Ultrafast Laser-Driven Plasma for Space Propulsion Terry Kammash, K. Flippo†, T. Lin, A. Maksimchuk, M. Rever, S. Banerjee, D. Umstadter
FOCUS Center / Center for Ultrafast Optical Science, University of Michigan, Ann Arbor, MI 48109-2099, USA
Y. Sentoku
General Atomics, San Diego, CA
V. Yu. Bychenkov
P. N. Lebedev Physics Institute, Russian Academy of Science, 117924 Moscow, Russia Lasers supported by the National Science Foundation FOCUS Center and the U of M Center for Ultrafast Optical Science, and funding from NASA Institute For Advanced Concepts
Accelerator Setup CR-39 Detector
Proton Beam
Target Normal Forward Direction
Laser Forward Direction
CUOS T3 Laser Parameters: • Ti:Sapphire / Nd:Glass • 1.053 mm (ωo), 527nm (2 ωo) • up to ~12 TW •5J • 400 fs • Contrast: 10-5:1 @ ωo, 10-7:1 @2 ωo • 2x1018 - 2x1019 W/cm2 Incident Laser Spot
FWHM = 4.3 um
Front Surface Deuteron Acceleration •Activation of 10B to 11C is achieved only by illuminating deuterons on the front surface. •No activation when deuterons were on the back surface, or without deuterons (i.e. no production of 11C detected from 11B (p,n)11C reaction). •Deuterons have about ½ the Emax of the measured protons 1000
Detection efficiency 15%
Counts/2 min
CD
Ilas =6x1018 W/cm2
Mylar film
Laser Deuterons
100 Decay for 11C 10
0
Boron sample
10
20 30 40 50 60 70 Time after shot (min)
10 B
11 C
n 10B(d,n)11C
reaction
K. Nemoto, S. Banerjee, K. Flippo , A. Maksimchuk, D. Umstadter App. Phys. Lett, 78, 595 (2001)
Radioisotope Activation with Protons 3000
NaI PMT to MCA
target
protons
Laser
Sample to MCA
Count (0.511 MeV)
collimator & shield
1000
NaI PMT
• •
•• •••• • •• •
• •• • • • •• •• ••• •••• • • • • • • • • •• •• • • •• •• •• •• • •• •• • •••••••• •• •• • • • • •• • • •• • •••••• • •••••••• • ••• •• • ••••••• •••••• • •••••• • • ••••••••• • •• •••• • • •• •• •••• •••••••••••• ••• •• •
400 200
•••••••••••••••••••••••••••••••
0
50
100
• • • • • •
Sort window
• • • ••• ••••• ••• •••••••••••••••••••••••••••••••••••••••• •••• •• ••••••••••••••••••••••••••••••
150 200 Channel
250
300
Count (0.511 MeV)
600
0.511 MeV
t = 20 min
• • • • • • • • • • • • •
•
•
• •
• •
• • • • •
100
• •
0
200
1000
Singles Spectrum 11B (p,n) 11 C 800
Counts
•
10
1000
0
Laser Induced 11 B (p, n)11 C
400
600
Time (sec)
800
1000
Laser Induced Cu (p,n) 63Zn
63 100
• •• • ••
t ~ 38 min
10
1
• • • • •• • • •• • • • • • • •• • • • • • • • • ••• • • • • •• ••• • •• • • •• • • •• • • • •• • • • •• • • • • • • • •• • • • • • • •• • • • •• • • • •• • •• •
0
2000
4000
6000
Time (sec)
8000
Material Effect on Proton Production Insulator
Conductor
Mylar (polyethylene terephthalate C10H8O4) • ρ~1.2 g/cm3 • σ=10-12 Ω-1m-1 • Z=4.3
Aluminum • ρ~2.7 g/cm3 • σ=3.6×107 Ω-1m-1 • Z=13
p+ p+
eE B
laser
target
p+
p+ e E
e-
p+
p+ laser
B target
Beam Profile Dependence on Initial Target Composition RCF (a,c,e,g) / CR-39 (b,d,f,h) detector stack images for 13µm Mylar, 10 µm silicon, 12.5 µm aluminum, and 12.5 µm copper targets. All pairs are single shot except (c) and (d) which were two separate shots. RCF records protons between ~0.2 and ~2 MeV, CR-39 records protons between ~2.5- ~4 MeV. Except (d) which recorded between ~1.2 MeV and 3 MeV
Beam Profile Dependence on Target Thickness (a) 6 µm, (b) 13 µm , (c) 25 µm, (d) 50 µm, and (e) 100 µm
Call out: White arrows point to beam filamentation, most likely a manifestation of the Weibel, instability.
