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 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 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 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 CLIC accelerating components Under testing in the CTF3 project at CERN Too high breakdown rates, 10 -4, aim: for final design Different setups have been tested: Geometries Materials: Cu and Mo best Frequencies: main linac f RF 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 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 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 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 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: n 0 = cm -3, T e = 5 keV -Determines λ D = 5.3×10 -7 m and ω pe = 5.6× /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 λ D, Δt = 0.2× 1/ω pe 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 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, I cu =0.01I th,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 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 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 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 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

Helga Timkó, University of Helsinki Laudatur Seminar, 16th Sept 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: