Download High intensity slow wave structures for relativistic particle

UNIVERSITY OF MARYLAND AT COLLEGE PARK
High-intensity optical slow-wave
structure for direct laser electron
acceleration
H.M. Milchberg, B.D. Layer, A. York, J. Palastro, T, Antonsen
University of Maryland, College Park
HEDSA 2009
Conventional accelerators
high energy physics
27 km circumference
LEP (CERN) (100 GeV)
SLAC (50 GeV)
3 km
R > Rmin
 synchrotron radiation loss
constraints:
Eaccel<106-7 V/m  structure breakdown
The SLAC structure is periodically modulated
Etransverse
Btransverse
Ez
EM propagation
& particle accel.
‘slow-wave’ structure
wave phase velocity < c
accelerator waveguide structure
internal breakdown (lightening!) and self-destruction
if wave fields are greater than ~ 107 Volts/m
Solution: use ‘milder’ fields over longer distance
view from space
50 GeV/(1.7x107 V/m) ~ 2 miles
‘conventional’ laserplasma wakefields:
intense laser pulse
enters gas jet and
relativistic electron
beam emerges
relativistic electron beam
relativistic electron
spectrometer
150 m
Plasma oscillation: “wake-field”
pulse speed is vg < c
-
+
E
E
+
E
E
+
E
Laser pond. force for
>1018 W/cm2 pushes
electrons out of the way
(e) (e)
100ps Nd:YAG laser
pulse
13 µm
13µm
But can we
imitate SLAC
using a
plasma?
(a)
200
35 fs Ti:Sapphire laser
pulse
200µm
(b)
r (µm)
YES! 
Axially modulated plasma
waveguide
Radially modulated
Axicon
-200
0~35 μm
(c)
50 fs transverse
interferometer probe
300 µm
z (µm)
50µm
35 µm
1000
(d)
50µm
35µm
Principle of plasma waveguide: example of hydrodynamic
shock generation
experimental electron density
profiles after pulse:
Plasma cross-section
during and immediately after pulse:
104 bar
pressure
blast wave
expansion
“hollows”
the Ne profile
0
25
radius (m)
A hollow electron density profile
acts as a focusing element
plasma index of refraction
n2  1 
N e (r )
N cr
Ne(r) lower in middle results in
index n larger there
focusing
‘Slow wave’ structure
Particle acceleration
quasi-phase matching
EM wave generation
Charged particle
dephasing
vparticle < vwave phase
Phase mismatch
vpump ≠ vgenerated
electron
Ez
Epump
z-vphaset
z-vpumpt
vphase>c
Lcoherence
k Lcoherence=
Slow wave picture
r
z
d
Bloch-Floquet condition:
E (r , z,  )  u(r , z,  ) exp( ik 0 z ) where u(r , z  d , )  u(r , z, )
u (r , z  d ,  )  u~(r ,  ) am exp( ik m z ) where km  2 m / d
m
Wave number of mth
axial harmonic
 m  k0  2m / d
mth harmonic is ‘slow’ if v phase,m   /  m  c
Electron acceleration: slow wave picture
Electron energy gain
U  e  E v dt  e  u~ exp i (k0 z  t ) ( am exp( ik m z )) v dt
m
L
z
U  e  E v dt  e  dz u~  am exp i (  dz ' (k0  k m   / v))
0
m
For the ‘matched’ case
get
k0  kn   / v  0
U  eE0 an L
dt  dz' / v
Quasi-phase matching picture
Example: density modulation
Mod period d=L1+L2
Accelerating region: low
plasma density (high index)
Ld1
Ld2
n1 > n2
Decelerating region: high plasma
density (low index)
The driving wave speeds up and slows down in successive portions of the
modulation so that the acceleration in the first part is not completely cancelled
by deceleration in the second part.
Energy gain
per period:
U  e( Ez1Ld1  Ez 2 Ld 2 )  eE0 ad
where
a 1
Outline
• reminder about clusters
-heating and plasma formation with femtosecond pulses (PRLs <2005)
-heating and plasma formation with long (many picosecond) pulses
• formation of axially modulated (corrugated) plasma fibres using long pulses
- axially modulated heating pulse
- tailored cluster flow
• direct laser acceleration
Clusters are essential!
Clusters
TOF mass spectrum†
Signal
60
Electrons/photons
40
X-ray signal*
few Å ~ 500 Å
~10-107 atoms—
explode in < 1 ps
Ions
20
0
0
5
10
Time (s)
15
Energetic
electrons/ions
Neutrons
>90% laser absorption
X-rays
Laser pulse
Cluster jet
EUV
Scattering
EUV spectrum*
X-rays: A. McPherson et al., PRL 72, 1810 (1994).
EUV and x-rays: * E. Parra et al., PRE 62, R5931 (2000).
Optical properties: Kim, Alexeev, Milchberg, PRLs 2003, 2005
Fast electrons and ions: Y. L. Shao et al., PRL 77, 3343 (1996);
† V. Kumarappan et al., PRL 87, 085005 (2001).
