Simulating Inhomogeneous Magnetized Plasmas – A New Approach Co-Investigators Bruce I. CohenPAT/ FEP Ronald H. CohenPAT/ FEP Andris DimitsPAT/ FEP Alex FriedmanPAT/ FEP Andreas KempPAT/ FEP Max TabakDNT/AX Principal Investigator David P. GrotePAT/FEP ERD-??? New Approach FI MFE Space e-cloud HIF Drift- Lorentz Continuing Proposal FY08 Proposed Budget $340k (FY07 Actual $200k) Tracking Number 07-ERD-016

We are seeking an expanded scope to this work Last year’s proposal was aimed at expanding the applicability of a novel particle-in-cell (PIC) time-advance algorithm by adding implicitness and collisions Now, we seek to address emerging needs by adding an increased focus on critical collision modelling capability – With NIF post-ignition planning, a greater need for Fast Ignition (FI) modelling has emerged – More advanced inter-particle collision models, both explicit and implicit, needed for FI and other HEDP studies

We are interested in inhomogeneous, dense, magnetized, multi-component plasmas Inhomogeneous magnetized plasmas also appear in Fast Ignition is an example Magnetic fieldHot electron density Gold cone Compressed fuel Laser (N/cm^3) (gauss) (LSP simulation by R. Town) Magnetic Fusion Energy (MFE) Heavy-Ion Driven IFE (HIF) Intense particle beams Space plasmas

A new algorithmic invention can relax the constraints on  c  t, greatly reducing computational effort This invention, the drift-Lorentz mover, combines two traditional movers, Boris and drift, in such a way that the correct behaviour is maintained with large time steps [R. Cohen, Phys. Plasmas (2005)] Currently implemented in an explicit, electrostatic code (WARP); has proven enabling for electron-cloud physics in particle beams (for example for HIF and LHC) HIF example - with mover, runtime decreased from months to days WARP-3D T = 4.65  s Oscillations Beam ions hit end plate 200mA K + Electrons bunching time (  s) Simulation Experiment Current (mA)

Need to improve the efficiency of collision algorithms for HEDP With Fokker-Planck-based, pair-wise, Monte-Carlo Collision (MCC) operator, the computational expense can be limiting – We seek to simplify the collision operator for select classes of particles while maintaining general validity for dense plasmas – Existing methods with weighted-particles [Nanbu&Yonemura, 1998] require a large number of particles because of noise. We seek to develop an efficient and energy-conserving description which allows a reduction in the particle number

Need to improve the accuracy of collision algorithms for HEDP We will assess the current MCC operators – do they include the relevant physics? – Do they fail to capture scattering off unresolved collective modes? – What is the bound electrons’ contribution to ion stopping in matter? – Do existing codes treat runaway electrons in resistive plasmas correctly? What are the related errors in heating and transport? We will fix the collision operators and runaway models

Progress to date – Collisionless ion-temperature-gradient simulations ITG is a classic MFE test problem studying instability of an inhomogeneous plasma We upgraded drift-Lorentz mover to higher density by adding partial implicitness Good results for this turbulent system – Correct linear growth rate – Correct saturation level  c  t = 5.4  c  t = 0.25

Progress to date – Implementation of collisions Generalization of an existing algorithm to unlike-particle scattering using a general unlike-particle Langevin Coulomb collision algorithm [Manheimer, et al., JCP 138, 565 (1997)] Simulation of collisional equilibration of unequal temperatures – Hydrogen/helium plasma with initial temperatures T H =1.5T He – 2D, Ncell=32, 0  t= , smoothing – Agreement with relaxation theory is good Porting into WARP has commenced (LSP will follow)

Deliverables are structured so that intermediate results are useful and publications will result Year 1 (FY07) Year 2 (FY08) Year 3 (FY09) Model Development -Add collisions to algorithm -Examine conventional implicit PIC at large  c  t as in LSP -Begin exploring implicit versions of the drift-Lorentz algorithm -Develop and benchmark advanced collision models -Add improved collisions to LSP -Implement first implicit version of drift-Lorentz mover in WARP code -Implement EM implicit drift- Lorentz model in LSP code -Implement advanced collisions in LSP Application of New Tools -Benchmark versus collisionless ITG calculation carried out in GK code -Benchmark versus collisional ITG -Test first implicit version of drift-Lorentz mover -Apply advanced collision models to transport for radiography sources -Apply EM implicit drift- Lorentz to Weibel and/or Titan e - transport exp’ts

Proposal is well-aligned with LLNL S&T strategic needs Will provide new capabilities for FI initially, and potentially MFE and other applications in long term. Time frame commensurate with planned experiments in FI Builds partnership with FI group in DNT through coordinated LDRD’s Will enhance PAT and DNT programs in IFE and HEDP Investment will leverage existing work, returning an increase in LLNL’s simulation capability Excellent computational physics - will enhance the state-of-the-art in plasma simulation This LDRD is designed to strengthen PAT’s role in HEDP applications, including inertial fusion energy, an Aurora priority

