Simulating Inhomogeneous Magnetized Plasmas – A New Approach Co-Investigators Bruce I. CohenPAT/...
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Transcript of Simulating Inhomogeneous Magnetized Plasmas – A New Approach Co-Investigators Bruce I. CohenPAT/...
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!