Nuclear fusion: T. Ditmire et al., Nature (London) 398, 489 (1999).
Why do 100ps pulses efficiently heat clusters?
H. Sheng et al, Phys. Rev. E 72, 036411 (2005)
•The far leading edge of the 100ps beam disassembles / ionizes the
clusters, leaving a cool high Z plasma that the remainder of the pulse heats.
•Much more efficient than heating an unclustered gas (for same average Z
in a plasma, up to 10x less pump energy required) -40-50% absorption
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High Z, cool,
under-dense
plasma
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50 Å ~ 600 Å
Single Ar cluster
Sub-critical plasma
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a
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Super-critical plasma
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Critical density layer
Cryogenic cluster jet
•enhanced absorption, even
for very long (100ps) pulses
• because absorption is
local to a cluster, can
ultimately form plasma
channels with Ne ~ 1018
cm3 electron density* and
lower
2 cm
• efficiently makes plasma
channels in anything that
decently clusters
• Typically 10X more
efficient than for equivalent
vol. average pressures of
unclustered gas
Controlled cryogenic cooling of
the jet enhances clustering
First modulation method- modulated Bessel beam
and uniform cluster flow
100-300mj 100ps Nd:YAG pulse, axially
modulated with diffractive optics, incident on
unmodulated cluster jet flows
Ex. ~2mm corrugation period
1.5 cm
1.5cm
Breakdown in atmosphere
Breakdown in Argon clusters
Guiding in corrugated hydrogen plasma
channels
15µm
(b)
(i)
(ii)
(iii)
1017 W/cm2
500 µm
• H2 jet cryogenically cooled to
enhance clustering
• Electron densities of ~1.5*1018
cm-3 on axis and ~3*1018 cm-3 at
channel wall for a delay of 1ns
700 µm
200 mJ
300 mJ
500 mJ
+ misalign.
Waveguide generation pulse energy
and alignment controls modulation features
Extended high intensity guiding
beads
continuous
No injection
700µm
No injection
injection
Pump scattering
injection
Pump scattering
Abel inversion
Abel inversion
1 mm
Extended high intensity guiding
660µm
without injection
1018cm-3
8
6
injection, 2x1017 W/cm2 at exit
4
laser
2
3 mm
Propagation simulation using the code WAKE*
(b)
1018 W/cm2
1.0
Simulation using
experimental density
profiles
Energy flux
0.2
µ
90
m
z
z
0.9 cm
* P. Mora and T. M. Antonsen Jr., Phys. Plasmas 4, 217 (1997).
r
Attenuation from
leakage at gaps
Second method: wire-tailored cluster flow,
unmodulated laser pulse
uniform 500mj 100ps Nd:YAG pulse incident
on axially modulated Argon cluster target
1mm corrugation period
1.5 cm
Features persist for the full life of the waveguide
B.D. Layer et. al, Opt Express 17, 4263 (2009)
Nitrogen cluster target @
Argon cluster target @
-150 deg C, 25 m wires
22 deg C, 25 m wires
0.5 ns
0.5 ns
1.0 ns
160 μm
1.0 ns
2.0 ns
2.0 ns
6.0 ns
6.0 ns
600 μm
600 μm
(200 consecutive shot averages)
320 μm
Direct laser acceleration- inverse Cherenkov
acceleration (ICA)
580-MW peak power
 31 MeV/m.
10 TW peak powers
are now routine, but
the need for neutralgas phase matching
strongly limits peak
intensities.
axicon
Nd:YAG laser pulse
Diffractive optic
Clustered H2 jet
Corrugated plasma waveguide
Radially polarized
fs laser pulse
Relativistic
electron bunch
Corrugated guide: simple estimates of dephasing
lengths and acceleration gradients
Estimate acceleration gradients using index modulation:
One full dephasing cycle
Accelerating-phase region:
low index
λ = 800nm
}
Ne1 = 3*1018 cm-3
Ne2 = 6*1018 cm-3
wch = 12μm
p = 1, m = 0
Ld1= ~260 μm
Ld2=~165 μm
n1 > n2
Decelerating-phase region: high
index
For P = 1 TW, Ez =0.55 GV/cm, giving an
effective gradient of 77 MV/cm
Wakefield comparison: Malka et al. used a 30 TW
laser at λ = 0.8 μm to produce an acceleration
gradient of ~0.66 GV/cm
This is a linear process with no threshold.
1 mJ regenerative amplifier alone
P = 20GW  Effective accel. gradient: 11 MV/cm
Direct laser acceleration- energy gain
• electrons distributed uniformly on axis 1 to 11 m behind pulse peak
• no transverse momentum
m=1 phase velocity matched
to initial electron velocity

