Muon Cooling RF Workshop, 7-8 July, 2009 Atomistic Mechanisms of rf Breakdown in high- gradient linacs Z. Insepov, J. Norem, Argonne National Laboratory S. Veitzer Tech-X Inc

2 Outlook  Unipolar Arc plasma models in various systems  Plasma-surface interactions  Plasma model development by MD  Self-sputtering of copper surface  Taylor cone formation  Coulomb explosion  Summary

3 Unipolar Arc model in tokamaks Plasma potential D ~0.1  m hot spot e e e Tokamak Plasma [Schwirzke, JNM 1984] n ~ m -3 surface Heating occurs via ion bombardment. Plasma fueling:  Evaporation of surface atoms  Tip explosion by high electric field Y~10

4 Unipolar Arc in glow discharge [A. Anders et al, J. Appl. Phys. (1994)] Superdense glow discharge in pseudospark (hollow Mo cathode filled with H 2 ) Heating occurs via ion bombardment. Plasma fueling:  Evaporation of surface atoms  Tip explosion by high electric field RF breakdown on Copper surface Typical parameters for self-sustained self-sputtering Heating via ion bombardment. Plasma fueling:  Evaporation of surface atoms  Tip explosion by high electric field [Insepov, Norem CAARI (2008)]

5 Unipolar Arc model for rf linacs (1) Fowler-Nordheim equation for electrons, (2) Langmuir-Child equation for ion current from plasma to the tip, (3) Richardson-Dushman equation for thermal emission of electrons from the tip, (4) Sputtering Flux by plasma ions – Bohm current The temperature rise depends on the total current, k – thermal conductivity. (1) (2) (3) (4)

6 Plasma model of RF breakdown (1) Fowler-Nordheim equation for electrons (  = 100, 200) (2) Langmuir-Child equation for ion current from plasma to the tip (d=1  m) (3) Richardson-Dushman equation for thermionic emission of electrons from liquid Cu (T=1300K) (4) Sputtering Flux was calculated from Bohm current (plasma ion fluxes) times the sputtering yield at 1300K

7 Plasma-surface interactions Radiation-induced mechanisms: Implantation (fast particles, light, impurities and highly-charged ions) can contribute to effects on sputtering, preferential sputtering, recoil implantation, cascade mixing, diffusion, gibssian adsorption (surface segregation), and radiation-enhanced segregation. Optical surfaces will be exposed to an expanding post-discharge EUV source plasma. Sputter fluxes depend on incident particle fluxes and energy determined by sheath field. Potential sputtering due to collisions of Highly Charged Ions (Xe+10 etc). The net sputter erosion via balance between erosion and redeposition.

8 Bridging the scales Engineering applications Length, [Ǻ] Understanding/prediction Time, s El. structure Ab initio Quant. Mechanics Atom. simulations Molecular Dynamics/ Monte-Carlo Kinetic MC Microstructure Thermo-chemistry Mesoscale Continuum Gas-, hydro-, hemo- dynamics Accelerated MD Hybrid MD/MC Kinetic models DSMC MD: HyDyn-scale: from nm to tens of  m MC: Penelope, MC SEE Radiation defects and damages Thermodynamics Chemical reactions TST Wien2k, Ab- init, AMBER ART CG-MD COGNAC

9 Plasma-model development plasma OOPIC and Vorpal need the self-sputtering data as an input d  D Coulomb explosion of tips and fragments

10 Sputtering Yield models Sigmund’s theory – linear cascades, not good for heavy ions and low energies Monte Carlo codes: binary collisions, not accurate at low energies Empirical models based on MC – suitable for the known materials Molecular dynamics developed at Argonne – time consuming but no limit for energies, ion masses, temperatures, dense cascades, thermal properties - can verify OOPIC and VORPAL

11 Sputtering theory and models Eckstein-Bohdansky’s model Sigmund’s theory Not applicable for light ion, high energy ions (no electronic stopping power). Needs adjustable parameters. [Bohdansky, NIMB B (1984)][P. Sigmund, Phys. Rev. B (1969)] Not applicable for heavy ions C 0, U s - adjustable parameter.

12 Yamamura’s empirical model Yamamura’s interpolation model based on Monte-Carlo code No temperature dependence

13 Why atomistic simulation? Background 2 Argonne showed that nanobump + high electric field can lead to the cluster evaporation [Insepov et al, PRST-AB 7 (2004)] Flyura Djurabekova and Kai Nordlund, University of Helsinki Atomistic simulations of breakdown triggers: progress report CLIC RF Breakdown Workshop, CERN 2008

14 MD model for energetic collisions Cu + Thermal balance is maintained by finite- difference method: elasticity & thermal diffusivity equations. Central red area are evaluated by atomistic MD simulation method.  Copper ion interacts with target via ZBL-potential  Copper atoms interact via N-body potentials  Copper target bombarded by Cu ions with E = 50 ev – 100 keV

15 MD model of Cu self-sputtering MD simulations T= K Plasma Sputtering Model MD gives the positions, energies and the probabilities of various processes: sticking, sputtering, back-scattering, energies.  Lattice parameter depends on T  Energy absorbing boundaries  The number of ions:

16 MD movies Ei=170 eV, T=300K Ei=100 keV, T=300K, Yield=9 Ei=8 keV, T=300K

17 Comparison of yield RT  Monte-Carlo data are 6 times lower than MD at E=100 ev  Empirical models should be evaluated based on MD data  Two EAM MD potentials give comparable results  Sigmund’s theory is not good for self-sputtering of Copper  Yamamura’s model is systematically lower than MD Results

18 T-dependence of Sputter Yield Ei=50 evEi=100 evEi=150 ev

19 Cu self-sputtering Yield: T= K This plot shows that surface self-sputtering by plasma ions can be an efficient plasma fueling mechanism for target temperatures T > 900K

20 Taylor Cone formation In a high electric field, surface atoms are field evaporated. This effect is used in Field Ion Microscope (FIM) [E. Müller, 1951] FIM HV FIM tip cooled to K Polarized gas atom Microchannel Plate Phosphor screen Gas ion Dyke-Herring’s model [C. Herring, J. Appl. Phys. 1952] Herring’s theory of transport phenomena was applied to a tip in field-emission experiments and surface tension and migration coefficients were obtained for a W tip. Taylor model [G. Taylor, Proc.R.Soc.1964]  ≈ 98.6  jet

21 Comparison with experiment time: 1ps time: 185 ps E m =10GV/m f=1.25 GHz T=800K

22 Coulomb explosion (CE) model E 0 = 10 GV/m; D = Å S =  D 2 /4 = ( )× m 2 N + =  S/e =  0 E S/e N q  A bell-shaped Cu tip on the surface and a cubic fragment in vacuum Charge density defined from  ~ 200

23 Energies of exploded atoms time=0time=40 pstime=0time=200 ps

24 Summary A unipolar arc plasma model is used to understand self-sustained and self-sputtered plasma formation and RF high-gradient breakdown An MD model was developed and self-sputtering yields of Cu-ions were calculated for a wide region of ion energies and surface temperatures and compared to experiment and other models. Sputtering yield was calculated for solid and liquid surfaces for and T= K and E=50–150 eV - typical for Unipolar Arc. Coulomb explosion mechanisms were simulated and the energies of Cu atoms were calculated. A Taylor cone formation in a high-electric field was simulated for the first time. The simulated apex angle of  is close to the experimental value of 98.6 . We are close to understanding of the whole plasma- surface interaction in rf linacs and we can mitigate the RF breakdown.