1. UltrafastLaser-Driven Plasma for Space Propulsion
Terry Kammash, K. Flippo†, T. Lin,
A. Maksimchuk, M. Rever,
S. Banerjee, D. Umstadter
FOCUS Center / Center forUltrafastOptical Science, University of Michigan, Ann Arbor, MI 48109-2099, USA
Y. Sentoku
General Atomics, San Diego, CA
V. Yu. Bychenkov
P. N.LebedevPhysics 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

2. Accelerator SetupProton BeamCUOS T3Laser Parameters: •Ti:Sapphire / Nd:Glass•1.053 mm (ωo), 527nm (2 ωo) •up to ~12 TW •5 J•400 fs•Contrast: 10-5:1 @ ωo, 10-7:1 @2 ωo•2x1018-2x1019W/cm2Target Normal Forward DirectionLaser Forward DirectionCR-39 DetectorFWHM = 4.3 um
Incident Laser Spot

3. 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 ½the Emaxof the measured protons101001000010203040506070 Counts/2 min Time after shot (min) Decay for 11CIlas=6x1018W/cm2Detection efficiency 15% 10B(d,n)11C reactionBoronsampleLaserMylar filmCD11C10BDeuteronsn
K.Nemoto, S.Banerjee, K.Flippo, A.Maksimchuk, D.UmstadterApp. Phys.Lett, 78, 595 (2001)

4. Radioisotope Activation with ProtonsNaIPMTto MCASampleprotonsLasertargetcollimator & shieldNaIPMTto MCA• ••••• • • • ••••••• • ••• • • • • • • • • • • • • • • • • • • •••• • • • • • •• • • •• •• • • • ••• • • • •• • • • • •• • • • • • • • • • • • •• • • • • • •• • • • • 110100100002000400060008000 Count (0.511 MeV) Time (sec) t ~ 38 minCu (p,n) Zn6363Laser Induced••••••••••••••••••••••••••••••••• • • • • •• •• ••• •• ••• • • • ••• • • ••• ••••• • • •• • •• •••• ••••• •• •• ••••• •• •• • • ••• •••••••••• •••• •• •• •• ••• • • ••••• • • ••• •••• • ••••• •••••• •••••••• • •• • • •••• ••• •••••••••••• • • • • • • • • • • • ••• • • • •• • • • • • • • • • •••• •• •• • •••• ••• ••••••• ••••••••••• ••••••••••••••••••••••••••••••••••••••••••••••••••••••02004006008001000050100150200250300 Counts Channel Singles SpectrumB (p,n) C11 110.511 MeVSort window• •• • • •••• • • • ••• • • • •• •• • •••• • • 101001000300002004006008001000 Count (0.511 MeV) Time (sec) B (p, n) C1111 t = 20 minLaser Induced

5. Material Effect on Proton ProductionEe- ConductorInsulatorp+ p+p+BBe- EMylar (polyethylene terephthalate C10H8O4) •ρ~1.2 g/cm3•σ=10-12Ω-1m-1•Z=4.3Aluminum•ρ~2.7 g/cm3•σ=3.6×107Ω-1m-1•Z=13p+ e-
p+
p+
laser
laser
target
target

6. 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

7. Beam Profile Dependence
on Target Thickness (a) 6 μm, (b) 13 μm , (c) 25 μm, (d) 50 μm, and (e) 100 μm(a) 4 μm, (b) 12.5 μm, (c) 25 μm, (d) 50 μm, and (e) 75 μm
Call out: White arrows point to beam filamentation, most likely a manifestation of the Weibel, instability.

8. 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, and12.5 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/encat 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

9. 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.