Ideal scaling
0
400
o=1000

400
v p,1  v z ,o
m=1 phase velocity set to c
o=100
v p,1  c
o=1000
Ideal scaling
o=100
o=30
30
time (ps)
60
o=30
0
30
time (ps)
it is better when electrons catch up with a faster wave than to start
them phase matched to a slower wave
60
Comparing direct accel to other schemes
parameters used for comparison:
=800 nm
wch=15 m
ao=.25
no=7x1018 cm-3
=.9

m=.035 cm
o=100
z=300 fs*c
for direct accel we have:
2 2
  z  p 2 
2
  4a0   1 2 p2 
w ch      w ch 
 = 1000
vacuum beat wave acceleration:
2
 ao wch   1 
   1
 1   2 
 2f   i2  8 2 
 = 8.3
semi-infinite vacuum acceleration:
 
1
ao o
2
 = 12.5
(best case scenario)
(1=22)
laser wakefield acceleration:
2
2
2






a
p
p
 
1


1/ 2 
2 2 
(1 a /2)      w ch 
2
0
2
0
 = 14.3
Electron Beam Density
final electron density
1
81m
num. (a.u.)
xf
-81m
• density peaks off axis; beam has
acquired sizeable transverse spread
• off-axis peaks mostly composed of low
energy electrons
0
number averaged final momentum
300
81m
pz (mec)
xf
-81m
-11 m
z
f
-1 m
0
• high energy electrons remain
confined to center of beam
only the ponderomotive transverse
force is significant for these electrons
Summary
•
Can make modulated plasma waveguides with two distinct methodsmodulating either the laser heating profile or the clustered target flow
•
Can control nearly every aspect of the waveguide by varying cluster
parameters and pump laser intensity
•
Gas cluster channels can be more than 10X less dense than
unclustered gas channels (1017’s-1018 ’s vs. 1019 ’s) and use 10X less
laser energy for generation-
•
Cluster-generated plasma waveguides are extremely stable
(longitudinal AND transverse) and can support finely engineered
structures.
•
One application:
Direct laser accelerator optical-frequency LINAC with no
damage threshold