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/