Plasma X-ray Sources and Imaging … an ICF perspective Advanced Summer School 9-16, Juy 2017, Anacapri, Capri, Italy Riccardo Tommasini LLNL-PRES-734513 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC
Outlook Motivation • Our problem: probing ICF targets • This requires the use of X-rays • Plasmas are efficient sources of X-rays Summary • What is ICF • Need to image ICF targets • Laboratory-generated X-ray sources: laser plasma • Basic Plasma parameters • Basics of Radiation emission from laser-plasmas • Imaging techniques • Application of Radiography to ICF targets Lawrence Livermore National Laboratory 2 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
Outlook Motivation • Our problem: probing ICF targets • This requires the use of X-rays • Plasmas are efficient sources of X-rays Summary • What is ICF • Need to image ICF targets • Laboratory-generated X-ray sources: laser plasma • Basic Plasma parameters • Basics of Radiation emission from laser-plasmas • Imaging techniques • Application of Radiography to ICF targets Lawrence Livermore National Laboratory 3 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
Nuclear energy is released when the final reaction products have less mass/nucleon than the reacting nuclei FUSION Yield/nucleon from FUSION FISSION Yield/nucleon from FISSION Atomic Mass number Lawrence Livermore National Laboratory 4 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
Temperatures of several keV are needed for fusion The DT reaction has the largest cross- section, ~100 times larger than any other, in the 10–100 keV energy interval At these temperatures the atoms are ionized: plasma The reactions involve the ions in the plasma Lawrence Livermore National Laboratory 5 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
Fusion of light nuclei results in lower total mass The mass difference is released as fusion energy D E= D ( mc 2 )=17.6MeV 4 He, 3.5MeV n, 14.1MeV D T + + = + + + The a -particles have high cross section and release energy into the fuel (self heating). The neutrons carry exploitable energy: n-Yield is the most important metric to assess success. Lawrence Livermore National Laboratory 6 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
Burn rate, fractional burn, areal density Assume equimolar, n D =n T =n, DT plasma assembled n’(t) = -(1/2) < s v> n(t) 2 to meet fusion conditions. The burn rate is: If < s v> stays constant (not true), we can integrate n( t ) = n 0 (n 0 /2 < s v> t + 1) -1 the equation over the confinement time t : f = n 0 t / (2< s v> -1 + n 0 t ) The fractional burn is: f=1-n( t )/n 0 tr / m ) / (2< s v> -1 + tr Plugging in n 0 = r /m, we get: f = ( tr tr / m ) Notice: t ∝ R = radius, therefore the tr tr terms lead to r R = areal density Lawrence Livermore National Laboratory 7 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
� � � � � � � � For areal density ~ 3g/cm 2 the fractional burn is 30% and fusion yield is ~10 5 MJ/g Estimate confinement time, t , for spherical DT assembly: <r> The mass-average radius of a uniform sphere is R 4𝜌 ∫ 𝑠 𝜍 𝑠 + 𝑒𝑠 4𝜌 ∫ 𝑠 𝑠 + 𝑒𝑠 = 3 < 𝑠 >= = 4 𝑆 4𝜌 ∫ 𝜍 𝑠 + 𝑒𝑠 4𝜌 ∫ 𝑠 + 𝑒𝑠 t = = R/(4c s ) Therefore: 𝜐 = (𝑆 −< 𝑠 >)/𝑑 6 c s = sound speed ~ 3 10 7 cm/s Plugging into the equation for f we get: 5-30keV f = r R / ( r R + 8mc s /< s v>) f = r R / ( r R + 7g/cm 2 ) c s ~ 3 10 7 cm/s 𝟒𝒉 𝑔 ∗ = 𝑔 r R= Areal density = 0.3 𝒅𝒏 𝟑 Estimate fusion yield = 14.1MeV f * 1/[(3+2)amu] = 8e10 J/g [Ref.: R. Betti - HEDP Summer School, University of California, Berkeley 12 August 2005] Lawrence Livermore National Laboratory 8 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
It is practically impossible to ignite a whole, homogeneous, sphere of cryogenic DT fuel at r R=3g/cm 2 • DT solid density = 0.25g/cm 3 At ρR=3 g/cm 2 : R=ρR/ρ=12cm and M= 4/3 p R 3 • DT, 0.25g/cm 3 r = 1.8kg of DT T=5keV Confinement time, at 5keV: t = R/(4c s ) ~ 100ns • • 1.8kg of DT at 5keV ~ 0.35TJ. Assuming 30% 24cm energy transfer efficiency, we need ~1TJ Power = 1TJ/100ns = 10 7 TW ~ 10 6 times any • 0.25g/cm 3 existing power plant r 5keV • If you managed to ignite it, it would release T 150TJ ~ 35 kilotons!!! • Change strategy: compression and hot spot r ignition…. [Ref.: R. Betti - HEDP Summer School, University of California, Berkeley 12 August 2005] Lawrence Livermore National Laboratory 9 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
