MIT participation in the FSC research program*

C. K. Li and R. D. Petrasso MIT

Experimental:

• LLE’s fuel-assembly experiments

• Development of advanced diagnostics

Theoretical:

• Effects of scatterings upon penetration, straggling,

and blooming of energetic electrons in plasmas

• Development of electron-in-plasma stopping

Monte-Carlo code

PhD training….Cliff Chen, Sabine Volkmer, Dan Casey

*Supported in part by DOE, LLE, LLNL and FSC

Develop critical diagnostic techniques for OMEGA EP --- R, neutron spectroscopy, proton radiography

Multiple scattering is relevant to physics of current interest

• Fundamental physics … since Bohr, Bethe, …• Fast ignition

– Electron penetration and straggling– Energy deposition profile– Beam blooming

• Preheat…determine tolerable levels• Astrophysics

(e.g. relativistic astrophysical jets)

0 20 40 60

r (mm)

B f

ield

B(r)

1-MeV electron tp=10ps

rb=10 mm

1.E+08

1.E+09

1.E+10

0 5 10 15 20

Beam energy (kJ)

Cu

rren

t (A

mp

)

1.E+10

1.E+11

1.E+12

B fi

eld

(Gu

ass)

MIT work focuses on dense, deeply collisional regimes: D < rG for which self-field corrections are unimportant

Regimes for which rG>D ,blooming, straggling, and penetration are determined by (collisional) binary interactions

Te=5 keV; =300g/cm3 DT plasma ne ~ 1026/cm3

Self fields dominate beam blooming only when rGD, relevant to fast ignition this corresponds to nb/ne > 10-2

1.E-09

1.E-08

1.E-07

0 5 10 15 20

Beam energy (kJ)

Dis

tanc

e (c

m)

0.001

0.01

0.1

0 5 10 15 20

Beam energy (kJ)

Rat

io

rG

D

nb/ne

(rG = D)

Self fields important

Scattering dominant

Only for very large energy deposition and very small deposition regions does rG approach D.

Te=5 keV; =300g/cm3 DT plasma ne~1026/cm3

1.E-09

1.E-08

1.E-07

1.E-06

0 10 20

Beam energy (kJ)

r G (

cm

)

rb= 10 mm

D

rb= 20 mm

rb= 30 mmrb= 40 mm

For fast ignition, multiple scattering must ultimately dominate over all other mechanisms in affecting energy deposition and beam divergence

When nb/ne <10-2, the interaction can be envisioned as the linear superposition of individual, isolated electrons interacting with the plasma

x

nb/ne~10-2

nb/nc~102

nb/ne~10- 5

ne

nb/ne > 10-2 : Weibel-like instabilities + ….

nb/ne < 10-2 : Multiple scattering

e beam

(I > 108 A)

~

15

20

25

30

-1 0 1 2 3 4

Log10 [kTe(eV)]

Lo

g10

[n

e(c

m-3

)]

EF=kTeEF=e2ne

1/3

kTe=e2ne1/3

For these collisional regimes, the plasmas are non-degenerate, weakly coupled

Classical

Degenerate

The angular and spatial distributions are calculated from the integro-differential diffusion equation

E

E

dEds

dEEPEf

0

'exp)(cos)12(4

1),(

1'

0

''σ,,,', vvvvxvxv dsfsfNfs

f

• Longitudinal distribution penetration and straggling

• Lateral distribution beam blooming

• Angular distribution mean deflection angle, <cos>

Importantly, for a hydrogenic plasma electron scattering is uniquely comparable to the ion scattering for <10

ei

ee

dd

dd

R

σ

σ

0.0

0.5

1.0

1.5

0 5 10 15 20

R

Z=1

Z=2

Z=3

~

The approximation Z(Z+1) dramatically overestimates the contributions from e-e scattering component for > 10

An effective Bragg peak results from the effects of straggling and blooming

Conventional Bragg peak resulted from the velocities match

0.1

1

10

100

1000

10000

0 0.2 0.4 0.6R (g/cm2)

dE

/d(

R)

(Me

V g

-1 c

m2 )

0 5 10 15 20

> R < R

Conventional e Bragg peak

Effective Bragg peak

4

1

the vv~

ddσ

Multiple scattering will be important for setting the requirements of Fast Ignition

= 300 g/cm3 Te = 5 keV

core

~5mm

~3mm

E ~ 40%

Region of uniform energy deposition

Region of enhanced energy deposition

1 MeV e

Atzeni model

This model<x>: ~ 14 mm

R: ~ 3 mm

B: ~ 5 mm

The effect of beam blooming reduces the electron beam intensity by at least ~ 60% for 1 MeV electrons

