Simulating Inhomogeneous Magnetized Plasmas – A New Approach

Co-InvestigatorsBruce I. Cohen PAT/ FEPRonald H. Cohen PAT/ FEP

Andris Dimits PAT/ FEPAlex Friedman PAT/ FEP

Andreas Kemp PAT/ FEPMax Tabak DNT/AX

Principal InvestigatorDavid P. Grote PAT/FEP

2008 08-ERD-???

New Approach

FIMFE

Spacee-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 coneCompressed

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 ct, 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 daysWARP-3DT = 4.65s

Oscillations

Beam ions hit

end plate

200mA K+

Electrons

Electrons bunching

0. 2. time (s) 4. 6.

Simulation Experiment0.

-20.

-40.

Cu

rren

t (m

A)

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

ct = 5.4

ct = 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 TH=1.5THe

– 2D, Ncell=32, 0t=0.00005, 1-2-1

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 ct 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

0.25

0.15

0.20

0.10

Research staff effort

FY07

FY08

FY09

Total FTE expense

Members of the team have been pioneers in

developing and applying particle simulations

$ k

$ k

$ k

Burdened

$200 k

$340 k

$340 k

Burdened

Andreas Kemp• PIC Collisions/FI

Max Tabak• FI expertise

0.20

0.05

0.05

0.20

0.15

0.15

0.00

0.10

FY07 FY08

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

FIMFE

Spacee-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 ct > 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 rcyclotronBz

Reference case

Old mover with ct = 5

Vz

Z

Instability never appears!

Vz

Z

Old mover with ct = 0.25

Energy well conserved ~30% energy loss

Snapshots of the longitudinal phase space show that

the traditional “mover” fails when used with ct > 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 ct > 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 ct = 5

Vz

Z

Electrostatic potential growth

ct = 0.25old mover

ct = 5 new mover

ct = 5old mover

Energy well conserved

Drift-Lorentz mover gives correct results 20 times

faster!