Using Highly Supersonic, Radiatively Cooled,. Plasma Slugs. J.P. Chittenden, M. Zepf, S.V. Lebedev, A. Ciardi and S.N. Bland. Imperial College, London, U.K..
Indirect Drive Inertial Confinement Fusion, Using Highly Supersonic, Radiatively Cooled, Plasma Slugs J.P. Chittenden, M. Zepf, S.V. Lebedev, A. Ciardi and S.N. Bland Imperial College, London, U.K. M. Dunne AWE Aldermaston, U.K.
Problem Z-pinches efficiently convert 10-20% of electrical energy to X-rays But delivery of X-ray energy into secondary hohlraum containing capsule is inefficient Premise Transport energy away from imploding Z-pinch into target hohlraum using high velocity slug Kinetic energy can then be converted into X-rays in close proximity to the capsule. Concept Strong radiative cooling ⇒ high Mach number, low divergence
Examples of radiatively cooled supersonic jets and slugs Young stellar objects Proto-planetary nebulae e.g. He 3-1475 e.g. HH 212
High power laser-plasma experiments
Conical Shocks
Knots
Borkowsky K. J. et. al. Ap.J. 482, L87, 1997 D.R. Farley et al. Phys. Rev. Lett. 83, 1982 (1999).
Conical Wire Arrays Jet
Laser shadowgraphy
B j
Gated X-ray images
Jet parameters on MAGPIE (1MA, 240ns rise-time) Radius ~ 1 mm Length ~ 20 mm Velocity ~ 2x105 m/s Density ~ 0.2 Kg/m3 Kinetic energy ~ 200 J Internal Mach number > 20 Quasi steady state conditions result in long duration (100ns) flow. For hohlraum heating we require a shorter, more intense burst
Slug generation: 1) Conical liner implosion
Modelled using 2D(r,z) resistive MHD code: explicit Eulerian hydrodynamics, implicit thermal and magnetic field diffusion, two temperature plus LTE ionisation, recombination radiation loss model plus probability of escape
8 4
12 8 4
206ns
0
Z Axis in mm
16 12 8 4 0 12
Power delivered to end is discontinuous and irreproducible.
0ns
16
Zippered implosion works in similar fashion to shaped charge travelling implosion wave falls just behind moving slug axial ∇P and ∇B2 accelerate slug Susceptible to Magneto-Rayleigh-Taylor instability here seeded by mapping cone onto r-z grid each RT bubble generates separate slug
12
0
Z Axis in mm
Conical tungsten liner, driven by MAGPIE generator (1MA, 240ns rise-time) (not really practical)
Z Axis in mm
16
216ns 8
4
0
4
R Axis in mm
8
12
Slug generation: 2) Coaxial plasma gun Radial disc of plasma driven by MAGPIE generator (1MA, 240ns rise-time)
Again susceptible to Magneto-Rayleigh-Taylor instability particularly where the plasma slips along electrode surfaces Could be improved using controllable driving pulse and tapered nozzle Full mass is gradually accelerated over the full current rise-time ⇒ efficient conversion to kinetic energy, but low terminal velocity ⇒ low power delivered to end-on target ( ½ ρv3 )
265ns
40
Z Axis in mm
Radial current plus azimuthal magnetic field produce axial jxB force.
50
30
220ns 20
jxB 10
jr
jz X
0 30
20
10
0
0 ns
10
Bθ
R Axis in mm
20
30
20
20
15
15
Z Axis in mm
Cylindrical liner implosion on ‘Z’ generator (18MA, 100ns rise-time) mass per unit length doubles between z=0 and z=5 mm
Z Axis in mm
Slug generation: 3) Variable mass liner
10 5 0 15
0 ns 10
5
0
5
10
Axial jxB force, both during and after implosion, accelerates plasma along axis Strong radiative cooling, rapidly cools plasma after launch to ~10 eV, internal Mach number is ~ 200 divergence of flow is extremely small
20
20
15
15
10 5 0 -15
93 ns -10
-5
0
5
R Axis in mm
90 ns 10
5
0
5
10
15
R Axis in mm
10
15
Z Axis in mm
Z Axis in mm
Collapse of bottom 5mm produces miniature coaxial plasma gun
5 0 15
15
R Axis in mm
Variation in implosion time produces a single, large scale and controllable Rayleigh-Taylor bubble
10
10 5 0 -15
96 ns -10
-5
0
5
R Axis in mm
10
15
At 96ns slug is 500µm diameter, 4mm long, 4x106 ms-1 velocity and delivers ~ 500kJ of kinetic energy to the boundary in 1ns !! Most probably an overestimate as narrow plasma column is likely to disrupt, thereby terminating jxB acceleration. More conservative slug parameters just after formation are ~ 2ns, 2x106 ms-1, 250kJ
Slug-driven ICF : AWE Eulerian 3T calculations 250kJ KE Tungsten slug, 2e8 cm/s, 4mm (2ns) long, 1mm diameter, 0.0398g/cc, 5eV Impacting 19.32g/cc Tungsten slab
Imperial College
Initial configuration (density)
Slug : Te ~ 1 keV Slab : T ~ 500 eV Tr ~ 0.5 keV P ~ 1.5 GBar P ~ 0.5 GBar
Predicted Temperature & Density profiles
Imperial College
AWE code PETRA 3T Eulerian IMP opacities SESAME EOS 1
Tr, t=0.3ns
Tr, t=0.2ns
500 Tr (eV)
0 0
1
x (mm)
Tr, t=0.1ns
2
0
1
x (mm)
Log(ρ ρ), t=0.3ns
To do : investigate disassembly time (~ ) & decay profile
2
0
1e+2 ρ (g/cc) 1e-5
3D GLIMMER viewfactor-hydro : capsule conditions
Imperial College Assumed drive = Rise to 500eV in 1ns gives 300eV capsule drive Converter foil flux
Tr (eV)
Calculation Geometry
Flux on wall
Flux on capsule
0
1 Time (ns) 2
