Simulating Fusion Plasmas



Thomas Hayward-Schneider
Max Planck Institute for Plasma Physics (IPP)
Garching, Germany
EUM ’22,        27th January 2022
@hattom




Disclaimer: these views are my own and do not reflect those of my employer.

Outline

  • Fusion
    • What is fusion?
    • How does it work?
    • Why do we care?
    • Why is it hard?
  • Tokamaks & ITER
  • Modelling
  • Outlook

Fusion

  • “Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles”
    – Wikipedia: “Nuclear fusion”
  • An ideal and clean source of electricity
  • The process used by the Sun
  • It’s the “opposite” of Nuclear fission (which releases power by splitting big atoms)
  • Mass difference \(\Rightarrow\) \(E=mc^2\) \(\Rightarrow\) voila

Fusion

  • Specifically, are there 2 small things which we can get to join together, Step ??? = Profit
  • Nuclei are + charged, repel each other
    • Must hit each other with high energy to convince them otherwise
  • “DT” wins: Deuterium (\(^2\)H) = heavy hydrogen; Tritium (\(^3\)H) = extra-heavy hydrogen
    • Gives us our target fusion reaction: \(^2\)D + \(^3\)T \(\Rightarrow\) \(^4\)He + \(^1\)n + 17.6 MeV
    • Peak at temperatures > 100 M °C

N.B. Different from the fusion process in the Sun

Fusion

  • In summary:
    • Get some Deuterium and Tritium
    • Heat them to >100 M °C
    • Make sure they stay put
    • Fusion happens
    • Profit

Fusion & Plasma

  • Hydrogen at 100 M °C
    • c.f. solar core (15 M °C); solar surface (5000 °C)
    • Fusion labs are hottest places in the solar system
  • Plasma – 4th state of matter (solid, liquid, gas, plasma):
    • Gases break apart at very high temperatures / low densities
    • Electrons and ions separate \(\Rightarrow\) all particles in a plasma are charged!
      • Charged particles interact with electromagnetic fields
    • Most of “stuff” in space, plus the outer planets, is a plasma
  • A lot of fusion physics is plasmas physics

Idea: use magnetic fields to “hold” our plasma
\(\to\) Magnetic Confinement Fusion


“We say that we will put the sun into a box. The idea is pretty. The problem is, we don’t know how to make the box.”
Pierre-Gilles de Gennes

Magnetic confinement

Red: no magnetic field
Kicked particle flies away

Blue: magnetic field (into screen)
Kicked particle gyrates

Magnetic confinement

  • So, along a straight magnetic field, particles stay on a line
  • Build a cylinder, but what about the ends?
    • No way to stop us losing particles at the ends
      • Join the ends together
        \(\to\) Torus

Magnetic confinement

  • Aaaaaaaaaalmost problem solved
  • Once we bend the ends, we no longer confine the plasmas
    \(\to\) Introduce twist (helix) to magnetic field

Option 1: External helix
Build complex 3D magnetic coils
\(\to\) Stellarator

Option 2: “Internal” helix
Drive current through plasma, induce additional field
\(\to\) Tokamak

Tokamaks

  • тороидальная камера с магнитными катушками” /
    “toroidal chamber with magnetic coils”
    – Wikipedia: “Tokamak”

ASDEX Upgrade, © IPP, ixtract

Key Parts


Cross-section of ASDEX Upgrade (IPP)



  • Magnetic coils
    • D-shaped coils (toroidal field)
    • Central solenoid (plasma current)
    • Large circular coils (shaping)
  • Vacuum vessel + pumps
  • Plasma wall (heat loads)
  • Heating systems (beams + radio waves)
  • Diagnostics (measuring the plasma)

Fusion progress

Fusion progress

Fusion progress

  • JET (DT) current record holder, 1997 campaign
                \(Q_{plasma} = P_{out} / P_{in} = 0.65\)
    • Few (2) tokamaks ran with “real” fusion fuel
    • Most science done without tritium
  • ITER goal:
               \(Q_{plasma} \ge 10\)
  • (Effective) size matters
    • Linear dimensions:
               ITER (global) \(\approx 2\times\) JET (Europe) \(\approx 4\times\) ASDEX Upgrade (Germany)

ITER

  • ITER is Big Science
  • Partners are: “China, the European Union, India, Japan, Korea, Russia and the United States”
    – ITER Organization, iter.org
  • Each partner contributes primarily in-kind
    • e.g. India builds and delivers the cryostat
  • Makes total ITER cost impossible to say, but a ballpark figure of ~$20B is probably reasonable
  • Located in Southern France
    • Assembly already well progressed (see ITER website/YouTube channel for details)
    • First plasma \(\approx\) 2025-ish
    • Full power \(\approx\) 10 years later
  • NOT a fusion power plant, but a demonstration of fusion at large scale (\(\approx 500\) MW\(_{th}\))
    \(\to\) EU’s roadmap is ITER \(\Rightarrow\) DEMO \(\Rightarrow\) Power Plant