1 MeV-electron beam: =15 kJ, pulse tp=10 ps, rb=10 mm

DT plasma: =300 g/cm3, Te = 5 keV

Including the effect of beam blooming provides a upper limit of the beam intensity

0.E+00

3.E+20

6.E+20

0 20 40 60 80 100

E (%)

Bea

m in

ten

sity

(W

/cm

2 )

Atzeni model

This model

Ignition window

• energy Eig

• power Wig

• intensity Iig

Highlights of scattering effects relevant to Fast Ignition and preheat

Penetration, blooming, and straggling

• Are insensitive to grad n effects over a

large density

• Depend only on <x>

• Have strong Z dependence

• Are quite insensitive over a wide range

in temperature of interest.

The insensitivity of scattering effects (R/<x> and B/<x>) and <x> upon indicates

that density gradients will not impact the general scope of these calculations

1 MeV e

0

200

400

600

0 10 20 30 40

Distance (mm)M

ass

Den

sity

(g

/cm

3)

Region of enhanced energy deposition

E ~40%

Region of uniform energy deposition

The effects of straggling and beam blooming are unaffected by density gradients, and are determined by the total areal density, <x> .

0

0.3

0.6

0 500 1000

g/cm3

<x>

g/c

m2

0

0.3

0.6

Rat

io

<x>

B/<x>

R/<x>

As a comparison, proton beam blooming is dramatically smaller

%1~B

x

%35~B

x

14 mm

5mm

0.14 mm

1- MeV electron

~17-MeV proton

Penetration drops precipitously with decreasing electron energy, while blooming and straggling increase

 

 

0.1 25 0.45 0.013 0.27 0.38 1.0 40 14 0.42 0.19 0.33 5.0 50 94 2.82 0.12 0.22 10 65 200 6.04 0.08 0.17

xR

xB

(MeV)

(%)

x>

(g/cm2)

x>

(mm)

*DT plasma =300g/cm3 at 5 keV

 

Penetration, blooming, and straggling have a strong dependence upon plasma Z

 

 

1 300 17.9 13.9 0.42 0.19 0.33 4 271 17.9 10.6 0.29 0.36 0.5113 249 17.9 6.3 0.16 0.67 0.8129 265 17.9 3.7 0.10 1.0 1.14 

xR

xB

(g/cm3)

x>

(g/cm2)

R

(mm)

x>

(mm)

*Assuming: same ne in each case

Even a small fraction of Au contamination in the DT plasma could significantly enhance energy loss and beam blooming (future work)

Scattering effects, which determine electron penetration, are important for evaluating the tolerable levels of electron preheat

 

 

10 DT 0.25 4.72 1.210-4 0.23 0.33 Be 1.85 0.57 1.110-4 0.31 0.42 CH 1.0 0.72 7.210-5 0.36 0.48100 DT 0.25 283 7.110-3 0.15 0.27 Be 1.85 31.0 5.710-3 0.26 0.39 CH 1.0 42.4 4.210-3 0.32 0.41  

xR

xB

(g/cm3)

x>

(g/cm2)

x>

(mm)

(keV)

~ 100% RDTice

Fast electron (2)

Hot electron (corona)

Indirect-drive NIF capsule

D 3 H e

2 0 m m C H

D 3 H e

2 0 m m C H

DT ICE

Direct-drive NIF capsule

D 3 H e

2 0 m m C H

D 3 H e

2 0 m m C H

DT ICEBe

~ 20% RBe

For relativistic astrophysical jets, electron energies ~ 1 MeV or much greater

R (FI) ~ R (jet) ~ 0.4 g/cm2

• R ( FI) ~ 10 mm ~10–3 cm

• R (Jet) ~ 104 light years ~1022 cm

These scattering calculations are directly relevant to penetration and blooming in relativistic astrophysical jets

That these results have direct applications to problems that differ in density and scale length by over 25 orders of magnitude is itself extremely appealing to physicists’ sense of beauty and generality.

As its contribution to the FSC, MIT is participating in a wide range of projects ----- experimental, computational, and analytic implosion physics

Summary

• Fuel assembly for cone-in-shell implosions• Nuclear diagnostics and advanced neutron

spectrometers• Proton radiography• Modeling of energetic electrons interaction with

plasmas --- FI, Preheat, Relativistic astrophysics• Development of a Monte-Carlo code