Electron transport in the shock ignition regime

Tony BellUniversity of Oxford

Rutherford Appleton Laboratory

Acknowledgements:• Guy Schurtz, Xavier Ribeyre et al (CELIA, Bordeaux)• Robert Kingham, Alex Robinson, Mark Sherlock (Imperial/RAL)• Michail Tzoufras (Oxford/RAL)

Key papers:• Betti et al PRL 98 155001 (2007)• Theobald et al Phys Plasmas15 056306 (2008)• Ribeyre et al PPCF (in press)

Shock ignition

• Compress target on low isentrope

• Final laser spike launches ignition shock

Figures from: Betti et al (2008) JPhys conf series 112 022024

Pre

ssur

e (G

bar)

Starting point: work at CELIA on off-axis drive

Does electron transport increase symmetry?

Benefits of going to higher laser intensity (‘fast shock ignition’)

Ribeyre et al PPCF 51 015013 (2009)

Gitomer et al Phys Fluids 29 2679 (1986)

I2=1016 Wcm-2m2: T~10-30keVI2=1017 Wcm-2m2: T~10-100keV

2112

cmgm10

log

4keV100012.0

ZTRscatter

Fast electrons produced by ignition pulse

Beg et al 1997: Thot = 100 (I2/1017 Wcm-2)1/3 keV

Can heat with 100keV electrons without excessive preheat

Pressure at critical: 0.32 (T/10keV) (ne/1022cm-3) Gbar

need strong shock convergencehigh T at critical

Pressure in core: 800 (T/5keV) (ne/5x1025cm-3) Gbar

Fast electron range

Betti et al PRL 98 155001 (2007): Ignition shock pressure ~ 1Gbar

Laser spike: ~ 6x1015Wcm-2, 47kJ, 540TW, 100-300psec, 310% 100keV electrons from instabilities - beneficial

Explore shock ignition driven by high energy electrons

using

KALOS electron transport code

Features of non-local transport:

• Reduced heat flow for scalelengths < 30 x mfp (‘flux limiter’)

• Increased heat flow at base of heat front

• Heat flow at angle to T

• Magnetic field where n x T = 0

212

cmgm10

log

41000012.0

Z

keV

Tscatter

mfp of 10keV electron at critical density ~ 80 m (laser =0.33m)

transport is non-local

Non-local electron transport

deflected heatflow

Non-local mag feld

Epperlein et al (1988)

Heat flow at angle to -T

Extra heat flow at base of heat front

Nishiguchi et al (1992)

Kingham & Bell (2002)

Reduced heat flowL < 30 mfp

Bell et al (1981)

Other ‘non-(non-local)’ effects

Borghesi et al (1998)

n x T source of magnetic field

Guerin et al PPCF 41 285 (1999)

Resistive electric field inhibition

with collisions

without collisions

Electron transport model requirements

• Kinetic: non-Maxwellian, anisotropic

• Energy range: 100 eV – 100 keV

• Density range: less than critical – more than solid

• Collisional to collisionless

• Magnetic field

• Implicit on electron plasma frequency timescale

• Unified treatment of thermal (0.1-30keV) with hot (10-1000keV) electrons

KALOS code

Expand velocity distn in spherical harmonics

f(x,y,v,,,t) = fnm(x,y,v,t) Pn|m|(cos) eim

• Any degree of anisotropy by expanding to any order

• Without collisions operates as efficient Vlasov code

• Collisions and B easily included

• E calculated implicitly

• Equations simple – efficient despite small explicit timestep

velocity coordinates in 3D

KineticaLaser-plasmaoSimulation

PPCF 48 R37 (2006)

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20 grid-points in magnitude of momentum

Spherical harmonics up to 10th order

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ExB drift & rotation

KALOS as a pure Vlasov code

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py

20 grid-points in magnitude of momentumSpherical harmonics up to 10th orderNo collisions

