Fast Ignition : Some Issues in Electron Transport
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Transcript of Fast Ignition : Some Issues in Electron Transport
Fast IgnitionFast Ignition: Some Issues in Electron Transport
•Some fundamentals of large currents moving through dense materials
•Some unexpected problems the community has faced and understood
•Some more unexpected problems that are under intense study
Richard R. FreemanThe Ohio State University
Elements of 2 lectures of Electron Elements of 2 lectures of Electron Transport in Fast IgnitionTransport in Fast Ignition
• Context of electron transport in FI• Concepts of time scales within a plasma• The role of Alfven and “return” currents• Overview of electrons in extreme laser fields• The “real” environment in experiment vs. “ideal”• Sheath fields and refluxing• Example #1 of Experimental Surprise:
– Low energy electrons spreading at front surface
• Example #2 of Experimental Surprise: - Short penetration depth of fast electrons
“Under-dense”Corona surrounding core
Relativistic “critical density”
“over-dense”Corona surroundingcore
MeV electron energy transfer (NMeV electron energy transfer (Ncc to 10 to 105 5 NNcc))
determines fast ignition threshold determines fast ignition threshold
1
100
104
Laser Electrons
Anomalous
Energy loss ?Shaping/collimating beam?
n/nc
“criticaldensity”
Fuel coredensity
~ 200
40µm
10nc 1000nc
200-300µm
fast electrons
UHI laser beam
Laser gets to this point eitherThrough non linear effects or cone
Laser converts E&M energy to fast Electrons with ~30% efficiency
Fast electron beam must stay Collimated to deliver its energy
•But the target is neutral when the ultra-intense laser hits it; But the target is neutral when the ultra-intense laser hits it; •the current comes from ionization; the current comes from ionization; •the material remains neutral; the material remains neutral; •What are the Dynamics under these Conditions?What are the Dynamics under these Conditions?
Elements of 2 lectures of Electron Elements of 2 lectures of Electron Transport in Fast IgnitionTransport in Fast Ignition
• Context of electron transport in FI• Concepts of time scales within a plasma• The role of Alfven and “return” currents• Overview of electrons in extreme laser fields• The “real” environment in experiment vs. “ideal”• Sheath fields and refluxing• Example #1 of Experimental Surprise:
– Low energy electrons spreading at front surface
• Example #2 of Experimental Surprise: - Short penetration depth of fast electrons
Richard Fitzpatrickhttp://farside.ph.utexas.edu/Teaching/plasma/lectures/Node6.html
Richard Fitzpatrickhttp://farside.ph.utexas.edu/Teaching/plasma/lectures/Node6.html
2 4 1/2e 0 eω = 4πe = 5.64×10 nen m
Time Scales of Associated with Neutralization are Directly Related to The Plasma Frequency (and thus the Density)
2
e
For dilute plasmas (ne~1018): 1310 sec (0.1 sec)p
Solid density plasmas (ne ~1024):1610 sec (0.1 sec)femto
Elements of 2 lectures of Electron Elements of 2 lectures of Electron Transport in Fast IgnitionTransport in Fast Ignition
• Context of electron transport in FI• Concepts of time scales within a plasma• The role of Alfven and “return” currents• Overview of electrons in extreme laser fields• The “real” environment in experiment vs. “ideal”• Sheath fields and refluxing• Example #1 of Experimental Surprise:
– Low energy electrons spreading at front surface
• Example #2 of Experimental Surprise: - Short penetration depth of fast electrons
There are two fundamental ideas that must be kept in mind when There are two fundamental ideas that must be kept in mind when Large current flows, especially in high density materialsLarge current flows, especially in high density materials
ALFVEN LIMTALFVEN LIMT
As the current I increases, the B field intensifies, until individual electronsAre bent back upon them selves by V X B forces. This value, in a vacuum,Is 17 kA
Confined current made up of fast moving charges
