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MIT participation in the FSC research program* C. K. Li and R. D. Petrasso MIT Experimental: LLE’s fuel-assembly experiments Development of advanced diagnostics Theoretical: Effects of scatterings upon penetration, straggling, and blooming of energetic electrons in plasmas Development of electron-in-plasma stopping Monte-Carlo code PhD training….Cliff Chen, Sabine Volkmer, Dan Casey * Supported in part by DOE, LLE, LLNL and FSC

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Develop critical diagnostic techniques for OMEGA EP --- R, neutron spectroscopy, proton radiography

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Multiple scattering is relevant to physics of current interest Fundamental physics … since Bohr, Bethe, … Fast ignition –Electron penetration and straggling –Energy deposition profile –Beam blooming Preheat…determine tolerable levels Astrophysics (e.g. relativistic astrophysical jets)

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B(r) 1-MeV electron t p =10ps r b =10 m MIT work focuses on dense, deeply collisional regimes: D < r G for which self-field corrections are unimportant

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Regimes for which r G > D,blooming, straggling, and penetration are determined by (collisional) binary interactions T e =5 keV; =300g/cm 3 DT plasma n e ~ 10 26 /cm 3 Self fields dominate beam blooming only when r G D, relevant to fast ignition this corresponds to n b /n e > 10 -2 r G D n b /n e (r G = D ) Self fields important Scattering dominant

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Only for very large energy deposition and very small deposition regions does r G approach D. T e =5 keV; =300g/cm 3 DT plasma n e ~10 26 /cm 3 r b = 10 m D r b = 20 m r b = 30 m r b = 40 m

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For fast ignition, multiple scattering must ultimately dominate over all other mechanisms in affecting energy deposition and beam divergence When n b /n e <10 -2, the interaction can be envisioned as the linear superposition of individual, isolated electrons interacting with the plasma x n b /n e ~10 - 2 n b /n c ~10 2 n b /n e ~10 - 5 nene n b /n e > 10 -2 : Weibel-like instabilities + …. n b /n e < 10 -2 : Multiple scattering e beam ( I > 10 8 A) ~

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E F =kT e E F =e 2 n e 1/3 kT e =e 2 n e 1/3 For these collisional regimes, the plasmas are non-degenerate, weakly coupled Classical Degenerate

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The angular and spatial distributions are calculated from the integro-differential diffusion equation Longitudinal distribution penetration and straggling Lateral distribution beam blooming Angular distribution mean deflection angle,

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Importantly, for a hydrogenic plasma electron scattering is uniquely comparable to the ion scattering for <10 ~ The approximation Z(Z+1) dramatically overestimates the contributions from e-e scattering component for > 10

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An effective Bragg peak results from the effects of straggling and blooming Conventional Bragg peak resulted from the velocities match > R < R Conventional e Bragg peak Effective Bragg peak

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Multiple scattering will be important for setting the requirements of Fast Ignition = 300 g/cm 3 T e = 5 keV core ~5 m ~3 m E ~ 40% Region of uniform energy deposition Region of enhanced energy deposition 1 MeV e Atzeni model This model : ~ 14 m R : ~ 3 m B : ~ 5 m

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The effect of beam blooming reduces the electron beam intensity by at least ~ 60% for 1 MeV electrons 1 MeV-electron beam: =15 kJ, pulse t p =10 ps, r b =10 m DT plasma: =300 g/cm 3, T e = 5 keV Including the effect of beam blooming provides a upper limit of the beam intensity Atzeni model This model Ignition window energy E ig power W ig intensity I ig

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Highlights of scattering effects relevant to Fast Ignition and preheat Penetration, blooming, and straggling Are insensitive to grad n effects over a large density Depend only on Have strong Z dependence Are quite insensitive over a wide range in temperature of interest.

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The insensitivity of scattering effects ( R / and B / ) and upon indicates that density gradients will not impact the general scope of these calculations 1 MeV e Region of enhanced energy deposition E ~40% Region of uniform energy deposition The effects of straggling and beam blooming are unaffected by density gradients, and are determined by the total areal density, . B / R /

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As a comparison, proton beam blooming is dramatically smaller 14 m 5m5m 0.14 m 1- MeV electron ~17-MeV proton

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Penetration drops precipitously with decreasing electron energy, while blooming and straggling increase 0.1 25 0.45 0.013 0.27 0.38 1.0 40 14 0.42 0.19 0.33 5.0 50 94 2.82 0.12 0.22 10 65 200 6.04 0.08 0.17 (MeV) (%) x> (g/cm 2 ) x> ( m) *DT plasma =300g/cm 3 at 5 keV

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Penetration, blooming, and straggling have a strong dependence upon plasma Z 1 300 17.9 13.9 0.42 0.19 0.33 4 271 17.9 10.6 0.29 0.36 0.51 13 249 17.9 6.3 0.16 0.67 0.81 29 265 17.9 3.7 0.10 1.0 1.14 (g/cm 3 ) x> (g/cm 2 ) R ( m) x> ( m) * Assuming: same n e in each case Even a small fraction of Au contamination in the DT plasma could significantly enhance energy loss and beam blooming (future work)

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Scattering effects, which determine electron penetration, are important for evaluating the tolerable levels of electron preheat 10 DT 0.25 4.72 1.2 10 -4 0.23 0.33 Be 1.85 0.57 1.1 10 -4 0.31 0.42 CH 1.0 0.72 7.2 10 -5 0.36 0.48 100 DT 0.25 283 7.1 10 -3 0.15 0.27 Be 1.85 31.0 5.7 10 -3 0.26 0.39 CH 1.0 42.4 4.2 10 -3 0.32 0.41 (g/cm 3 ) x> (g/cm 2 ) x> ( m) (keV) ~ 100% R DTice Fast electron (2 ) Hot electron (corona) Indirect-drive NIF capsule D 3 He 20 m CH D 3 He 20 m CH DT ICE Direct-drive NIF capsule D 3 He 20 m CH D 3 He 20 m CH DT ICE Be ~ 20% R Be

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For relativistic astrophysical jets, electron energies ~ 1 MeV or much greater R (FI) ~ R (jet) ~ 0.4 g/cm 2 R ( FI) ~ 10 m ~10 –3 cm R (Jet) ~ 10 4 light years ~10 22 cm These scattering calculations are directly relevant to penetration and blooming in relativistic astrophysical jets That these results have direct applications to problems that differ in density and scale length by over 25 orders of magnitude is itself extremely appealing to physicists’ sense of beauty and generality.

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As its contribution to the FSC, MIT is participating in a wide range of projects ----- experimental, computational, and analytic implosion physics Summary Fuel assembly for cone-in-shell implosions Nuclear diagnostics and advanced neutron spectrometers Proton radiography Modeling of energetic electrons interaction with plasmas --- FI, Preheat, Relativistic astrophysics Development of a Monte-Carlo code

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