(a) 4 µm, (b) 12.5 µm, (c) 25 µm, (d) 50 µm, and (e) 75 µm
Comparison with Simulation Images: Contrast enhanced RCF images of proton beam profiles after a drift of 5 cm from target exit from experiments with 13 microns of Mylar (a) top left, and 12.5 microns of aluminum (b) bottom left. Compare an electron beam profile from a simulation (c) by L. Gremillet, et al. [Phys. Plasmas 9, 941(2002)], showing the transverse electron profile jb/enc at 20 microns inside a silica target for a propagating monoenergetic electron beam of energy 500 keV, after 405 fs of propagation, which is also the beam duration. Image reproduced with permission.
Silica Observed profiles
e-beam simulation
Magnetic Field from Simulation vs. Proton Beam Profile E field configuration plot from the simulation at 405 fs. Notice the similarities in the simulation slices to proton beam images in row (I) of the previous slide.
e-beam induced B field evolution is very similar to that of the proton beam profile seen from Mylar previously. And as shown by M. Honda, J. Meyer-ter-Vehn and A. Pukov, PRL 85 2128 (2000) the ions can follow the electron filaments in as little as 60 fs.
Electron Distribution From Al Target X-ray Film Line Out
Target Holder Shadow
Top View X-ray Film Protons Target
0째
laser
Holder
X-ray Film
Protons From Front Surface 16
Maximum Proton Energy [MeV]
14 12 10 8 6 4 2 0 0
Ei max ~ 13 Âľm
50
100
150
Target Thickness [microns]
200
Simulation of proton beam Sentoku’s[1] recent 1-D PIC simulations predict a 5 MeV beam from the front surface for a 400fs laser pulse, with about 13 MeV from the rear. This agrees well with the observed 4 MeV trend, and a maximum of about 12 MeV.
[1] Y. Sentoku Phys. Plasmas 10 2009 (2003)
Deuteron Acceleration Preliminary Results Deuteron coating d+
Where 1. 2. 3. 4. 5.
p+
No deuteron coating p+
do highest energy deuterons come from? The BACK of 12.5um Al The FRONT of 6 um Mylar The FRONT of 13 um Mylar The FRONT of 12.5 um Al The BACK of 13 um Mylar
Proton Energy Scaling with Pulse Duration and Intensity 14.5 MeV
Current T-cubed System > 30 MeV Future HERCULES System
From Y. Sentoku, T. E. Cowan, A. Kemp, and H. Ruhl Physics of Plasmas 10, 2009 (2003)
Peak Proton Energy vs. Spot Size 6000
f/3.3 off-axis parabola f/1.5 off-axis parabola
Peak Proton Energy [keV]
5000
E = 190.87d x d 1.704 E =190.87
Power Scaling Fit
1.7404
4000
For intensities of ~ 19
2
1.4 x 10 W/cm 3000
For intensities of ~ 19
2
2.5 x 10 W/cm 2000
1000
0 3
3.5
4
4.5
5
5.5
Spot size diameter [microns]
6
6.5
7
Spot Size Comparison Total Intensity vs. Diameter for f/1.5 Paraboloid 4.3 FWHM Spot Size
120
80 60 60000
40
Intensity [a.u.]
Total Energy [%]
100
40% in FWHM
20
Profile of 4.3Âľ m FWHM Spot
50000 40000 30000 20000 10000 0 -15
-10
-5
0
5
10
15
Radial Position [Âľ m]
0 0
5
10
15
20
25
30
Spot Size Diameter [um]
35
40
45
50
Spot Size Comparison Total Intensity vs. Diameter for f/3.3 Parabaloid FWHM Focal Spot of 6.4 Microns 8-17-01 120
80 60 Profile of 6.4 µ m FWHM Spot 60000
40
35% in FWHM
20
Intensity [a.u.]
