# Presentation: 636552

## Kinetic Approach to microscopic-macroscopic coupling in fusion plasmas

- Koichi Noguchi
- Physics & Astronomy Dept., Rice Univ.
- Giovanni Lapenta
- Plasma Theory Group, Theoretical Division, LANL, USA

- Collaborators: J.U Brackbill (Particle Solutions),
- W. Daughton (U Iowa), S. Markidis (UNM),
- P. Ricci (Dartmouth), R. Nebel, E. Evstatiev, J. Park (LANL)

## Motivation: simulation of burning plasmas

- Lavender Field, Provence, near ITER

## Outline

- Multiscale processes in plasmas, the case of ITER
- The implicit moment PIC method
- Benchmarks
- Applications:
- 3D reconnection
- Reconnection in low beta plasmas
- Fusion applications

## 1 – Multiple scales 

- Fusion Devices
- Space
- Role of micro-macro coupling

## Scales involved in plasma physics

- Scales where the various terms become important (SI UNITS)

## ITER: Multiscale - Multiphysics

- Ions: D @ 10keV
- α: fusion generated

- Source: ITER web site

## Gyrokinetic PIC

**Gyrokinetic PIC**

## Multiscale coupling in space plasmas

- High Collisionless
- Small scales, non gyromotion
- Macro/micro coupling
- Methods developed there could be used for ITER.

- Gombosi et al., Univ. Michigan

- G. Lapenta, AGU Fall meeting, 2004

- Example of CELESTE3D

## 2 – Simulating micro-macro coupling

- A possibility: implicit moment PIC
- Description of implicit moment PIC

## Fundamental Equations (Classical)

- We consider collisionless plasmas
- Vlasov-Poisson model

**- Vlasov equation**

**- Maxwell equations**

** ****(Newton equations)**

- Eulerian formulation

- Lagrangian formulation

## Explicit PIC Computational Cycle

## Summary of the Stability constraints

**Summary of the Stability constraints**

## 
Maxwell equations: implicit second order formulation for the field E
Newton equations: implicit form 
Solver: Implicit moment method

- Maxwell equations: implicit second order formulation for the field E
- Newton equations: implicit form
- Solver: Implicit moment method

**Implicit formulation (Classical)**

- Particle mover

- Field Solver

## Implicit Moment Method

- Fluid equations

## ITER: Multiscale - Multiphysics

- 

- 

- D,T

- D,T

## 4 – V&V and applications

- Reconnection physics in 3D
- Parallelization & Relativity
- Inertial Electrostatic Confinement

## TEST: GEM challenge

- Explicit:
- Pritchett, JGR
- 106, 3783 (2001)

- Implicit:
- CELESTE3D

- Explicit [Pritchett, JGR, 106, 3783 (2001)]
- Grid 512 X 256 grid,
- 9,000,000 particles,
- Time step:
- massively parallel computer
- Celeste3D [Ricci et al., GRL, 29, 2088, (2002)]
- Grid: 64X64
- 200,000 particles,
- Time step:
- Workstation

- Electron outflow

- Ion density

- Ion outflow

- Bz

- x

- x

- x

- x

- Implicit:
- CELESTE3D

- x

- T=0

- T=8

- T=16

- T=32

- T=24

- T=48

- z

## Performance – See Poster

- New PRASEK project:
- CELESTE
- FLIP (MHD)
- DEMOCRITUS (plasma-material interaction, kinetic)
- GLOW (plasma-material interaction, fluid)
- Relativity
- C++ object oriented
- Parallel

**(logarithmic axis)**

## 
Maxwell equations: New scheme for current prediction 
Newton equations: Implicit form, relativistic 
Solver: Implicit moment method,Newton-Krylov method,Energy conserving method

- Maxwell equations: New scheme for current prediction
- Newton equations: Implicit form, relativistic
- Solver: Implicit moment method,Newton-Krylov method,Energy conserving method

**New Relativistic Formulation**

- Particle mover

- Field Solver

## Test: relativistic 1D two-stream instability

- Growth Rate :
- Im(p)

- V0=0.9c, 100,000 particles, 128 mesh, Te=0.01eV
- tp=0.01 (Explicit), 0.2 (Implicit)

## Can we use CELESTE in low beta, high toroidal field?

- Electron acceleration

**Explicit**

**Implicit**

- BT=0

- BT=BP

- Vye

- Mi/Me=180

## Summary

- _Question_: how can we study burning plasmas kinetically
- _Possibility_: consider implicit moment PIC
- Fully kinetic
- Able to capture micro-macro modeling
- Extensive application to space plasma physics

- _Conclusions_:
- The method is mature
- Recent upgrades
- Parallelization
- Relativity
- Suite of relevant applications

## R&D100 prize in 2005

- CartaBlanca: A High-Efficiency, Object-Oriented, General-Purpose Computer Simulation Environment

- PARSEK
- General tool for PIC simulations
- Includes:
- Implicit kinetic PIC (Celeste)
- Implicit fluid PIC (Flip)
- Plasma-material interface (Democritus)

## Waves

**Waves**

- Light

- Langmuir

- whistler

- Ion acoustic

- Brackbill, Forslund JCP, 1985

## Orbits -Gyromotion

- No averaging, accuracy determined by t, x
- Accurate gyroradius and drift motions at large t
- Valid at all beta
- Valid at all: ρk┴
**Short scales are not eliminated and the energy channel towards them remains open**

## Drifts and Gyroradius

- Vu, Brackbill, JCP, 116, 384 (1995)

## 3D reconnection: micro-macro coupling

**3D reconnection: micro-macro coupling**

- Large scale  processes

- Small scale processes

- Question: Is the small/large scale coupling captured?

## Simulation of the small scale processes (LHDI) 

- Free energy: diamagnetic drift
- Driving: density gradient
- Stabilization: high beta
- Frequency:
- Wavelength:
- Direction:
- Seen in space and experiments (e.g. MRX)
- Present only on the edges of the sheet
- Requires a kinetic treatment

- Simulation with L=di

- Daughton, Lapenta, Ricci, JCP, 116, 384 (1995)

## Effect of microinstabilities captured correctly

- .55

- 1.1

- 2.2

- L/ρi

**L**

- explicit

- implicit

- Current intensification
- Temperature anisotropy

- Reconnection is
- enhanced (_Poster:_
- _FZ1.00008_)

## Can we use CELESTE in low beta, high toroidal field?

- We considered reconnection with different:
- B toroidal (guide field)
- Using a Harris equilibrium
- We computed:
- Reconnection rate
- Onset
- Ion/electron decoupling mechanism
- Break-up mechanism
- As BT increases we kept the same t, even while the gyrofrequency increased.

- Reconnection rate

- Explicit

- Implicit

- BT=0

- BT=BP

- BT=10BP

## IEC Simulation –  See posters: BP1.137-138 LP1.107