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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
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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magnetic field
advection
electric field
20 grid-points in magnitude of momentum
Spherical harmonics up to 10th order
No collisions
ExB drift & rotation
KALOS as a pure Vlasov code
Fxy.agl
px
py
20 grid-points in magnitude of momentumSpherical harmonics up to 10th orderNo collisions
ExB drift & rotation
0
0
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)
x
xx
x
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 = 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
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