Total Energy [%]
100
50000 40000 30000 20000 10000 0 -20
-10
0
Radial Position [µ m]
10
20
0 0
5
10
15
20 25 30 Spot Size Diameter [um]
35
40
45
50
Material Effects on Plume Profile Proton Beam Images Using a CCD
Target Plane Dark Side Illuminated Side
Laser Propagation Direction
25 um Al Target
Proton Beam is Emitted Normal to Target
25 um Mylar Target
25 um Mylar Target with 2.4 Torr He
4 Al Target, 4MeV beam No backfilled gas, 200 mTorr ambient
4 um Al Target with 2 Torr H2
Plume Evolution in 1 Torr H2 Ambient Backfill 25 mm Mylar
12.5 mm Al +1 ms
+4 ms
~32000 m/s
+1 ms
~31000 m/s
3.194 cm 2.222cm
65.5us +14+ms
+4 ms
3.069 cm 2.138 cm
1 cm
Target Geometry Curved Target Geometry 25 µm Al
Radius of curvature ~ 0.2 mm >1.4 MeV, 55º div. @ 1.5x1019 W/cm2
>2 MeV, 38º div. @ 1.2x1019 W/cm2
Radius of curvature ~ 0.5 mm
Laser
Target Holder
> 1.4 MeV, 44º div. @ 1.6x1019 W/cm2
> 3 MeV, 28º div. @ 1.2x1019 W/cm2
Target
Protons
Target Geometry ~100 Micron Half Wire Cross-sections Focus on flat surface
CR-39
Focus on round surface
Protons
Protons
Protons
Wire orientation: Laser
Flat Beam Images: Focusing on flat surface (840) creates an ion beam, while focusing on the round side produces a cylindrical-like spray
Laser
Wire position Round
la s
er
la se r
Target Surface Geometry Use a material which will “trap” the laser light, to enhance the generation of hot electrons. Electron Microscopy Murnane et al. APL 62 (1993) used gratings and clusters, of LaserBlack™ Kulcsar et al. PRL 84 (2000) used metallic “velvet”. Both showed enhanced X-ray yield from enhance electron heating from efficient coupling.
LaserBlack® is > 96% absorptive at 1 mm. 100 µm
2 µm
Laser Spot Size ~ 6 microns
Results: •30 mm Laserblack target ~ 8.2 MeV •Enhancement in the number of maximum energy protons •Beam profile does not suffer, regardless of which surface has been coated, i.e. no imprinting even from rear-side
>1.3MeV 31º div.
Proton Radiography Thin Film Target Proton Beam
T-cube Laser Mesh Approximate Region Sampled by Beam
1 mm Area of Image at Right
The possibility exists to use the laser produced proton beam for very small scale imaging or even lithography. The image on the left is a 5x magnified proton radiograph captured on RCF of a mesh with 10 micron wires and 30 micron grid spacing.
Radiochromic Film 1 mm
51.8 lines high
Future Laser Development Energy
Pulse width
Repetition Rate
Compressed Output
Oscillator
1 nJ
10-15 fs
80 Mhz
N/A
Cleaner (106 contrast)
1 mJ
15 fs
10 Hz
N/A
Regenerative Amplifier
100 mJ
350 ps
10 Hz
N/A
4-pass Amplifier
1-1.5 J
350 ps
10 Hz
20-30 TW @ 25 fs
2-pass Amplifier
7-10 J
350 ps
0.1 Hz
100-200 TW @ 25-40 fs
50 J
350ps
0.1 Hz
1 PW @ 30-40 fs
High-Power Amplifier
Current Hercules
Proton Acceleration Summary • Simulation and experiment support proton acceleration at the laser-irradiated side of the target of a 4 MeV beam, on the back of the underdense plasma under these conditions. • And a 12 MeV beam from the rear-surface of Al due to recirculation sheath enhancement. • Beam spectrum has bands of energies due to “ion fronts.” • Beam profile smoothes out as initial target conductivity increases. • Filamentation and structures similar to the electron simulation by Gremillet et. al have been observed. • Demonstrated beam profile modification with modest geometry, and enhancement of number at the maximum energy achieved by initial target geometry and surface conditions • CR-39 response is highly non-linear when scanned optically. • By using a highly absorptive material we have increased the number of maximum energy protons without sacrificing beam quality. No imprint of LB on beam profile, unlike Roth et. al • New 30 fs laser has produced 1021W/cm2 on target in a 1 micron spot, expect high efficiency acceleration
Ion Acceleration Physics Relativistic Electron Cloud (Beam) Model OneDimensional Poisson’s Equation ∇·E=-4 πenb Where: e=electron charge nb=beam electron density Can readily show: Ez=2πenbh Where: h=thickness of electron cloud R=radius of electron cloud d=diameter of electron cloud