Self consistent B field of current I
RETURN CURRENTRETURN CURRENT
Laser pulse of 1 psec duration focused to a spot size of 30 µm, an absorbed laser intensity of 10 18 W/cm2, corresponding to an energy per pulse of ~7J,(1014 fast electrons @200keV). Take the bunch to be ~60 μm in length(corresponding to the RMS 200 keV fast electron range in AL) and a diameter of the laser spot size (30 μm), the magnetic field on the surface of the cylinder would be 3200 MG, with a concomitant magnetic field energy of 5 kJ!concomitant magnetic field energy of 5 kJ! --A.Bell, et al., Plasma Phys Control Fusion 39 653 (1997)
Simple energetics
requires a return current
Laser Ionization creates fast forward electron stream
Large number of slow electrons are drawn in to neutralize the fast electrons
The original fast electron beam, if it exceeds the Alfven limit, filaments into many small components, each separated by return currents
What must exist, at times scales ~10-16 sec, everywhere in the material: ( jfast = nfast x vfast ) = ( jslow = nslow x vslow )
But vslow << vfast
Thus, a new “limit” to keep in mind: nfast << nslow
Elements of 2 lectures of Electron Elements of 2 lectures of Electron Transport in Fast IgnitionTransport in Fast Ignition
• Context of electron transport in FI• Concepts of time scales within a plasma• The role of Alfven and “return” currents• Overview of electrons in extreme laser fields• The “real” environment in experiment vs. “ideal”• Sheath fields and refluxing• Example #1 of Experimental Surprise:
– Low energy electrons spreading at front surface
• Example #2 of Experimental Surprise: - Short penetration depth of fast electrons
In working on experiments in current generation in solid materials from In working on experiments in current generation in solid materials from ionization by ultra-intense lasers—the reality is often very messyionization by ultra-intense lasers—the reality is often very messy
laser1 kJ0.5 psI2 ~ 3x1020
+
--
--
-
-
-++
++
e-
ions+
e-
e-
solid target
B > 10 MG
sc ~ MV
In the relativistic regime the quiver energy ofIn the relativistic regime the quiver energy of
electrons in the laser EM field exceeds melectrons in the laser EM field exceeds meecc22
• Relativistic quiver energy of a free electron is
(-1) mec2 where =(1+I2/1.4x1018Wcm-
2)1/2
•At 1021 Wcm-2 quiver energy is 10 MeV scaling as I1/2
•Electric field is 100 kV/nm or 180 a.u. scaling as I1/2
field ionizes bound electrons
with up to 4 keV binding energy
-evB/c
-eE
Trajectory has forward motion
due to magnetic force in plane polarized beam
In the relativistic regime the quiver energy ofIn the relativistic regime the quiver energy of
electrons in the laser EM field exceeds melectrons in the laser EM field exceeds meecc22
• Relativistic quiver energy EQ of a free electron is
(-1) mec2 where
=(1+I2/1.4x1018Wcm-2)1/2
Elements of 2 lectures of Electron Elements of 2 lectures of Electron Transport in Fast IgnitionTransport in Fast Ignition
• Context of electron transport in FI• Concepts of time scales within a plasma• The role of Alfven and “return” currents• Overview of electrons in extreme laser fields• The “real” environment in experiment vs. “ideal”• Sheath fields and refluxing• Example #1 of Experimental Surprise:
– Low energy electrons spreading at front surface
• Example #2 of Experimental Surprise: - Short penetration depth of fast electrons
Modeling is now done with “Ideal” Modeling is now done with “Ideal” Laser PulsesLaser Pulses
Modeling is now done with “Ideal” Modeling is now done with “Ideal” Laser PulsesLaser Pulses
A “REAL” interaction environmentA “REAL” interaction environment
Target : 50m CH E ~ 600J
p = 5ps; I ~ 5x1019 Wcm-2
Time = To-80ps
100m
Laser
Density (x10 19 cm-3)
0200 100150300 250 50
Longitudinal distance (m)
Original target surface
4
2
1
3
Ever-present prepulse creates plasma on front of Ever-present prepulse creates plasma on front of target, here measured by interferometrytarget, here measured by interferometry..
