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
3
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
5
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
6
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))
7
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
?????
9
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 :
11
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
13
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
14
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.
15
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%
16
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
17
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18
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In the non-double layer regime

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