Energy Deposition of MeV Electrons in Compressed Fast-Ignition Targets

C. K. Li, F.H. Séguin and R. D. Petrasso MITAnnual Meeting of FSC atLaboratory for Laser Energetics26-27 January, 2006

0.00

0.05

0.10

0.15

0 5 10 15 20 25

Penetration (μm)

E (keV/μm3)

Uniform model

This model

MIT

Summary

Classical Coulomb collision dominates interactions of energetic electron in dense core of fast-ignition targets

Electron energy loss, penetration and scattering are inextricably coupled together

Blooming and straggling effects lead to a non-uniform, extended region of energy deposition

This result significantly changes the energy deposition profiles regardless of the electron beam radius

MIT

nb/ne~10-2

nb/ne > 10-2 :

self fields, instabilities, ….

nb/ne < 10-2 : scattering

Laser

For the interior of a FI capsule, scattering dominates other mechanisms in affecting energy deposition, beam blooming, and straggling

MIT

Electron scattering must be included in calculating the energy deposition

%.~ 50B

x

%~B 40

x

1 MeV e

14 .1 m

14 .1 m

18.8 MeV p

MIT

<x>

e

dx

dE

ds

dE

plasma

B

B

R R

Scattering reduces the electron linear penetration, and it results in longitudinal straggling and beam blooming

Combine all these effects, the energy deposition profile is modified

The effects of energy loss and scattering must be treated with a unified approach

E

E

dEds

dEEkPEf

0

1

0

124

1'exp)(cos)(),( '

Scattering

Energy loss

dPd

dnEk i

)(cos

σ)( 1Where:

1.E-02

1.E-01

1.E+00

1.E+01

0 20 40 60 80 100

DE (%)

r o-2

sin

4 (/2

)(ds

/d

)

Moller

Rutherford

MIT

Scattering are insensitive to plasma screening models

8

10

12

14

No

rmn

ize

d k 1

(E)

DebyeinterparticeTF

-3

-2

-1

0

0 0.2 0.4 0.6 0.8 1

E/E0

k 1(E

)(d

E/d

s)-1

Debye

interparticle

TF

k1(E)

1

1

ds

dEEk

ln

lnln/)(

eeei

ds

dEE

421

2

1

1

2

14

k

Plasma screening:

D ---- Debye length

d ---- inter-particle distance

TF ---- Thomas-Fermi

= 300 g/cm3; Te = 5 keV

scatteringEnergy loss

Multiple scattering enhances electron linear-energy deposition

ds

dE

dx

dE 1cos

= 300 g/cm3; Te = 5 keV

0

5

10

0 0.4 0.8 1.2

Electron energy (MeV)

Me

V g

-1 c

m2

dx

dE

ds

dE

E

E

dEds

dEE

0

1

1'

''expcos k

where

MIT

The qualitative features of this model --- penetration, blooming and straggling --- are replicated by Monte Carlo calculations for solid DT

1 MeV e 1 MeV e

This model Monte Carlo

MIT

For electrons with low energies, blooming and straggling become important even with little energy loss (DE)

0

20

40

0 5 10 15 20

0

0.2

0.4

0 0.2 0.4 0.6 0.8 1

<x>1/2

0

2

4

6

0 2 4 6

R

DE ~60%

ST

DV

(

m)

DE ~40%

DE ~25%

B

B

10 MeV

1 MeV

0.1 MeVR

B

R

MIT

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

Conventional Bragg peak results from the velocity match

0.1

1

10

100

1000

10000

0 0.2 0.4 0.6R (g/cm2)

Me

V g

-1 c

m2

R R

Conventional Bragg peak

Effective Bragg peak

4

1

the vv~

ddσ

MITdE/d(R)

Effects of scattering are integrated in a simple formula for energy deposition

Where: RE dx

dE

220

0

2

21

2

2

2

2

1B

xx

EE

r

dxee

dsdE

E

R

E

πθδ

)(

)(

cos

Stopping power

Energy straggling

Beam blooming

Range straggling

MIT

Combining these effects, electron energy deposition is notably different than the uniform model prediction

rb = 10 μm

rb = 20 μm

0.0

20.0

40.0

60.0

0.00

1.00

2.00

3.00

0.00

0.20

0.40

0.60

0.00

0.05

0.10

0.15

0 5 10 15 20 25

Penetration (μm)

E (keV/μm3)

rb = 1 μm

rb = 5 μm

Uniform model

This model

Density (g/cm3)

Distance (m)

0 5 10 15 20 25

300

0

1-MeV e

MIT

Summary

Classical Coulomb collision dominates interactions of energetic electron in dense core of fast-ignition targets

Electron energy loss, penetration and scattering are inextricably coupled together

Blooming and straggling effects lead to a non-uniform, extended region of energy deposition

This result significantly changes the energy deposition profiles regardless of the electron beam radius

MIT