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CMS
Plasma-Wall Interactions –
Part II: In Linear Colliders
HIP
Helga Timkó
Department of Physics
University of Helsinki
Finland
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
 Future
Helga Timkó, University of Helsinki
Simulations
Plans for a Multi-scale Model
Laudatur Seminar, 16th Sept. 2008
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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 1970’s
 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!
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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CLIC = Compact Linear Collider
‘only’ 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
 Can
colliders more effective than circular ones
reach higher energies
 With CLIC, post-LHC physics can be done, e.g. for
Higgs physics this means:
 LHC
 CLIC
should see Higgs(es), should rule out some theories
would be able to measure particle properties
 To be built in
three steps
 Two-beam
acceleration
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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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
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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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.
Helga Timkó, University of Helsinki
for modelling fusion reactor plasmas (sheath and edge)
Laudatur Seminar, 16th Sept. 2008
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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 & BC’s into account
 Calculating plasma parameters, macro quatities
 Solving Maxwell’s equations, (Poisson’s 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 «
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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Solvers for
the Particle Mover and the Poisson’s Equation
 Discretised equations of motion:
 In 1D el.stat. case, with the leapfrog method, in
the Boris scheme:
 Poisson’s equation determining the electric field
from charge density values at grid points:
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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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 λD = 5.3×10-7 m and ωpe = 5.6×1013 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:
Δx = 0.5 λD, Δt = 0.2× 1/ωpe
 Amazing: whole set of equations can be rescaled 
universal results; only the incl. of collisions gives a scale
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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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.
 Cu+
const. electron thermoemission current (cathode)
flux of evaporated neutral Cu atoms, Icu=0.01Ith,e
ions sputter Cu with 100% probab., neutral Cu is
reflected back when hitting the walls
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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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:
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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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:
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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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: Doesn’t really
matter what the dimensions of the system are (nm or μm)
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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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
MPI Greifswald
K. Matyash
R. Schneider
HIP, Helsinki
H. Timko
F. Djurabekova
K. Nordlund
- Helsinki Institute of Physics
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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Thank You!
Bibliography:
D. Tskhakaya, K. Matyash, R. Schneider and F. Taccogna: The ParticleIn-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/
Helga Timkó, University of Helsinki
Laudatur Seminar, 16th Sept. 2008
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