Download Plasma density effect on Ion beam acceleration

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 by PW laser
3. Proton acceleration by normal and oblique
incident PW lasers
4. Plasma density effect on ion beam
acceleration
5. Heavy ion acceleration and quark-gluon
plasma research
6. Conclusions and discussions
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. Could PW laser beam accelerating particles
serve for high energy physics instead of (or parallel to) accelerators
RHIC and LHC in future?
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
application to QGP research are presented and discussed
2. Electron acceleration by PW laserdriven wake field
Wake-field: Electrons
are accelerated, like surf
in laser-driven plasma
wave
Laser intensity 3x1020w/cm2,electron
energy >300MeV is observed
(Mangles et al., PRL94(05)
Some electrons are trapped and
accelerated in the bubble as
shown in the bubble black rod.
2. Electron resonance acceleration
in PW laser-plasma interaction
vz 1
Resonant acceleration :  ~ 1  g (r )(1  )
vg
Where
vz axial velocity for electron, v g group velocity for laser.
200
400
20
2
 mc (MeV)
2
L
(z-z )/
L
a0=16 (IL=3.16x10 W/cm )
v =0.99 (n =0.08n )
g
0
cr
B0=24 MG
B0Z=5 MG
100
0
00
200
55
10
15
20
0
25
time (ps)
Maximal kinetic energy ~180MeV
Maximal kinetic energy ~170MeV for
for Gaussian CP laser
planar laser (Liu and He, PRE2004)
3. Proton acceleration by PW laser
incident on normal direction
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 garget rear side is
generated when electrons penetrate through the target.
3. Proton acceleration by PW laser
incident on normal direction
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 PW laser
incident on normal direction
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 plot. Laser intensities of up to 1020 w/cm2,
But the pulse duration is < 100fs.
3. Proton acceleration by PW laser
incident on normal direction
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 plot. Laser intensities of up to 1020 w/cm2,
But the pulse duration is < 100fs.
3. Larger oblique angle of PW laser
effect on proton acceleration
Numerical simulation conditions (APL,90,
031503(07) by Zhou and He):
(a) Laser intensity I0=3x1020 w/cm2. PF-PIC.
(b) C+ H2+ foil (5eV), thickness: 19< z /
micron <26; density: in the propagating
direction, there is a linear rise to n0 within
1.0 micron on both sides, n0/100 at z=19.
(c)

(d)
  0 ,60
=0.2, 1, 3 g/cm3


3. Larger oblique angle of PW laser
effect on proton acceleration
Protons and carbon ions accelerated from the front and rear surfaces
of CH target deviate from the normal direction (I=3x1020 w/cm2) due to
non-Gaussian asymmetric sheath field at the target surfaces.
3. Larger oblique angle of PW laser
effect on proton acceleration
3. Larger oblique angle of PW laser
effect on proton acceleration
  0 , fast electrons are of x-like angle distribution,
p / p//  1 ;   60  , fast electrons along the
target surface generated by surface quasi-static EM
fields. Proton density distribution is no longer of a
symmetrical Gaussian-like structure. In particular,
two-Bragg energy peaks are observed in the
backward-accelerated proton beam. It confirms that
the front-surface electrons confined by the EM
fields can seriously influence on the emission of
the backward-accelerated protons. The conversion
efficiencies of laser energy into electron energy:
35% (0。) and 18% ( 60。) for >1 MeV. Electronproton efficiencies : 14% (0。) and 25% (60。) for
>2MeV.
4. Plasma density effect on Ion beam
acceleration
Relativistic electrons move across the foil,
JAP (07) by Zhou, Yu and He
4. Plasma density effect on Ion beam
acceleration
4. Plasma density effect on Ion beam
acceleration
I. Lower density
II. Density 1g/cm3
III. Better collimation,
Lower energy
4. Plasma density effect on Ion beam
acceleration
5. Heavy ion acceleration and
quark-gluon plasma
(1). Finding quark and gluon and understanding QGP
in laboratory are an essential mission in high
energy physics and high energy astrophysics
(2). 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.
5. 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
5. Heavy ion acceleration and
quark-gluon plasma
. Heavy ion beam (high-Z charged particles) could
also be accelerated to 100 GeV/ nucleon by PW
laser with intensity over 1024 w/cm2 that could be
reached by multi-PW beam irradiation.
. 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
5. Heavy ion acceleration and
quark-gluon plasma
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 ) .
4γ 2
5. Heavy ion acceleration and
quark-gluon plasma
T. Esirkepov et al. PRL 92, 175003 (2004).
5. 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
5. 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 mz c z ,  z 
c
z

 1  


m p qz
2

p
 mz e




2




1/ 2
5. 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 2  0.938GeV
m 2p q z2
mz2 e 2
 1)mz c 2
5. 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
6. 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.
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