Onset of Coherent Electromagnetic Structures in the REB …€¦analytical modelling of the laser...

Onset of Coherent ElectromagneticStructures in the REB-DT fuel

Interaction of fast Ignition Concern

C. Deutsch*, A. Bret**, M-C. Firpo***, L. Gremillet+, E. Lefebvre+ and A. Lifschitz**LPGP, Université Paris-Sud, 91405 Orsay, France

**ETSII, Universitad Castilla-la-Mancha, 13071 Ciudad-Real, Spain***LPTP, Ecole Polytechnique, 91118 Palaiseau, France

+CEN, B3, 91680 Bruyères le Châtel, France

Frontiers Plasma Physics/TechnologyBANGKOK, March 5-7 2007

Complete scheme for the fast ignition with hole boring in the outer layers of the DT precompressed core

Schematic view illustrating the formation of a coaxial beam channel

FILAMENTATION LINEAR ANALYSIS

0Vk b =⋅rr

kc/ωp

Lin

ear

δ/ω

p

Tp = Tb = 100 eVNp/Nb = 10 EReb = 1 MeV

n = 0.0635 n1 = 0.

n = 0.0635 n1 = 0.026

n = 0. n1 = 0.026

n = 0. n1 = 0.

0.4 0.8-0.1

0

0.1

0.2

0.3

0.4

0.5

0.2 0.6 1

(c)

kc/ωp

Qua

si-L

inea

r δ/

ωp

Tp = Tb = 100 eVNp/Nb = 10 EReb = 1 MeV

n = 0.0635 n1 = 0.

n = 0.0635 n1 = 0.026

n = 0. n1 = 0.026

n = 0. n1 = 0.

0 0.2 0.4 0.6 0.8 1

0

0.01

0.02

0.03

0.04

-0.01

(d)

kc/ωp

δ/ωp

Tp = 500 eV Tb = 500 keVNp/Nb = 1000 EReb = 1 MeV

QL

QL

n = 0.0584

n = 0.

L

L

0.0001 0.001 0.01 0.1 1

-0.04

-0.03

-0.02

-0.01

0

0.01

(a)

In summary, we have demonstrated through an efficient analytical modelling of the laser produced REB interacting with outer less dense layers of the supercompressed DT core that the initial in depth propagation phase of the REB within fast ignitor scenario could be effective on a time scale afforded by the linear growth of the electromagnetic instability, provided due account is given to temperature distributions in projectiles and target, respectively.

Those considerations are even more appropriate for nonrelativistic proton beams which might offer the best option for driving fast ignition, provided their laser efficiency could be increased above 20 percent.

♦ Investigation of the growth rates for the Weibel electromagnetic instability (WEI) in FIS conditions for ICF

♦ p

max

ωδ for REB in the MeV energy range

appears manageable in wedged configuration♦ For intense relativistic electron beams, quasi-

linear growth rates remain below linear ones.♦ δ ≤ 0 for protons in the few tens MeV energy

range ♦ Proton fast ignition (PFI) looks highly

promising

Filamentation in FIS conditions for ICF

H. RUHL, Plasma Sources Sci. Technol. 11, A 154 (2002)

Various InstabilitiesTwo-Stream Instability

Filamentation Instability

Weibel Instability

Beam

Beam

Beam

Ek

kE

Ek

Extreme k-orientations

Maxwell + relativistic Vlasov Eqs. (linear)

Collisionless, no finite size effects

FIS conditions : current + return current

Ions form fixed background

Dielectic tensor T (k, ω). Eigenvectors associated with eigenvalue 0 yield angle (k, E)

Dispersion equation( )

( )

( )( ) ( )[ ] 0kkTkTkTkTionFilamentat-Stream-Two

zxxz22

xzz22

zxx2

k//y0 Ek branch Weibel

2yy

2 =−η−−η−η−η

=

4444444 34444444 2143421

c/ ),k ,(k K z, // Beam 2zx ω=η=

PROSPECTIVE

• Fast ignitor conditions seem able to mitigate the growth of the EMITSF instability

• REB stopping compatible with ICF hot spot ignition

• More work needed to unravel the transition of coherent EM structure → Full non linear ones