direct laser acceleration of electrons in the corrugated...
TRANSCRIPT
Andrew YorkBrian Layer
John PalastroThomas AntonsenHoward Milchberg
Institute for Physical Science and Technology University of Maryland, College Park, Maryland, 20742
UNIVERSITY OF MARYLAND AT COLLEGE PARKINSTITUTE FOR PHYSICAL SCIENCE AND TECHNOLOGY
Direct laser acceleration of electrons in the corrugated plasma waveguide
1.5cm
650 µm
500µm
Laser wakefield acceleration has made GeV electrons available in a compact setup using terawatt lasers
40 terawatt,40 femtosecond
laser pulseElectric discharge plasma waveguide
Laser wakefield acceleration has made GeV electrons available in a compact setup using terawatt lasers
40 terawatt,40 femtosecond
laser pulseElectric discharge plasma waveguide
Laser wakefield acceleration has made GeV electrons available in a compact setup using terawatt lasers
40 terawatt,40 femtosecond
laser pulse
~30 picoCoulombs of ~1 GeV electrons
Electric discharge plasma waveguide
e-
Laser wakefield acceleration has made GeV electrons available in a compact setup using terawatt lasers
But:
This is inherently nonlinear- you need terawatt lasers to do wakefield acceleration
The SLAC structure is a TM-mode microwave waveguidewith periodic structure to phase-match acceleration.
Ez
Etransverse
Btransverse
EM propagation& particle accel.
‘slow-wave’ structurewave phase velocity < c
A linear process:There's no minimum microwave power
The SLAC structure is a TM-mode microwave waveguidewith periodic structure to phase-match acceleration.
Ez
Etransverse
Btransverse
EM propagation& particle accel.
‘slow-wave’ structurewave phase velocity < c
internal breakdown (lightning!) and self-destructionif wave fields are greater than ~ 107 Volts/m
accelerator waveguide structure
There is a maximum power, though.
The SLAC structure is a TM-mode microwave waveguidewith periodic structure to phase-match acceleration.
50 GeV in 3.2 km
50 x109 V/(1.7x107 V/m) = 2 miles
Solution: use ‘milder’ fields over longer distanceview from space
Ez
Etransverse
Btransverse
EM propagation& particle accel.
‘slow-wave’ structurewave phase velocity < c
internal breakdown (lightning!) and self-destructionif wave fields are greater than ~ 107 Volts/m
accelerator waveguide structure
1.5cm
650 µm
500µm
Another solution: replace the copper tube with a (much smaller) tube made of plasma!
Tube made of plasma. No more “damage threshold”
Now, instead of megawatt microwave klystrons:
You can accelerate with terawatt OR gigawatt optical lasers!
This might seem a little crazy
Bunch of relativistic electrons
e- Wheee!
But...
1 mm
Terawatt, femtosecond laser pulse
Microstructured plasma waveguide
PRL 99, 035001 (2007)
We've already done the hardest part:making the plasma tube
1 mm
The structured plasma can phase-match direct acceleration
e-
Relativistic electron bunch
Radially-polarized femtosecond laser pulse
Our simulations show we can get good acceleration gradients with modest lasers
PRL 100, 195001 (2008)
1 mm
The structured plasma can phase-match direct acceleration
e-
Relativistic electron bunch
Radially-polarized femtosecond laser pulse
Our simulations show we can get good acceleration gradients with modest lasers
Even small lasers would give big acceleration gradients:
1.9 TW: >80 MeV/cm30 GW: >10 MeV/cm(over many centimeters)
The structured plasma can phase-match direct acceleration
e-
Relativistic electron bunch
Radially-polarized femtosecond laser pulse
Our simulations show we can get good acceleration gradients with modest lasers
27µm
-27µm
300
0
pz (m
e c)
xi
zi-11 µm -1 µm
Acceleration depends on electron injection:
Total charge and efficiency seem promising. In our 2 TW drive-beam simulations:
-27µm
300
0
pz (m
e c)xi
zi-11 µm -1 µm
About 40 pC of charge can fit in each “bucket”
Each “bucket” absorbs about 1%
of the drive pulse
energy.
