plasma-wall interactions – part i i : in linear collider s
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Helga Timk ó. Plasma-Wall Interactions – Part I I : In Linear Collider s. 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 - PowerPoint PPT PresentationTRANSCRIPT
CMS
HIP
Plasma-Wall Interactions – Part II: In Linear Colliders
Helga Timkó
Department of Physics
University of Helsinki
Finland
Helga Timkó, University of Helsinki Laudatur Seminar, 16th Sept. 2008 2
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
Helga Timkó, University of Helsinki Laudatur Seminar, 16th Sept. 2008 3
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 4
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 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
Helga Timkó, University of Helsinki Laudatur Seminar, 16th Sept. 2008 5
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 6
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)
Helga Timkó, University of Helsinki Laudatur Seminar, 16th Sept. 2008 7
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 8
Solvers forthe 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 9
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 10
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, Icu=0.01Ith,e
Cu+ 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 11
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 12
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 13
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 14
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 GreifswaldK. MatyashR. Schneider
HIP, HelsinkiH. TimkoF. DjurabekovaK. Nordlund
Helga Timkó, University of Helsinki Laudatur Seminar, 16th Sept. 2008 15
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/