ExB drift & rotation

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py

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ExB drift & rotationAfter nearly one rotation

Tests:• Collisions• Advection• Electric field

Reproduce Spitzer conductivity

KALOS as a Fokker-Planck code

Uses an approximate electron-electron collision term

Epperlein & Haines Phys Fluids 29 1029 (1986)

KALOS time-dependent calculation for T proportional to sin(kx)

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Comparison with Spitzer conductivity

x

Spitzer applies in limit of:• long scalelength• small temperature variation• steady state (long times)

Simulations to test effect of varying

hot electron temperature

Parameters relevant to possible expts

(not fusion targets)

n=1022cm-3

100 micron

T=3keV

T=150eV

Initial conditions at start of ‘ignition pulse’

density

temperature

Cylindrical target

Polar drive, absorbed intensity = 8x1016 cos2Wcm-2

Absorption at n = 1022 cm-3

Constant for 32psec

Thot=100keV

n=3x1023cm-3

n=5x1021cm-3

Electron pressure (Mbar)

800

0

t = 0 psec

Electron pressure (Mbar)

800

0

t = 32 psec

Pmax=640Mbar at edge of high density

lower pressureat absorption surface

symmetric pressure

central preheat(but not for fusion R)

coronal heating

n=1022cm-3

100 micron

T=3keV

T=150eV

Reduced intensity: initial conditions

density

temperature

Cylindrical target

Polar drive Iabsorbed = 8x1015 cos2Wcm-2

Absorption at critical: n = 1022 cm-3

Constant for 28psec

Thot=10keV

n=3x1023cm-3

n=5x1021cm-3

Electron pressure (Mbar)

400

0

t = 28 psec

Polar drive Iabsorbed = 8x1015 cos2Wcm-2

Thot=10keV

Electron pressure (Mbar)

400

0

t = 28 psec

Polar drive Iabsorbed = 8x1015 cos2Wcm-2

Thot=10keV

Pressure lower by only 50%

Less energy intocorona

Less energyinto core:Stronger shock

Less symmetric

Lack of symmetry compensatedfor by hydro?(Ribeyre et al)

n=3x1023cm-3

n=5x1021cm-3

n=1022cm-3

100 micron

T=1keV

T=50eV

density

temperature

Cylindrical target

Polar drive Iabsorbed = 1.5x1015 cos2Wcm-2

Absorption at n = 1022 cm-3

Constant for 32psec

Thot=3keV

Further reduce intensity & larger scalelength

larger scalelength

Electron pressure (Mbar)

80

0

t = 32 psec

Polar drive Iabsorbed = 1.5x1015 cos2Wcm-2

Thot=3keV

Large pressure asymmetry

Much lower pressurein core

Max pressure occurs at critical

-0.16 to 0.85 MG

Magnetic fieldElectron pressureup to 330 Mbar

Electron density

0.5 to 30x1022cm-3

Qradial

-6.7x1015 to .3x1015 Wcm-2

Qtheta

-2.5x1015 to 4.5x1015Wcm-2

|QSpitzer|up to 41x1015 Wcm-2

Iabsorbed = 8x1015 cos2Wcm-2, Thot=10keV, t=28psec

More details of calculation at intermediate intensity

Electron density Electron pressure

Heat flow into target

Iabsorbed = 8x1015 cos2Wcm-2, Thot=10keV, t=28psec

Planar target

5x1021cm-3

3x1023cm-3

240 Mbar

120 Mbar (T=250eV)

5x1015 Wcm-23x1015 Wcm-2

300m

75m

Magnetic field

480 kG Electric field along surface3x107 Vm-1

Heat flow along surface

Conclusions

Energetic electrons are useful:

Deposit energy at high density - giving high pressure

Spread energy around target allowing uneven irradiation

Preheat not a problem

Crucial parameter:

electron range compared with ablation scalelength & target radius

Prospect of integrated simulation of transport expts relevant to shock ignition