Non Double-Layer Regime: a
new laser driven ion acceleration
mechanism toward TeV
1
outline

significance、implications、goals for high energetic
ion beams

one-stage acceleration：target normal sheath
acceleration (TNSA)、phase-stable acceleration or
radiation pressure acceleration(RPA)

multi-stage acceleration for TeV proton beam：
non double layer regime

Tens TeV or even higher energetic heavy ion beam
2
1.Motivation and current situation of laser-plasma ion acceleration
The produced high energetic ion by target normal sheath acceleration(
TNSA）experimentally：




energy gain：67 MeV for proton and 500MeV for Carbon ion.
acceleration field strength: 100 GV/m -- 10000 GV/m
energy spread: 20%
good repetitiveness
applications：ion cancer therapy、fast ignition of
thermonuclear fusion、high energy physics and astrophysics
goals ：mono-energetic、collimated、higher energy、higher
transfer efficiency
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2.One stage acceleration
2.1(a) TNSA
Thick solid target
Typical values:
k BTe  2 MeV ,
ne  2.5  1019 cm 3 ,
TNSA
D  2um
1
1
K BTe
K BTe
12 V


2
2
ETNSA  
 (4 ne K BTe )  10
, D  (

2)
eD 
m
4 ne e

4
2.One stage acceleration
2.2 circularly polarized laser-thin target interaction for ion acceleration -----phase stable acceleration or radiation pressure acceleration
v
Thin solid target
From an immobile sheath to a moving
sheath/double layer
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2.One stage acceleration
2.2 circularly polarized laser-thin target interaction for ion acceleration
------phase stable acceleration or radiation pressure acceleration
green：proton
blue：electron
(a) The light pressure balances the electrostatic pressure to form
double layer (electron and ion layer) structure,
matching condition:
a0 
1 ne
(
)( d )
n

cr
2
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2.One stage acceleration
b.The ion dynamical motion obeys：
dp
2I

dt  mi c 2
1  p2  p
1  p2  p
scaling law : p>>1， dp/dt ∝ (1/p2) , p ∝ t1/3, x1/3
（T. Esirkepov et al.,
PRL92,175003 (2004)）
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2. One stage acceleration
Phase space (x~px)
t=18TL
px
0.16
A
A
0.12
B
B
0.08
1050
1060
100x/L
X. Yan et al., PRL 100, 135003 (2008) ; Bin.Qiao et al,PRL 102,145002(2009);
X. Yan et al., PRL 103, 135001 (2009); M. Chen et al., PRL 103, 024801(2009);
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Linearly polarized laser pulse + thick solid target (2002)
TNSA regime
length:
energy:
ld
67MeV
Circularly polarized laser pulse + thin solid target (2008)
Phase stable regime:
length: tens mm
energy: GeV
Circularly polarized laser pulse + combination target
Non-double-layer regime
length: cm
energy: TeV
?????
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3.multi-stage acceleration for proton beam: non double
layer regime
The light pressure exerted on the electron layer is larger than the
electrostatic pressure. The electron layer is pushed out by the
ponderomotive force before double-layer is formed.
matching condition:
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Wakefield structure、electron and proton density
a0 sin 2 ( t
Simulation parameters：
), 0  t  20Tl

40
T
l
laser pusle: a  

a0 , 20Tl  t  35Tl
a0=250；foil : 20nc，D=0.5mm；gas length:12000mm，0.01nc
double layer:
D
1 nc
a0 l  2l
2 ne
Non-double
layer :
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Wakefield structure, phase space and energy distribution of proton beam
t=5000Tl
t=12000Tl
Maximum relativistic factor Gamma=580，Wmax >0.5TeV, 8 times higher than that in12the
double-layer regime
Dynamical process in the non-double layer regime versus
background gas density
distance between
the electron and
proton layer
maximum
electrostatic field
maximum
energy
Dephasing
length
Maximum energy scaling ：W
max
Minimum gas density：
 eEmax Ldp
1 a02 nc

mec 2
6 ne
ne  0.0005nc
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4.Heavy ion toward tens TeV
4.1 dynamical equation in describing the acceleration process of heavy ion
Assuming the same acceleration length for both proton and heavy ion
dp proton
edt

dpz
E
qz dt
p proton 
mproton v
v2
1 2
c
  proton mproton c
1/ 2


Z


2
2
2
EZ  ( z  1)mz c   1   proton ( )   1 mz c 2


A 


L
Defining the dephasing length ratio between heavy ion and proton：  z L
proton
the maximum energy of heavy ion reads:
1/2


Z 2
2
EZ  ( z  1)mz c   1   proton ( )   1 mz c 2


A 


2
 Z a02 nc
me c 2
6 ne
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Simulation results for carbon ion beams: the same laser
and plasma parameters as given for proton beam
t= 0.5Tl
t= 0.6Tl
In the non-double layer regime: the electron layer runs faster than the
carbon ion layer . The double-layer structure can’t be formed in the
laser-foil stage.
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Wakefield structure, electron density, carbon ion density,
laser pulse
t=5000Tl
t=15000Tl
The acceleration
process is terminated
at t=15000Tl ,meanwhile
the laser pulse is
completely absorbed,
suggesting that the
dephasing length is
equal to pump
depletion length.
The inset in Fig.(d) indicating: the energy transfer efficiency converted to carbon
ion is greater than 30%
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Heavy ion information
The longitudinal phase
space and energy
spectrum of the trapped
carbon ion at t=15000Tl
Maximum energy of
carbon ion versus time in
unit of laser cycles (a);
maximum energy for
different ion with charge
number Z (b).
1/ 2


Z 2
2
EZ  ( z  1)mz c   1   proton ( )   1 mz c 2


A 


2
 Z a02 nc
6
ne
me c 2
C6+ : 3.2TeV
Cu29+ : 16TeV
Au50+ : 25TeV
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THANK YOU!
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