ITER

© ITER Organization, http://www.iter.org/

For scale: tiny human bottom right

ITER

© ITER Organization, http://www.iter.org/

For scale: tiny human in center.
Central donut diameter ~16-20m

ITER

© ITER Organization, http://www.iter.org/

Key Parts (Plasma Physics)


ASDEX Upgrade (IPP)



  • Core plasma
    • Turbulence (microscale)
    • MHD (Magnetic Hydro Dynamics) (macroscale)
    • Energetic Particles (mesoscale) \(\leftarrow\) (my field)
    • Heating
  • Edge
    • Wall interaction
    • Atomic physics
    • Plasma boundary condition
    • Turbulence
  • Diagnostics
  • Materials science

+Technology, …

Physics challenges

  • Many time and length scales

Energetic Particles

  • OK, suppose fusion works
    • Recall our target fusion reaction
      • \(^2\)D + \(^3\)T \(\Rightarrow\) \(^4\)He (3.5 MeV) + \(^1\)n (14.1 MeV)
    • 14.1 MeV neutron is gone, heats some water, makes some steam, turbine, power
    • Helium atom (alpha particle) carries a lot of energy
      • ITER largely “self-heated”
      • Roughly 10 B °C
      • Makes “hottest place in solar system” look pretty cold
      • Resonate with magnetic waves in the plasma

Modelling

Some models for the core plasma:

  • MHD: conducting “fluid dynamics”, but add magnetic fields
    • Equilibrium; current & pressure driven instabilities
  • Kinetics: 6 dimensional problem. 3D location + 3D velocity
    • Recall what I said about particles in magnetic fields
    • Replace fast helix with slow ring
      \(\Rightarrow\) 6D \(\to\) 5D, removes fastest waves \(\to\) gyrokinetics (GK)
  • Plasma motion modifies the electro-magnetic fields
    • Maxwell equations

Modelling: top-down vs bottom-up?

  • Several approaches possible to study interaction of X + Y
    • Find a model which can describe both X + Y
    • Couple together a tool for X with a tool for Y
  • Aim: build a hierarchy, validate with expensive model, explore with reduced model
    • An example:
      • Energetic particles: large instabilities, high frequencies, discrete & coherent instabilities
      • Turbulence: small scale, lower frequencies, broad spectra
  • More detailed:
    • Build workflows with heating, equilibrium, transport, …
    • Requires effort to standardize conventions, data formats, …
      • Briefly mentioned in S. Pinches ITER site presentation @ EUM 2021

Finally, my work

  • We co-develop a particle-in-cell (PIC) 5D gyrokinetic code “ORB5”
    • Originally used for microturbulence, now used extensively for energetic particle physics
    • Offers the possibility to look at EP physics + turbulence (+MHD instabilities)
  • My focus is on simulations predicting alpha particle driven instabilities in ITER
  • Particle-in-cell: Lagrangian, Monte Carlo approach
    • Follow (\(\approx\)M\(\to\)B) particles in 3D fields
    • Solve fields from particles
      • Fields solved with Finite Elements
    • Repeat


Turbulence with ORB5



https://spc.epfl.ch/research/theory/codes/research_theory_codes_orb5/

Finally, my work

  • We co-develop a particle-in-cell (PIC) 5D gyrokinetic code “ORB5”
    • Originally used for microturbulence, now used extensively for energetic particle physics
    • Offers the possibility to look at EP physics + turbulence (+MHD instabilities)
  • My focus is on simulations predicting alpha particle driven instabilities in ITER
  • Particle-in-cell: Lagrangian, Monte Carlo approach
    • Follow (\(\approx\)M\(\to\)B) particles in 3D fields
    • Solve fields from particles
      • Fields solved with Finite Elements
    • Repeat


EP physics with ORB5

https://spc.epfl.ch/research/theory/codes/research_theory_codes_orb5/

Reduced model

  • We also work with, e.g. a pair of codes
    • Linear eigenvalue solver (solves frequency & shape of the instability)
    • Hybrid perturbative code (evolve interaction between alpha particles and mode)
    • We know it’s not perfect, \(\Rightarrow\) validation
  • Much cheaper, more robust
    • Now being coupled to more complex workflows

Outlook

  • ITER is coming, the fusion world is watching and preparing
    • ITER likely the final fusion science project
    • Later machines will be technology demonstrations
  • Modelling and simulation is important
    • General trends:
      • Big: expensive HPC
      • Connected: complex workflows
      • Ensemble: Validation, Uncertainty Quantification
  • My work is very important
    • ITER first machine with significant self-heating

Backup

Stellarators:


CC-BY 3.0 T Klinger et al., and The Wendelstein 7-X Team

Machines: JET

Machines: JET

Machines: ASDEX Upgrade

Machines: ASDEX Upgrade

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