Palastro et al., PRE 77, 036405 (2008)
Cluster Jet (Ar, H2,N2)
How we made the plasma tube:
Spatially modulated 500mj 100ps Nd:YAG
laser pulsePeriodically Modulated
Plasma Waveguide
Axicon
Breakdown in atmosphere, mm-scale corrugations
1.5cm
Diffractive optic to shape the waveguide
creation pulse
We have a lot of control over the shape and density
of the plasma tube.
Cluster Jet (Ar, H2,N2)
Spatially modulated 500mj 100ps Nd:YAG
laser pulsePeriodically Modulated
Plasma Waveguide
Axicon
Diffractive optic to shape the waveguide
creation pulse
1.5cm
Breakdown in argon clusters, 100's μm-scale corrugations
We have a lot of control over the shape and density
of the plasma tube.
How we made the plasma tube:
Cluster Jet (Ar, H2,N2)
Periodically Modulated
Plasma Waveguide
Axicon
1.5cm
Diffractive optic to shape the waveguide
creation pulse
Spatially modulated 500mj 100ps Nd:YAG
laser pulse
35µm
50µm
Small corrugations are crucial if we're going to
extend this technique to ion acceleration
Breakdown in atmosphere, 10's μm-scale corrugations
How we made the plasma tube:
Cluster Jet (Ar, H2,N2)
We've demonstrated terawatt guiding in these tubes*. They're corrugated optical waveguides!
Periodically Modulated
Plasma Waveguide
Axicon
100mj 50-70fs Ti:sapphire laser pulse
(delayed ~2ns relative to YAG pulse)
1.5cm
Diffractive optic to shape the waveguide
creation pulse
Spatially modulated 500mj 100ps Nd:YAG
laser pulse
13 µm
So far we've demonstrated guiding of a linearly polarized laser pulse.
We need to guide a radially polarized pulse (a TM waveguide mode) for effective acceleration.
*PRL 99, 035001 (2007)
•Use a ‘Ring Grating’ (RG)- a transmissive diffraction grating lithographically etched into a fused silica disk
•Image the RG through an axicon to the line focus
•Creates a modulated plasma spark that evolves into a modulated channel
•Different ring gratings give us different modulation periods
100ps pulse
Pulse images the RG from 60cm upstream
The ring grating
In the lab, it looks like this:
Second method- tailored cluster flow
Ar or N2
Cluster Jet
100ps Nd:YAG laser pulse
Modulated Plasma Waveguide
Axicon
60fs Ti:Al2O3 laser pulse
60 fs transverse interfer. probe
1.5 cm
1030 µm
330µm
Cluster flow can be tailored to make extremely small features in the plasma channel
Transverse Phase Shift
Nitrogen cluster target @
-150 deg C
Argon Cluster target @ 22 deg C
200 μm
50 μm
600 μm
(200 consecutive shot average)
Radial Electron Density
60 μm dia.
Abel Inversion
Abel Inversion
5*1018 cm-3
at wall
9*1018 cm-3
at wall
~3*1018 cm-3
on axis
~2*1018 cm-3
on axis
Conclusions
•Optical-frequency linac with no damage threshold•Simple, unoptimized model shows strong acceleration•Plasma structures are under control•Need radial polarization: diffractive optics?
•Need an injector: solid target? wakefield acceleration?•Extension to ions needs study
Guiding in corrugated hydrogen plasma channels
• 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
15µm
1017 W/cm2
(b) (i) (ii) (iii)
700 µm
500 µm
200 mJ 300 mJ 500 mJ+ misalign.
Waveguide generation pulse energyand alignment controls modulation features
Why use a 100ps laser pulse and clusters?