Hot Spot ignition: heat only a small fraction (~1%) of compressed fuel to ignition temperatures and use self heating DT “Cold” DT shell • Assume compression is achieved by laser: Typical Hot Spot laser pulse: t L = 1ns 85g/cm 3 Assume t = t L /10= R/(4c s )=100ps è R~0.12mm • T=5keV + + Assume ρR=1 g/cm 2 è ρ~85g/cm 3 • Total Mass = ( 4/3) p R 3 r ~ 0.6 mg • • This mass at 5keV ~ 0.12MJ. Assuming 30% ~1000g/cm 3 energy transfer efficiency, we need 0.39MJ. • Power = 0.39MJ/1ns = 390TW power ~0.1mm • This is manageable 1000g/cm 3 the energy released in the “hot-spot” and r transported by the a -particles heats the surrounding cold fuel (self heating) to the ignition T=5keV temperature: fusion burn wave. The pressure in the H-S needs to reach p = 0.12MJ/(4/3 p R 3 ) ) ~ 160 Gbar r [Ref.: R. Betti - HEDP Summer School, University of California, Berkeley 12 August 2005] Lawrence Livermore National Laboratory 10 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
NIF can concentrate the 1.9 MJ from 192 laser beams into 1 mm 3 Matter temperature >10 keV Radiation temperature >0.350 keV >10 3 g/cm 3 Densities Pressures >100 Gbar Lawrence Livermore National Laboratory 11 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
The NIF uses Indirect Drive geometry Laser The laser beams heat the inner walls of a Beams Au hohlraum, generating a plasma, which in turn generates X-rays The X-ray radiation ablates the surface of Ablator the outer shell (e.g. CH) inducing an inward rocket reaction that compresses the fuel: implosion X-rays Au can DT = The implosion's main purpose is to gas hohlraum compress and act as a "pressure amplifier” and reach > 300Gbar DT ice The hohlraum is used to improve radiation drive uniformity on the capsule=Ablator+Fuel Laser Beams Lawrence Livermore National Laboratory 12 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
The trick of ICF is to turn 100 million atmospheres of pressure into 300 billion atmospheres of pressure E laser ~ 1.8 MJ E x-ray ~ 1.3 MJ produced by hohlraum Plasma The implosion's main purpose is to Shell Surface explodes compress and act as E absorbed ~ 150 kJ a "pressure amplifier" P ablator ~ 100 Mbar Fuel and remaining ablator accelerate inwards M. Marinak KE fuel ~ 14 kJ Speed ~ 370 km/s P stagnation ~ need 300+ Gbar 2 mm initial “Ablator” (~195 microns thick) "hot-spot" DT ice (fuel) layer (~69 microns thick) 0.1 mm at stagnation Lawrence Livermore National Laboratory 13 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
Compression in 3D is spoiled by fuel asymmetries Peak High frequency compression asymmetries: seeded by target imperfections and amplified by hydro- instabilities. Low frequency asymmetries: seeded by variations in the drive (hohlraum) D.S. Clark, et. al. Phys Plasmas 23 , 056302 (2016) Lawrence Livermore National Laboratory 14 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
Rayleigh-Taylor instability is due to inertia Hot spot Hot spot “Cold” fuel “Cold” fuel Acceleration phase: the heavy Deceleration phase, the heavy cold cold fuel is unstable on the outer fuel is unstable on the inner front, front because heavier than hot spot Pre-existing imperfections or defects grow in time as capsule implodes with growth rates that are amplified by instabilities. Lawrence Livermore National Laboratory 15 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
We need to look at the imploding fuel to understand what can disrupt ignition The imploding fuel is a plasma. “Cold” DT fuel = dense plasma Dense plasmas are opaque to visible light. We Hot spot need X-rays to image the dense plasma in the = fuel: X-ray Radiography Low density plasma Plasmas emit X-rays. X-ray imaging using plasma X-ray sources can be used to look at the implosion. Let’s look at some plasma properties → Lawrence Livermore National Laboratory 16 R Tommasini, Adv. Summer School, 9-16, Juy 2017, Anacapri, Capri, Italy LLNL-PRES-734513
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