10. Electron Distribution From Al TargetProtonsX-ray FilmlaserTargetTop ViewTarget Holder ShadowX-ray Film Line OutX-ray FilmHolder0°

11. Protons From Front Surface0246810121416050100150200Target Thickness [microns] Maximum Proton Energy [MeV] Eimax ~ 13 μm

12. 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)

13. Deuteron Acceleration
Preliminary Results
Deuteron coating
No deuteron coatingp+d+ p+
Where do highest energy deuterons come from?
1.The BACK of 12.5um Al
2.The FRONT of 6 um Mylar
3.The FRONT of 13 um Mylar
4.The FRONT of 12.5 um Al
5.The BACK of 13 um Mylar

14. Proton Energy Scaling with Pulse Duration and IntensityFrom Y. Sentoku, T. E. Cowan, A. Kemp, and H. RuhlPhysics of Plasmas 10, 2009 (2003) 14.5 MeV> 30 MeV
Current T-cubed System
Future HERCULES System

15. Peak Proton Energy
vs. Spot SizeE = 190.87d1.7404010002000300040005000600033.544.555.566.57Spot size diameter [microns] Peak Proton Energy [keV] f/3.3 off-axis parabolaf/1.5 off-axis parabolaPower Scaling FitFor intensities of ~ 1.4 x 1019 W/cm2For intensities of ~ 2.5 x 1019 W/cm2 E =190.87 x d 1.704

16. Spot Size ComparisonTotal Intensity vs. Diameter for f/1.5 Paraboloid 4.3 FWHM Spot Size02040608010012005101520253035404550Spot Size Diameter [um] Total Energy [%] Profile of 4.3μm FWHM Spot0100002000030000400005000060000-15-10-5051015Radial Position [μm]Intensity [a.u.] 40% in FWHM

17. Spot Size ComparisonTotal Intensity vs. Diameter for f/3.3 Parabaloid FWHM Focal Spot of 6.4 Microns 8-17-0102040608010012005101520253035404550Spot Size Diameter [um] Total Energy [%] Profile of 6.4 μm FWHM Spot0100002000030000400005000060000-20-1001020Radial Position [μm] Intensity [a.u.] 35% in FWHM

18. Material Effects on Plume Profile
Proton Beam Images Using a CCDLaser Propagation Direction
Target
Plane
Dark Side
Illuminated
Side
4 Al Target,
4MeV beam
No backfilled gas,
200 mTorr ambient
4 um Al Target
with 2 Torr H2
25 um Mylar Target
25 um Mylar Target
with 2.4 Torr He
25 um Al Target
Proton Beam is
Emitted Normal to Target

19. Plume Evolution in 1 TorrH2
Ambient Backfill12.5 mm Al+4 ms+1 ms+4 ms+14 ms3.069 cm25 mm Mylar2.138 cm~31000 m/s2.222cm3.194 cm~32000 m/s1 cm+ 65.5us
+1 ms

20. Target Geometry>1.4 MeV, 55º div. @ 1.5x1019 W/cm2>2 MeV, 38º div. @ 1.2x1019 W/cm2> 1.4 MeV, 44º div. @ 1.6x1019W/cm2> 3 MeV, 28º div. @ 1.2x1019W/cm2LaserProtonsTargetTargetHolderCurved TargetGeometry 25 μm Al
Radius of curvature ~ 0.2 mm
Radius of curvature
~ 0.5 mm

21. Target Geometry
~100 Micron Half Wire Cross-sections
Focus on
flat surface
Focus on
round surface
Wire orientation: ProtonsLaserProtonsProtonsLaserWire positionCR-39FlatRound laserlaser
Beam Images:
Focusing on flat surface (840) creates an ion beam, while focusing on the round side produces a cylindrical-like spray

22. Target Surface GeometryElectron Microscopyof LaserBlack™ 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-side100 μm2 μmMurnane et al. APL 62 (1993) used gratings and clusters, 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. Laser Spot Size ~ 6 micronsUse a material which will “trap”the laser light, to enhance the generation of hot electrons. >1.3MeV31ºdiv.