•The far leading edge of the 100ps beam disassembles / ionizes the clusters, leaving a cold plasma that the remainder of the pulse heats.•Much more efficient than heating an unclustered gas (for same average Z in a plasma, 3x-10x less pump energy required)
50 Å ~ 600 ÅSingle Ar cluster
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Critical density layer
Under-dense plasma
Sub-critical plasma−ξ Eint/4π < 0
Super-critical plasmaa
H. Sheng et al, Phys. Rev. E 72, 036411 (2005)
Our next project: generating a radially polarized femtosecond-scale, multi-millijoule pulse.
Corrugated guide: simple estimates of dephasing lengths and acceleration gradients
n1 > n2One full dephasing cycle
Estimate acceleration gradients using index modulation toy model:
Accelerating-phase region: low index
Decelerating-phase region: high index
λ = 800nmNe1 = 3*1018 cm-3
Ne2 = 6*1018 cm-3
wch = 12μm
p = 1, m = 0
} Ld1= ~260 μm
Ld2=~165 μm
For P = 1 TW, Ez =0.55 GV/cm, giving an effective gradient of 77 MV/cm (14% “efficiency”)
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
Accelerating-phase region: low plasma density (high index)
Decelerating-phase region: high plasma density (low index)
n1 > n2Mod period d
Ld1 Ld2
Simplified density modulation:
So, what's the gradient? A toy model:
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 cycle: adeELELEeU dzdz 02211 )( −≈−−≈∆ where 1<a
Model this real waveguide:
As this simplified
waveguide:
Lucky for us, there's already a proof-of-principle experiment for electron acceleration by a radially polarized laser pulse
580-MW peak power gave 31 MeV/m.
10 TW peak powers are now routine, but neutral-gas phase matching limits peak intensities for ICA.
A more realistic model: FDTD simulations*
3000 μm
130 μm
*Using MEEP, http://ab-initio.mit.edu/wiki/index.php/Meep
Plasma density vs. r and z
Electrons per cm3
Plasma density vs. r and z
e-
A more realistic model: FDTD simulations*
3000 μm
130 μm
*Using MEEP, http://ab-initio.mit.edu/wiki/index.php/Meep
Plasma density vs. r and z
Electrons per cm3
Plasma density vs. r and z
e-
A more realistic model: FDTD simulations*
3000 μm
130 μm
*Using MEEP, http://ab-initio.mit.edu/wiki/index.php/Meep
Plasma density vs. r and z
Electrons per cm3
Plasma density vs. r and z
e-
A more realistic model: FDTD simulations*
3000 μm
130 μm
*Using MEEP, http://ab-initio.mit.edu/wiki/index.php/Meep
Plasma density vs. r and z
Electrons per cm3
Plasma density vs. r and z
e-
A more realistic model: FDTD simulations*
3000 μm
130 μm
*Using MEEP, http://ab-initio.mit.edu/wiki/index.php/Meep
Plasma density vs. r and z
Electrons per cm3
Plasma density vs. r and z
e-
A more realistic model: FDTD simulations*
One full dephasing cycle Accelerating-phase region: low index
Decelerating-phase region: high index
λ = 6.4 μmNe1 ~=0.5*1017 cm-3
Ne2 ~= 0.5*1018 cm-3
wch ~= 40μm
tpulse ~=300 fs
3000 μm
130 μm
*Using MEEP, http://ab-initio.mit.edu/wiki/index.php/Meep
Plasma density vs. r and z
Electrons per cm3
Plasma density vs. r and z
Simulation includes: Plasma dispersion Finite pulse duration Leakage effectsCylindrical coordinates
-25
+33
-38
+59
Accelerating field Ez seen by a relativistic electron vs. propagation distance
-64
+93
-92
+123
Ez
-111
+138
-113
+130
-98
+103
-72
+69
-45
+39
Net gain!
(~3% “efficiency”, room for optimization)