Elements of 2 lectures of Electron Elements of 2 lectures of Electron Transport in Fast IgnitionTransport in Fast Ignition
• Context of electron transport in FI• Concepts of time scales within a plasma• The role of Alfven and “return” currents• Overview of electrons in extreme laser fields• The “real” environment in experiment vs. “ideal”• Sheath fields and refluxing• Example #1 of Experimental Surprise:
– Low energy electrons spreading at front surface
• Example #2 of Experimental Surprise: - Short penetration depth of fast electrons
Debye Sheathwhereion(local) ≤ Debye(local)
Ion frontNe, hot
Ne, cold
Nion
Ion charge sheet
Nion ~ exp z ion
A Schematic of how Sheath Fields are set up due to Target Neutrality: A Schematic of how Sheath Fields are set up due to Target Neutrality: Acceleration Mechanism for ProtonsAcceleration Mechanism for Protons
Ne,hot + Ne, cold = Nion
Electric Field (constant) ~ TElectric Field (constant) ~ Thothot/e/e lion
REFLUXING REGION: VREFLUXING REGION: Vhothot is max at ion charge sheet is max at ion charge sheet
And is zero at ion frontAnd is zero at ion front
Refluxing electrons dominate the targetRefluxing electrons dominate the target
So why can fast electrons (>MeV) “reflux” in thin targets So why can fast electrons (>MeV) “reflux” in thin targets without immediately colliding with the ions of the material and without immediately colliding with the ions of the material and stopping, or at least lose energy quickly?stopping, or at least lose energy quickly?
Remember your Jackson E&M? The Coulomb cross-section for charged particles drops at theRemember your Jackson E&M? The Coulomb cross-section for charged particles drops at the44thth power of the relative velocity. For fast enough electrons, they simply don’t “see” the material power of the relative velocity. For fast enough electrons, they simply don’t “see” the material
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
0.1 1 10 100 1000
Temperature eV
Resis
tivit
y O
hm
m
Current expts
DT fuel
Au cone ??
Ohmic limit in FI
CD1 g/cc
D2
10 g/cc
100 g/cc
Au
CD
So-called “Spitzer” regime: hotter material has lower resistivity. The fast electrons do not feel the materials resistivity, but the
return current does, and this is the rub
Remember the RETURN CURRENT? This is where theRemember the RETURN CURRENT? This is where thematerial’s resistivity enters the problemmaterial’s resistivity enters the problem
Elements of 2 lectures of Electron Elements of 2 lectures of Electron Transport in Fast IgnitionTransport in Fast Ignition
• Context of electron transport in FI• Concepts of time scales within a plasma• The role of Alfven and “return” currents• Overview of electrons in extreme laser fields• The “real” environment in experiment vs. “ideal”• Sheath fields and refluxing• Example #1 of Experimental Surprise:
– Low energy electrons spreading at front surface
• Example #2 of Experimental Surprise: - Short penetration depth of fast electrons
Experimental Studies of LaserExperimental Studies of LaserGenerated Electrons: MethodGenerated Electrons: Method
First results of side-imaging of currentsFirst results of side-imaging of currents
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Al/Cu alloy KAl/Cu alloy K image -showing image -showing spreading at entry surface and rapid axial attenuationspreading at entry surface and rapid axial attenuation
• 6 beam 1
500 µm
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Horizontal(axial)
Vertical(radial)
90 m
32 m
Z
r
BB
ro
Ez
E X B
Hot electron sourceRegion (critical)
Typical computed electrontrajectory
Blow-off
BB ~1/r~1/r
BB ~~ n
solid
Variabledensity
Return current
Cf: Forslund and Brackbill PRL 48 1614 (82)Cf: Forslund and Brackbill PRL 48 1614 (82) J. Wallace, PRL 55 707 (85)J. Wallace, PRL 55 707 (85)
Elements of 2 lectures of Electron Elements of 2 lectures of Electron Transport in Fast IgnitionTransport in Fast Ignition
• Context of electron transport in FI• Concepts of time scales within a plasma• The role of Alfven and “return” currents• Overview of electrons in extreme laser fields• The “real” environment in experiment vs. “ideal”• Sheath fields and refluxing• Example #1 of Experimental Surprise:
– Low energy electrons spreading at front surface
• Example #2 of Experimental Surprise: - Short penetration depth of fast electrons
ProblemProblem: : How can this transport distance be so short when How can this transport distance be so short when the stopping distance of a few MeV electronthe stopping distance of a few MeV electron
in Al is as much as a millimeter?in Al is as much as a millimeter?
