1. Short pulse modelling in PPD N. J. Sircombe, M. G. Ramsay, D. A. Chapman, S. J. Hughes, D. J. Swatton. nathan.sircombe@awe.co.uk www.awe.co.uk

2. Outline  Background  Short pulse LPI  Transport  Plans for short pulse modelling

3. Background  The twin petawatt arms on ORION will provide a means to heat matter to extreme temperatures and allow us to study its properties.  The mechanisms by which the short pulse laser delivers its energy, how this energy is distributed and how it is transported into the material are complex and interdependent.

4. Background  Currently there is a reliance on a number of empirical relations, which may be limited to a specific target configuration or laser system.  A more predictive modelling capability will help us to…  Understand, challenge or support these assumptions  Optimise experiments to make the best use of ORION’s available short-pulse capability.  There are clear similarities between the problems faced in predicting the outcome of full-scale ORION experiments and developing a fast ignition point design

5. Short pulse LPI  Modelling interaction of SP laser in  Planar targets  Variety of plasma profiles, target angles  Cone geometry  Effect of low-density cone fill  Effect of ‘missing’ cone tip  Using PIC codes and direct Vlasov solvers  CCPP PIC code – EPOCH  Developed by C. S. Brady (CFSA Warwick)  Direct, 2D, Vlasov – VALIS  Developed with T. D. Arber (CFSA Warwick)

6. Hot electron generation in planar targets  Characterise energy spectrum of hot electrons in experiments fielded on Omega  To produce radiographic source from bremsstrahlung  With and without a long-pulse created ‘pre plasma’  Intended to improve absorption and generation of hot electrons  …but low density pre-plasma generates very high energy electrons  Potential problem for FI (e.g. foam filled cones, fuel ‘jets’ entering the cone etc.)  Bremsstrahlung radiation can be modelled using EPOCH particle probe data as a source in MCNPx

7. 2D ‘Cone’ Geometries  In a full 2D cone geometry, the presence of a long scale length pre- plasma:  allows more energy to be coupled into hot electrons  produces higher energy electrons  produces a more divergent beam  creates a larger effective hot electron source, as the beam is refracted.  If the short pulse laser misses the cone tip the pre-plasma has a detrimental effect  Produces a hot electron beam which is divergent  originates over a larger area  not directed at the assembled fuel. 90 o 0o0o -90 o 0 100 MeV 200

8. VALIS  2D2P Direct Vlasov Solver  Explicit, Conservative, Split scheme using PPM advection  Laser boundaries for LPI  Domain decomposition over 4D (2D2P) phase space  N.J. Sircombe and T.D. Arber, J. Comp. Phys. 228, 4773, (2009)

9. Hot electrons from short scale length plasmas  500nc, 3.5 micron scale length plasma ramp  1.37e20W/cm 2 from LH boundary  System size  80 microns in space, +/- 24  in momentum  (nx, npx, npy) = (8192, 200, 220)  Estimate T hot Using fit to Boltzmann distribution over three energy ranges*  [0.1, 1), [1,5) and [5,10] MeV  ‘Head’ of electron ‘beam’ not well described by Boltzmann dist. * Not an ideal solution! see M. Sherlock PoP (2009)

10. ux -20 -32 x t=76fs (x,ux) phase space (immobile ions) t=226fs -20-32 x 40-40 x 0  T hot peaks and falls  7.3 MeV at 200fs, 1.5MeV at 400fs  Apparent ‘steady state’ by 200fs

11. Mobile Ions  Preliminary results with mobile ions  Profile steepening, ion acceleration at front surface  Evidence of IAW, ion trapping in pre-plasma -8 40-40 x 0 fe fi -26 x t=200fs

12. Transport  Modelling hot electron transport in solid density targets using THOR II  Explicit Monte Carlo Vlasov-Fokker-Planck solver in 2D3P or 3D3P  Eulerian grid  Self-consistent fields via return current argument

13. Buried Layer modelling  Range of intensities  Al layer buried at various depths in CH target  Lee-More resistivity model for metals, capped Spitzer model in plastic  Absorption based on Ping et al. PRL  Beg-scaling for hot electron energies  Fixed divergence angle

14. Plans  Overarching aim is to provide a predictive short pulse modelling capability in support of ORION experiments  Requires that we  Scale existing models to larger systems, higher densities and 3D  Couple hydro and kinetic models  Add additional physics

15. Integrated modelling  Plan to couple transport models into hydro codes  Early stages of using hydro code data as an initial condition in EPOCH  Currently looking at characterising hot electron source using EPOCH/VALIS over wide parameter range to replace empirical scaling  Aim to model…  LP interaction, target compression, pre- pulse effects in CORVUS.  Short pulse interaction, hot electron generation in EPOCH using density & temperature from CORVUS  Hot electron transport and target heating in THOR using hot electrons from EPOCH and density / temp from CORVUS.