23. T-cube LaserThin Film TargetMeshRadiochromicFilm51.8 lines highProtonRadiographyThe 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. Proton Beam1 mm1 mmApproximate Region Sampled by BeamArea of Image at Right

24. Future Laser Development
100-200 TW@ 25-40 fs0.1 Hz350 ps7-10 J2-pass Amplifier20-30 TW@ 25 fs10 Hz350 ps1-1.5 J4-pass Amplifier1 PW @ 30-40 fs0.1 Hz350ps50 JHigh-Power AmplifierN/A10 Hz350 ps100 mJRegenerativeAmplifierN/A10 Hz15 fs1 mJCleaner(106contrast) N/A80 Mhz10-15 fs1 nJOscillatorCompressed OutputRepetitionRatePulse widthEnergyCurrent Hercules

25. 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. alhave 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

26. Ion Acceleration Physics Relativistic Electron Cloud (Beam) Model One- Dimensional
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 cloudd
R
Ez

27. Physics Continued
Energy conservation for electrons in cloud PE=KEPE≈πe2nbh2KE=( γb-1)moc2where γb=Relativistic ParameterHence: h=√(γb-1)moc2/πe2nb= =√(γb-1)/πrenb Where: re=classical electron radius re=e2/moc2=2.8×10-13Substituting into exp. for Ezwe get Ez=2c√πmo(γb-1)nb

28. 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

29. Continued
The Ion Energy Ei=ZEb=ZeEzhEi=9MeV (Z=1) Mean Ion Velocity Viis given by ½miVi2=ZeEzh And the ion acceleration time tiis ti=h/Vi or ti=√mi/Ze2nb

30. 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

31. Two Asymptotic Regimes for Ion Acceleration
2.“Adiabatic” regime corresponding to
shorter, sub picosecondpulses i.e.
τ<<ti
Here ion distribution is “steeper”
and the form
dni/dv~ exp-( v2/2CS 2)
For the adiabatic expansion electron cooling takes place according
Te=Te0(ti/t)2

32. Ion Velocities
MaxiumIon Velocities: Isothermal vmax=2CSln(d/h) Adiabatic vmax=2√2CSln(d/h) Note in both instances: Ion Acceleration is more efficient when(d/h)>>1i.e. for larger focal spots

33. 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)

34. Relationship Between Ion Energy, Laser and Target Parameters
Combining we get: εe=√πe2IRh η/cSince h≈λ= laser wave length, thenεe=√πe2IRh η/cAndεi=Z εeIf we express intensity Iin units of 1018W/cm2and Rand λin microns thenεi=Z εe≈√ηIRλMeV

35. An Example
I=1021W/cm2
η=0.10
R=2.5 μm
Then
εi=14 MeV

36. Thrust
F=NiMiωVi
Mi = ion mass (proton) = 1.6 ×10-27kg
ω= representation rate ≈1kHz
Vi = ion velocity (14 MeV) = 5.2×107 m/s

37. Plasma Expansion in Vacuum
Ion acceleration time ti=h/vi= 19×10-15secPulse length (projected) τ=30×10-15Thenτ>tiExpansion is Isothermal vi max= 2 CSln(d/h) CS= √ZTe/mi=3×107m/sec vi max= 108m/sec Vi initial≈5×107m/sec

38. Specific Impulse
Note improvement in energy transfer efficiency for increasing (d/h), namely for larger aspect ratios
27.6×107
27.6×107
4.61
100
23.5×107
23.5×107
3.91
50
13.8×107
13.8×107
2.3
10
9.7×107
9.7×107
1.61
5
Max Isp(s)
Vimax(m/s)
ln(d/h)
d/h

39. Accomplishments Thus Far
1.Generate a RelativisticallyConsistent Mathematical Expression for the energy of the ejected ion as a function of laser and target parameters, i.e. Ei=z √ηIRλwhere z = ion chargeη= energy conversion efficiency R= radius of focal spotλ= laser wave length

40. Accomplishments Thus Far
2.Experimentally validated Ei~ √IEi~ √λ 3.Indirectly established relationships relating Eito Rand dependence on η. More work is needed in this area! Just purchased 5 parabolic mirrors to investigate thoroughly dependence of Eiand total number of ejected particles on R.

41. Accomplishments Thus Far
4.Experimentally established dependence of Eion target thickness “t”, optimized t≈10λ
5.Experimentally established conditions for
filamentationinstability
P =5Pc=5[17(ωo/ωp)2GW]
4Tc/ωpa0≤2R
c = speed of light
a0=8.5×10-10λ[μm] I1/2[W/cm2]
ωp=plasma frequency
R= radius of focal spot

42. 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 Cermetreactors using Uranium, Plutonium or Americium as fuel.