ε(τ0 ) ε 0  τ 
T ( )   0 
 
T ( 0 )   
4/ 3
1/ 3
6. Heavy ion acceleration and
quark-gluon plasma
PW laser can be used to explore QGP instead of the
traditional accelerators, such as RHIC and other
new one. Relativistic momentum equation or
relativistic Vlasov equation can be used to
investigate such heavy ion beam
Numerical simulation shows that when laser
(intensity I≥1023W/cm2 ) interacts with CH target foil
(thickness l~λ), kinetic energy of protons can reach
over 4GeV . The laser piston model shows that
protons undergo two stages:
longitudinal field E / /  2πenel acceleration, which is
generated by charge separation; laser light
reflection to transfer laser energy to target with
reflectivity κ  (1 1 2 ) .
4γ
6. Heavy ion acceleration and
quark-gluon plasma
T. Esirkepov et al. PRL 92, 175003 (2004).
6. Heavy ion acceleration and
quark-gluon plasma
From numerical simulation and analytical estimation,
as t  , ion kinetic energy asymptotically
 ik  mi c 2 (3It / nelmi c)1/ 3
where I is laser intensity, l is foil thickness
2 L
 L  L
~
max (  ik) 
2
2 L  N i mi c N i
Ni
For  L  10kJ ( / 1m), ne  5.5 1022 cm 3 , l  1m
2
The acceleration time tac  ( L / N i mc 2 ) 2 t L  16 ps
3
and acceleration length Xac=ctac=4.8mm
 ik  30GeV
6. Heavy ion acceleration and
quark-gluon plasma
We may estimate kinetic energy of heavy
ions from relativistic momentum equation for
proton
dPp
dPz
 Ee 
edt
qdt
vz
Pp   p m p c, Pz   z m z c z ,  z 
c
z

 1  


m p qz
2

p
 mz e




2




1/ 2
6. Heavy ion acceleration and
quark-gluon plasma
Kinetic energy for heavy ion scaled from proton
E z   z  1mz c 2  ( 1   p2
2
z
2
2
 ( 1   p 2  1) Az m p c ,
Az
m p c  0.938GeV
2
m 2p q z2
mz2 e 2
 1)mz c 2
6. Heavy ion acceleration and
quark-gluon plasma
If proton kinetic energy reaches 100GeV (laser
intensity about 1024w/cm2), and z/A~1/2, then
Ez  50 Az GeV
It means that in the frame of center of mass, zparticle colliding with kinetic energy 100AGeV may
generate QGP.
During the collision of two beams, the number of
reaction with cross section  is
N  N i2 / s  2 1010 / cm 2  106 ,   10 24 cm 2
Where s is the beam sectional area
7. Conclusions and discussions
7. Conclusions and discussions
(1) Charged particle accelerations in PW laser
interaction with matters have extensively
investigated, to understand mechanism is
challenging. Now only the PW lasers of x100J/0.5ps
is used for experiments, numerical simulations are
limited by computer capability. Today kinetic
energy~ GeV is possibly gained.
For the sub-picosecond intense-laser beam
interacting with plasma:
In present day electron acceleration can accelerated
up to relativistic energy of hundreds MeV with
approximate monoenergy and small divergent angle
by wake-field and betatrron resonance acceleration.
7. Conclusions and discussions


Proton beam accelerated from front and rear target
surfaces are not completely aligned along the target
normal due to electric sheath being not a Gaussian
spatial profile if oblique incident angle large enough.
The number of protons may be less than that in normal
incident.
Target density can significantly influence proton
acceleration, for higher density TNSA is more effective
than shock acceleration, while for lower density both
acceleration processes are comparable. A lower density
target is favorable to higher energy of TNSA.
For tens femtosecond laser interaction with plasma, in
higher density target protons accelerated by both TNS
and shock have less energy at target rear, but more
collimation.
7. Conclusions and discussions
 Conversion efficiency of laser energy to protons is
about 5.6% for lower density and only 0.3% for higher
density. The proton number about 8.8x1012 (1MeV)
and the carbon ion number about 4.7x1012 (1MeV) for
lower density are roughly estimated.
(2) Due to advancing the study of fast ignition of inertial
fusion driven by PW laser, based on present-day CPA
technology, to obtain PW laser intensity over
1024w/cm2 is confident if tens beams are used and
each beam has 2kJ/1 ps and the focused spot ~2 m
.
It means that there are possibility to design QGP
experiment and to experimentally explore many
important phenomena occurring in astrophysics in
near future.
Thanks