16. Areas of interest  SP absorption and subsequent transport in realistic, ORION / HiPER scale targets  Additional physics for kinetic codes  Collision operators  Ionisation  Hybrid models  Optimisation of kinetic algorithms and parallel communications  Ready for future HPC on many 10,000’s of cores  AMR-Vlasov

17. nathan.sircombe@awe.co.uk www.awe.co.uk

18. Additional Slides VALIS

19. VALIS – intro.  Any kinetic model of plasma will be closely related to Vlasov’s equation  Describes evolution of particle density, in response to self- consistent fields from Maxwell’s equations in a 6D phase space  (3 x space, 3 x momentum)  For now, restrict our selves to two spatial and two momentum dimensions: (x, y, u x, u y ).  A ‘2D2P’ model  N.J. Sircombe and T.D. Arber, J. Comp. Phys. 228, 4773, (2009)

20. Approach  Take the 2D2P phase space and ‘grid’ it up  f is then a 4D fluid  We can build the algorithm on ones developed for Eulerian fluid codes.  Operator splitting. Split updates of 4D phase space into a series of 1D updates, interleaved to ensure the complete timestep is symmetric and time-centred 1.Update in x for ½ a step 2.Update in y for ½ a step 3.Update in u x for ½ a step 4.Update in u y for 1 step 5.Update in u x for ½ a step 6.Update in y for ½ a step 7.Update in x for ½ a step  Each of these updates is then just a 1D advection

21. VALIS Scaling  Scaling  2D2P Vlasov problems can become very large, very fast*  Must make efficient use of HPC Some choices (such as any non-local elements to algorithm) can make this very difficult  Again: the explicit, split, conservative approach pays dividends – it can be parallelised via domain decomposition, across all four dimensions, and scales well.  Cost of each doubling of n pe, is negligible  Parallel IO is also a necessity, and included in VALIS’ IO subsystem Relative increase in runtime vs. n pe on CRAY XT3, triangles represent dual- core nodes, squares single core. * e.g. 2D2P SP-LPI problem with mobile ions (1024, 512, 256, 256) => 512 Gb memory footprint, and therefore >512Gb restart dumps.

22. 1D 500nc problem - T hot estimate  T hot peaks and falls (insufficient dumps to establish if a ‘steady state’ is reached).  Need to repeat runs to correct problems  Some clipping of distribution at ~12 MeV due to the momentum domain being too small  Immobile ions Time (fs)FrontIntegratedRear 150 NA 200 7.3 MeV5.6 MeVNA 300 5.3 MeV6.7 MeV3.5 MeV 400 1.5 MeV4.3 MeV5.0 MeV 500 5.0 MeV3.0 MeV1.8 MeV

23. Application in 2D (keV) ‘long’ ‘medium’ ‘short’ 0 degrees 10 degrees 30 degrees

24. 2D ‘Long’

25. 2D ‘Medium’

26. 2D ‘Short’

27. VALIS Future Development  Addition of:  Multi-species physics  Mobile ions, ponderomotive steepening etc.  Collisional physics (Krook operator)  Transport in dense material  In anticipation of future, massively parallel HPC Optimisation of:  Domain decomposition scheme  Communications  Core algorithm

28. Additional Slides EPOCH

29. Introduction  Particle-in-cell simulations of the 1D and 2D test problems performed using EPOCH (Extendable Open PIC Collaboration)  Runs in 1D performed with mobile and immobile ions  Problems with self-heating encountered in 2D – flatten ramp at 100n c instead of 500n c

30. 1D test problem  Density profile at t=500fs  Red = electrons Blue = ions Green = electrons with immobile ions  Little deformation of front surface observed with immobile ions

31. 2D test problem  Runs performed with mobile and immobile ions  Electron density profile at t=250ps with mobile (bottom) and immobile (top) ions  Immobile ion run used 80x80 micron box  Mobile ion run used 40x40 micron box (to reduce self- heating)

32. 2D test problem contd.  x-px electron phase space plots at t=100fs (left) and t=250fs (right) for mobile ion case