Plasma-Wall Interactions

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Plasma-Wall Interactions Part II In Linear
Colliders

• Helga Timkó

Department of Physics University of
Helsinki Finland
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Plasma-Wall Interactions Outline

• Part I In Fusion Reactors
• Materials Science Aspect
• Materials for Plasma Facing Components
• Beryllium Simulations
• Arcing in Fusion Reactors
• Part II In Linear Colliders
• Arcing in CLIC Accelerating Components
• Particle-in-Cell Simulations
• Future Plans for a Multi-scale Model

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Last Week Arcing in Fusion Reactors

• Arcing continuous gas discharge, between
  electrodes or within the plasma sheath
• Causes in fusion reactors
• Erosion,
• Impurities
• And thus, plasma instabilities ? harder to reach
  confinement
• Research on arcing has been done since 1970s
• Search for arc-resistant materials, ideal surface
  conditions
• Theoretical and experimental modelling of arcing
  in simplified geometries
• All in all, in fusion reactors arcing not so
  critical any more
• But for future linear colliders it is!

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CLIC Compact Linear Collideronly 47.9 km ?

• A proposed e- e linear collider, with a CM
  energy of up to 3 TeV in the final design (cf.
  LEP max. 209 GeV)
• Linear colliders more effective than circular
  ones
• Can reach higher energies
• With CLIC, post-LHC physics can be done, e.g. for
  Higgs physics this means
• LHC should see Higgs(es), should rule out some
  theories
• CLIC would be able to measure particle properties
• To be built in
• three steps
• Two-beam
• acceleration

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CLIC accelerating components

• Under testing in the CTF3 project at CERN
• Too high breakdown rates, 10-4, aim 10-7 for
  final design
• Different setups have been tested
• Geometries
• Materials Cu and Mo best
• Frequencies main linac fRF
• was lowered 30 ? 12 GHz
• Most challenging is the high
• accelerating gradient to be
• achieved, already lowered too
• 150 ? 100 MV/m
• Need a theoretical model
• of breakdown to systemise

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What is PIC and what can we simulate with it?

• PIC Particle-in-Cell method
• Basic idea simulate the time evolution of macro
  quantities instead of particle position and
  velocity (cf. MD method)
• Need superparticles
• Restricted to certain regime of particle density
  given by reference values (those define
  dimensionless quantities)
• Kinetic approach of plasma, but can be applied
  both for collisionless and collisional plasmas
• Many application fields solid state and quantum
  physics as well as in fluid mechnics
• Has become very popular in plasma physical
  applications
• Esp. for modelling fusion reactor plasmas (sheath
  and edge)

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The PIC Algorithm

• Setting up the
• simulation
• Grid size, timestep,
• superparticles, scaling
• Solving the equations of motion particle mover
  
• Moving particles, taking collisions BCs into
  account
• Calculating plasma parameters, macro quatities
• Solving Maxwells equations, (Poissons eq. in
  our case)
• this can be done with different solvers
• Obtaining fields and forces at grid points
• In PIC, everything is calculated on the grid,
  interpolation to particle positions is done by
  the weighting scheme

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Solvers forthe Particle Mover and the Poissons
Equation

• Discretised equations of motion
• In 1D el.stat. case, with the leapfrog method, in
  the Boris scheme
• Poissons equation determining the electric field
  from charge density values at grid points

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Scaling in PIC Grid size and timestep

• In the code, everything is scaled to
  dimensionless quantities ? easier to analyse
  physically, faster code
• Initial values give the scale for the
  simulations, only a few orders of magnitudes can
  be captured
• Need a good guess n0 1018 cm-3, Te 5 keV
• Determines ?D 5.310-7 m and ?pe 5.61013
  1/s, the internal units of the code
• For an arc, densities are only rising! ? model is
  limited
• Stability conditions
• Compromise btw. efficiency and low noise
• ?x 0.5 ?D, ?t 0.2 1/?pe
• Amazing whole set of equations can be rescaled ?
  universal results only the incl. of collisions
  gives a scale

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Our Model

• In collaboration with the Max-Planck-Institut f.
  Plasmaphysik, Greifswald
• 1D electrostatic, collision dominated PIC scheme
• Simplistic surface interaction model
• Assuming const. electron thermoemission current
  (cathode)
• Const. flux of evaporated neutral Cu atoms,
  Icu0.01Ith,e
• Cu ions sputter Cu with 100 probab., neutral Cu
  is reflected back when hitting the walls

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Including collisions

• Arcing highly collision dominated, so is our
  model
• Including only 3 species electrons, neutral Cu,
  Cu ions
• Multiply ionised species ignored
• Most important collisions are taken into account

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A Typical Output

• Macro quantities as a function of time
• Flux and energy distributions, currents
• Note the sheath!
• Animations by K. Matyash

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The Plasma Sheath

• Sheath a thin layer of a few Debyes near the
  wall
• All physics happens in the sheath
• Field density gradients, collisions
• Outside, the potential is constant, field is
  zero Doesnt really matter what the dimensions
  of the system are (nm or µm)

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Future plans Integrated Modelling of Arcing

• Multi-scale model aimed an integrated
• PIC MD model of arcing
• Collaboration between
• Max-Planck-Institut für Plasmaphysik
• Helsinki Institute of Physics

MPI Greifswald K. Matyash R. Schneider HIP,
Helsinki H. Timko F. Djurabekova K. Nordlund
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Thank You!

• Bibliography
• D. Tskhakaya, K. Matyash, R. Schneider and F.
  Taccogna The Particle-In-Cell Method,
  Contributions to Plasma Physics 47 (2007) 563.
• Computational Many-Particle Physics, Springer
  Verlag, Series Lecture Notes in Physics,
  Vol. 739 (2008)
• Editors H. Fehske, R. Schneider and A. Weiße
• Information
• http//clic-study.web.cern.ch/clic-study/
• http//beam.acclab.helsinki.fi/knordlun/arcmd/