Fast Ignition Fast Ignition: Some Issues in Electron Transport Some fundamentals of large currents moving through dense materials Some unexpected problems

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?





Richard Fitzpatrickhttp://farside.ph.utexas.edu/Teaching/plasma/lectures/Node6.html

http://farside.ph.utexas.edu/

Richard Fitzpatrickhttp://farside.ph.utexas.edu/Teaching/plasma/lectures/Node6.html

http://farside.ph.utexas.edu/

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





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





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





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..





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





Experimental Studies of LaserExperimental Studies of LaserGenerated Electrons: MethodGenerated Electrons: Method

First results of side-imaging of currentsFirst results of side-imaging of currents

400 450 500 550

450

500

550

600

650

col

row

2500 5000 7500 10000_1803_4s56_SPE_x_rs_sm

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

425 450 475 500 525 550

2500

5000

7500

10000

2500

5000

7500

10000

col

_1803_4s56_SPE_x__x

450 500 550 600 650

2500

5000

7500

10000

2500

5000

7500

10000

row

_1803_4s56_SPE_x__x

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)





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

4.

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

200

400

600

800

1000

1200

-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

Documents

Fast Ignition Fast Ignition: Some Issues in Electron Transport Some fundamentals of large currents moving through dense materials Some unexpected problems