R d Ez
Physics Continued Energy conservation for electrons in cloud PE=KE PE≈πe2nbh2 KE=( γb-1)moc2 where γb=Relativistic Parameter Hence: h=√(γb-1)moc2/πe2nb= =√(γb-1)/πrenb Where: re=classical electron radius re=e2/moc2=2.8×10-13 Substituting into exp. for Ez we get Ez=2c√πmo(γb-1)nb
Example We begin with γb=10 nb=1019cm-3 h=10µm Ez=913GV/m Over a distance of h=10 µm, the electron acquires an energy of Eb=9 MeV
Continued The Ion Energy Ei=ZEb=ZeEzh Ei=9MeV (Z=1) Mean Ion Velocity Vi is given by ½miVi2=ZeEzh And the ion acceleration time ti is
ti=h/Vi
or ti=√mi/Ze2nb
Two Asymptotic Regimes for Ion Acceleration 1. “Isothermal” expansion relevant to long pulse lengths i.e. τ>ti (ti=1ps) Ions acquire exponential distribution in velocity dni /dv ~ exp-( v/CS) Where CS=√ZTe/mi = ion sound speed
Two Asymptotic Regimes for Ion Acceleration 2. “Adiabatic” regime corresponding to shorter, sub picosecond pulses i.e. τ<<ti Here ion distribution is “steeper” and the form dni /dv ~ exp-( v2/2CS2) For the adiabatic expansion electron cooling takes place according Te=Te0(ti/t)2
Ion Velocities Maxium Ion Velocities: Isothermal vmax=2CS ln(d/h) Adiabatic vmax=2â&#x2C6;&#x161;2CS ln(d/h) Note in both instances: Ion Acceleration is more efficient when (d/h)>>1 i.e. for larger focal spots
Relationship Between Ion Energy, Laser and Target Parameters Consider power balance between laser and ejected electrons: [nb(γb-1)moc2]c=ηI Where η=Efficiency of energy transfer Rewrites as εe=ηI/nbc Also electron must exceed Coulomb Energy to penetrate the target i.e. nb= εe/(πe2hR)
Relationship Between Ion Energy, Laser and Target Parameters Combining we get: εe=√πe2IRh η/c Since h≈λ = laser wave length, then εe=√πe2IRh η/c And εi=Z εe
If we express intensity I in units of 1018 W/cm2 and R and λ in microns then εi=Z εe≈ √ ηIRλ MeV
An Example I=1021W/cm2 η=0.10 R=2.5 µm
Then εi=14 MeV
Thrust F=NiMiωVi Mi = ion mass (proton) = 1.6 ×10-27 kg ω = representation rate ≈ 1kHz
Vi = ion velocity (14 MeV) = 5.2×107 m/s
Plasma Expansion in Vacuum Ion acceleration time ti=h/vi = 19×10-15 sec Pulse length (projected) τ=30×10-15 Then τ>ti Expansion is Isothermal vi max = 2 CS ln(d/h) CS= √ZTe /mi =3×107 m/sec vi max= 108 m/sec Vi initial ≈ 5×107 m/sec
Specific Impulse Note improvement in energy transfer efficiency for increasing (d/h), namely for larger aspect ratios d/h 5 10 50
ln(d/h) 1.61 2.3 3.91
Vimax (m/s) Max Isp (s) 9.7×107 13.8×107 23.5×107
9.7×107 13.8×107 23.5×107
100
4.61
27.6×107
27.6×107
Accomplishments Thus Far 1. Generate a Relativistically Consistent Mathematical Expression for the energy of the ejected ion as a function of laser and target parameters, i.e.
Ei =z √ηIRλ
where z = ion charge η = energy conversion efficiency R = radius of focal spot λ = laser wave length
Accomplishments Thus Far 2. Experimentally validated Ei~ √I Ei~ √λ 3. Indirectly established relationships relating Ei to R and dependence on η. More work is needed in this area! Just purchased 5 parabolic mirrors to investigate thoroughly dependence of Ei and total number of ejected particles on R.
Accomplishments Thus Far 4. Experimentally established dependence of Ei on target thickness “t”, optimized t≈10λ 5. Experimentally established conditions for filamentation instability P =5Pc=5[17(ωo/ωp)2 GW] 4Tc/ωpa0 ≤2R
c = speed of light a0=8.5×10-10 λ [µm] I1/2[W/cm2] ωp=plasma frequency R= radius of focal spot
Accomplishments Thus Far 4. Experimentally established energy of ions ejected from front and rear surfaces of target which appear to agree well with simulations 5. Established dependence of proton beam profiles on materials, surface conditions and geometry 6. Carried out designs of space Nuclear Reactor for use in LAPPS. Likely candidates are gas-cooled Cermet reactors using Uranium, Plutonium or Americium as fuel.