Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Some numerical techniques developed in the Heavy-Ion Fusion program Short-Pulse Laser Matter Computational Workshop Pleasanton, California - August 25-27, 2004 J.-L. Vay - Lawrence Berkeley National Laboratory Collaborators:  A. Friedman, D.P. Grote - Lawrence Livermore National Laboratory  J.-C. Adam, A. Héron - CPHT, Ecole Polytechnique, France  P. Colella, P. McCorquodale, D. Serafini - Lawrence Berkeley National Laboratory The Heavy-Ion Fusion program has developed, and continues to work on, numerical techniques that have broad applicability:  Absorbing Boundary Conditions (ABC)  Adaptive Mesh Refinement (AMR) for Particle-In-Cell (PIC)  Advanced Vlasov methods (moving grid,AMR)  Cut-cell boundaries

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Maxwell Maxwell => Split Maxwell Split Maxwell => Berenger PMLBerenger PML => Extended PML Extended Perfectly Matched Layer Principles of PML field vanishes in layer surrounding domain, layer medium impedance Z matches vacuum’s Z 0. If with u=(x,y), Z=Z 0 => no reflection. If and with u=(x,y), Z=Z 0 => no reflection.

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Extended PML implemented in EM PIC code Emi2d Extended PML

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory The Adaptive-Mesh-Refinement (AMR) method addresses the issue of wide range of space scales well established method in fluid calculations potential issues with PIC at interface –spurious self-force on macro-particles –violation of Gauss’ Law –spurious reflection of short wavelengths with amplification AMR concentrates the resolution around the edge which contains the most interesting scientific features. 3D AMR simulation of an explosion (microseconds after ignition)

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory 3D WARP simulation of High-Current Experiment (HCX) Modeling of source is critical since it determines initial shape of beam RunGrid sizeNb particles Low res.56x640~1M Medium res.112x1280~4M High res.224x2560~16M Very High res.448x5120~64M WARP simulations show that a fairly high resolution is needed to reach convergence

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Example of AMR calculation with WARPrz: speedup ~10.5 RunGrid sizeNb particles Low res.56x640~1M Medium res.112x1280~4M High res.224x2560~16M Low res. + AMR56x640~1M R (m) Z (m) Refinement of gradients: emitting area, beam edge and front. Z (m) R (m) zoom

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory MR patch key in simulation of STS500 Experiment MR off Current history (Z=0.62m) MR on Current history (Z=0.62m) Mesh Refinement essential to recover experimental results Ratio of smaller mesh to main grid mesh ~ 1/1000 MR patch

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory New MR method implemented in EM PIC code Emi2d coarse Extended PML M coarse fine Outside patch: F = F M Inside patch: F = F M -F C +F F F C Mesh refinement by substitution core Laser beam =1  m, W.cm -2 (P osc /m e c~8,83) 2  =28/k 0 10n c, 10keV Patch Applied to Laser-plasma interaction in the context of fast ignition

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Comparison patch on/off very encouraging MR off MR on same results except for small residual incident laser outside region of interest no instability nor spurious wave reflection observed at patch border

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Backup slides

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory challenging because length scales span a wide range:  m to km(s) Goal: end-to-end modeling of a Heavy Ion Fusion driver

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Time and length scales in driver and chamber span a wide range Length scales: electron cyclotron in magnet pulse electron drift out of magnet beam residence  pb  lattice period betatron depressed betatron  pe transit thru fringe fields beam residence pulse log of timescale in seconds In driverIn chamber  pi  pb electron gyroradius in magnet ~10  m D,beam ~ 1 mm beam radius ~ cm machine length ~ km's Time scales:

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Illustration of instability in 1-D EM tests Space onlySpace+Time o: E, x:B Most schemes relying on interpolations are potentially unstable.

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory 3D WARP simulation of HCX shows beam head scrapping Rise-time  = 800 ns beam head particle loss < 0.1% z (m) x (m) Rise-time  = 400 ns zero beam head particle loss Simulations show: head cleaner with shorter rise-time Question: what is the optimal rise-time?

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory 1D time-dependent modeling of ion diode EmitterCollector VV=0 d virtual surface didi ViVi I (A) Time (s) N = 160  t = 1ns d = 0.4m “L-T” waveform N s = 200 irregular patch in d i Time (s)  x 0 /  x~10 -5 ! time current AMR ratio = 16 irregular patch in d i + AMR following front Time (s) Careful analysis shows that d i too large by >10 4 => irregular patch Insufficient resolution of beam front => AMR patch MR patch suppresses long wavelength oscillation Adaptive MR patch suppresses front peak

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Specialized 1-D patch implemented in 3-D injection routine (2-D array) Extension Lampel-Tiefenback technique to 3-D implemented in WARP  predicts a voltage waveform which extracts a nearly flat current at emitter Run with MR predicts very sharp risetime (not square due to erosion) Without MR, WARP predicts overshoot Application to three dimensions T (  s) V (kV) “Optimized” VoltageCurrent at Z=0.62m X (m) Z (m) STS500 experiment

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Researchers from AFRD (PIC) and ANAG (AMR-Phil Colella’s group) collaborate to provide a library of tools that will give AMR capability to existing PIC codes (on serial and parallel computers) The base is the existing ANAG’s AMR library Chombo The way it works WARP is test PIC code but library will be usable by any PIC code Effort to develop AMR library for PIC at LBNL

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Example of WARP-Chombo injector field calculation Chombo can handle very complex grid hierarchy

Vay 08/25/04 The Heavy Ion Fusion Virtual National Laboratory Split Maxwell Extended PML Berenger PML Extended Perfectly Matched Layer Maxwell If and => Z=Z 0 : no reflection. Principle of PML: Field vanishes in layer surrounding domain. Layer medium impedance Z matches vacuum’s Z 0 If with u=(x,y) => Z=Z 0 : no reflection.