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

Outline

Background

Short pulse LPI

Transport

Plans for short pulse modelling

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.

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

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)

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

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.

90o

0o

-90o

0 100MeV

200

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)

Hot electrons from short scale length plasmas 500nc, 3.5 micron scale length plasma

ramp 1.37e20W/cm2 from LH boundary System size

80 microns in space, +/- 24 in momentum

(nx, npx, npy) = (8192, 200, 220)

Estimate ThotUsing 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)

ux

-20-32x

t=76fs

(x,ux) phase space (immobile ions)t=226fs t=226fs

-20-32x

40-40x0

Thot peaks and falls 7.3 MeV at 200fs, 1.5MeV at 400fs

Apparent ‘steady state’ by 200fs

Mobile Ions

Preliminary results with mobile ions Profile steepening, ion acceleration at front surface Evidence of IAW, ion trapping in pre-plasma

-840-40x0

fe fi

-26x

t=200fs

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

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

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

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.

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

nathan.sircombe@awe.co.uk

www.awe.co.uk

Additional Slides

VALIS

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, ux, uy).

A ‘2D2P’ model N.J. Sircombe and T.D. Arber,

J. Comp. Phys. 228, 4773, (2009)

0

fm

ef

t

f

eux B

uE

u

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-centred1. Update in x for ½ a step2. Update in y for ½ a step3. Update in ux for ½ a step4. Update in uy for 1 step5. Update in ux for ½ a step6. Update in y for ½ a step7. Update in x for ½ a step

Each of these updates is then just a1D advection

0)(

x

Uxc

t

U

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 npe, is

negligible Parallel IO is also a necessity, and

included in VALIS’ IO subsystem

Relative increase in runtime vs. npe 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.

1D 500nc problem - Thot estimate

Thot 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) Front Integrated Rear

150 NA NA NA

200 7.3 MeV 5.6 MeV NA

300 5.3 MeV 6.7 MeV 3.5 MeV

400 1.5 MeV 4.3 MeV 5.0 MeV

500 5.0 MeV 3.0 MeV 1.8 MeV

Application in 2D

(keV

)

‘long’

‘medium’

‘short’

0 degrees

10 degrees

30 degrees

2D ‘Long’

2D‘Medium’

2D ‘Short’

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 HPCOptimisation of: Domain decomposition scheme Communications Core algorithm

Additional Slides

EPOCH

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 100nc instead of 500nc

1D test problem

Density profile at t=500fs Red = electrons

Blue = ionsGreen = electrons with immobile ions

Little deformation of front surface observed with immobile ions

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)

2D test problem contd. x-px electron phase space plots at t=100fs (left) and

t=250fs (right) for mobile ion case