Here’s where the “Return Current” and Here’s where the “Return Current” and the material properties raise their headsthe material properties raise their heads
1.
Fast forward current feels not material resistance
2.
Electric Field is set up by neutrality condition to drive return current
3. Return Current, made up of vast numbers of slowly moving electrons.These electrons feel the resitivity of the material and through ohmic processes heat the material and setup a potential within the material.This potential acts to slow and stop the fast electrons in a much shorter distancethan Coulomb collisions would predict
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pote
ntia
l
MaximumFast electronKinetic energy
d
Potential stops fast electrons in muchShorter distance than collisions. EffectDepends upon resistivity of material andNumber of fast electrons
Extra Material (if time)Extra Material (if time)
• Experiments where Nfast > Nbackground
S.B - 7th FIW - 04/2004- 8
Gas jet experiment : study of a new regime of electron transport (nfast > nbackground)
= 350 fs 1,057 µmE = 5 J
= 528 nm= 350 fs
1 0.1 J mm
-
Gas Jet (He, Ar)
P = 30, 50, 70, 80 bar
Interaction beam Probe beam
E 0.0
16
= =
Other diagnostics (X, OTR)
Time resolved shadowgraphy
The delay between the CPA and the probe beam is changed from shot to shot
S.B - 7th FIW - 04/2004- 9
Gas jet experiment : propagation in transparent mediadirect observation of electron jets and cloud
ps= 20
1080 mjets
CPA beam
Gas jet (Ar 70 bar)
Ti
(20m)
Al (15m)
at 1.2 mm from nozzle
Electronic jets moving at cExtended electronic cloud moving at c/2
Gremillet et al. PRL 1999 Borghesi et al. PRL 199940
0µ
m jets
Fused silica
Vacuum
S.B - 7th FIW - 04/2004- 10
Expansion of electron cloud obtained by shadowgraphy time-series
Gas jet: Ar 70 bar
Gas atomic density: 2.7 x 1019
cm-3
Laser intensity: 3 - 4 1019 W/cm2
By changing the delay between the CPA beam and the probe
beam we can reconstruct the evolution of the electron cloud
CPA beam
t0 t0 + 4 ps t0 + 13 ps
-200
0
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-10 0 10 20 30 40 50 60 70
Data Gas Jet ExperimentC
lou
d r
ad
ius
- p
erp
en
dic
ula
r d
ire
cti
on
(m
icro
ns
)
delay (ps)
He 30 107 m/s
He 80 1.4 10 7 m/s
Ar 30 2 107 m/s
Ar 70 3 107 m/s
• minimal size of electronic cloud m
• vcloud c/30 c/10
• vcloud increases with plasma density
• vjets c/2 at least
Electron cloud velocity increases with plasma density
S.B - 7th FIW - 04/2004- 11
He 30 : 2 1019 cm-
3
He 80 : 6 1019 cm-
3
Ar 30 : 7 1019 cm-3
Ar 70 : 2 1020 cm-3