Actual The research team has broad experience in developing simulation tools for both MFE and ICF David Grote (PI) PIC expertise Bruce Cohen GK/collisions/implicit Ron Cohen Algorithm inventor Andris Dimits PIC Collisions Alex Friedman PIC/implicit Research staff effort FY07 FY08 FY09 Total FTE expense Members of the team have been pioneers in developing and applying particle simulations $ k Burdened $200 k $340 k Burdened Andreas Kemp PIC Collisions/FI Max Tabak FI expertise FY07FY08

Conclusion Goal: Provide better simulation capability for FI, IFE, MFE, space plasmas, etc. Approach: Expand the capabilities of PIC codes for inhomogeneous magnetized plasmas Deliverables: Develop and implement implicit version of drift-Lorentz mover, coupled with advanced collision models, with a focus on the FI application Team: Includes experts in and developers of implicit modelling, collision techniques, and Fast Ignition Budget: FY08 $340k Importance: New techniques will enhance simulation capabilities in projects across the Lab Exit Plan: We look forward to being more competitive in seeking funding from the new joint HEDP program office

Last year’s slides

The new method developed via this LDRD will give LLNL a competitive advantage in modelling systems involving inhomogeneous plasmas For ICF (especially fast ignition, our principal emphasis), high densities, strong magnetic fields, & sharp gradients coexist For MFE, gyrokinetics is well established but is complex, especially when collisions become important, and fails in presence of field nulls (as in FRC’s) For space plasmas, e.g. the earth’s bow shock, large gradients and nulls in the magnetic field appear For all of these application areas, there are problems with large variations in magnetization. They are difficult to treat with conventional approaches New Approach FI MFE Space e-cloud HIF Drift- Lorentz

Existing FI codes suffer from inefficiencies LSP is the principal code used by LLNL’s Fast Ignition group LSP’s implicit time differencing & particle / fluid hybrid model enable stable, large-  t simulation of dense plasmas (competing codes are explicit, with other “tricks” for dense plasmas) But: the electron cyclotron period must be resolved---expensive when B is large. With  c  t > 1 : – Current methods yield an overly-large gyroradius – If this “numerical gyroradius” is larger than the physical gradient scale length, particles sample grossly inaccurate fields – Possible cause of poor energy conservation

We will combine the drift-Lorentz mover with collisions and implicitness Collisions – Straightforward since code follows particle orbits – Simpler than in gyrokinetics (which follows gyrocenters, and so must transform to a synthesized particle location and back to effect a collision) Implicitness – Allows circumvention of plasma oscillation time scale – Critical for high density plasmas – e.g. FI – The largest single piece of the proposed effort Emphasis on needs of Fast Ignition Further benchmarking will be done with model problems from MFE experience WARP will be used as the test bed - it provides a great development environment and is most familiar to the investigators Once developed, algorithms will be implemented in LSP

Why now? Invention has recently been validated for electrostatic collisionless applications This proposal will provide essential and timely capabilities, needed as planned FI experiments begin (Omega EP, Titan) It will help address critical issues as they emerge This proposal is coordinated with a new DNT LDRD proposal on particle simulations for plasmas driven by short pulse lasers (Richard Town, PI). The connection will provide guidance on requirements for FI simulation.

An example demonstrates the benefit of the drift-Lorentz mover Electrostatic two-stream instability Counterstreaming proton beams in solenoid field Finite beam radius ~ 10 rcyclotron BzBz

Reference case Old mover with  c  t = 5 Vz Z Instability never appears! Vz Z Old mover with  c  t = 0.25 Energy well conserved ~30% energy loss Snapshots of the longitudinal phase space show that the traditional “mover” fails when used with  c  t > 1

Two methods have traditionally been used “Old” Newton-Lorentz mover (F=ma) is straightforward It advances velocities of particles in time, then positions. But it is inaccurate at large timestep – gyroradius too large – problem if gradient length ~ gyroradius Drift-kinetics (and its extension, gyrokinetics) implements analytically-derived “drifts” (E X B, grad B, polarization, …). It specifies velocities of gyro-centers. But it fails to capture weakly-magnetized dynamics accurately Also, collisions require “synthesizing” actual particles New method interpolates “carefully” between these limits using an interpolation fraction .

Drift-Lorentz mover allows  c  t > 1  Allows timestep to be set by next larger timescale It interpolates between Newton-Lorentz and drift kinetic limits Particle position advance using veff – In limit  = 1, directly follows the particle orbit – In limit  = 0, follows magnetic drifts only  is chosen so as to preserve the correct gyroradius Resulting algorithm captures correct drift and parallel dynamics reciprocal of numerical gyroradius scale factor for old mover

New mover with  c  t = 5 Vz Z Electrostatic potential growth  c  t = 0.25 old mover   c  t = 5 new mover  c  t = 5 old mover Energy well conserved Drift-Lorentz mover gives correct results 20 times faster!