Atomistic Mechanisms of rf Breakdown in high-gradient linacs

1. 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 e + + + + - - - - - - - - - - + + + + + + + + + + • Heating occurs via ion bombardment. • Plasma fueling: • Evaporation of surface atoms • Tip explosion by high electric field Tokamak Plasma n ~ 1022 m-3 Plasma potential lD~0.1 mm e e hot spot Y~10 surface [Schwirzke, JNM 1984]

4. Unipolar Arc in glow discharge Typical parameters for self-sustained self-sputtering Superdense glow discharge in pseudospark (hollow Mo cathode filled with H2) RF breakdown on Copper surface • Heating occurs via ion bombardment. • Plasma fueling: • Evaporation of surface atoms • Tip explosion by high electric field • Heating via ion bombardment. • Plasma fueling: • Evaporation of surface atoms • Tip explosion by high electric field [Insepov, Norem CAARI (2008)] [A. Anders et al, J. Appl. Phys. (1994)]

5. Unipolar Arc model for rf linacs (1) (2) (3) (4) (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.

6. Plasma model of RF breakdown (1) Fowler-Nordheim equation for electrons (b = 100, 200) (2) Langmuir-Child equation for ion current from plasma to the tip (d=1 mm) (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 • 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. 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.

8. Bridging the scales 1 10-3 10-6 10-12 1 108 1010 102 104 106 Kinetic models DSMC Time, s ART CG-MD COGNAC Wien2k, Ab-init, AMBER Continuum Gas-, hydro-, hemo- dynamics Microstructure Thermo-chemistry Mesoscale Accelerated MD Hybrid MD/MC Thermodynamics Chemical reactions TST Kinetic MC Radiation defects and damages Atom. simulations Molecular Dynamics/ Monte-Carlo MD: HyDyn-scale: from nm to tens of mm MC: Penelope, MC SEE El. structure Ab initioQuant. Mechanics Length, [Ǻ] Understanding/prediction Engineering applications

9. Plasma-model development Coulomb explosion of tips and fragments plasma d~ 1.5lD OOPIC and Vorpal need the self-sputtering data as an input

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 • Sigmund’s theory • Eckstein-Bohdansky’s model Not applicable for heavy ions C0, Us - adjustable parameter. Not applicable for light ion, high energy ions (no electronic stopping power). Needs adjustable parameters. [P. Sigmund, Phys. Rev. B (1969)] [Bohdansky, NIMB B (1984)]

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

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

14. MD model for energetic collisions Cu+ Central red area are evaluated by atomistic MD simulation method. Thermal balance is maintained by finite-difference method: elasticity & thermal diffusivity equations. • 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 Plasma Sputtering Model MD simulations T=300-1300K • Lattice parameter depends on T • Energy absorbing boundaries • The number of ions: 102-106 MD gives the positions, energies and the probabilities of various processes: sticking, sputtering, back-scattering, energies.

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

17. Comparison of yield data @ RT Results • 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

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

19. Cu self-sputtering Yield: T=300-1300K 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] Dyke-Herring’s model 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. Microchannel Plate Polarized gas atom [C. Herring, J. Appl. Phys. 1952] Phosphor screen Taylor model FIM tip cooled to 20-100K Gas ion a ≈ 98.6 jet HV FIM [G. Taylor, Proc.R.Soc.1964]

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

22. Coulomb explosion (CE) model • A bell-shaped Cu tip on the surface and a cubic fragment in vacuum • Charge density defined from b~ 200 E0 = 10 GV/m; D = 55 - 125Å S= D2/4= (0.2-1.2)×10-16 m2 N+ = s S/e = 0E S/e Nq  10 - 100

23. Energies of exploded atoms time=0 time=40 ps time=0 time=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=300-1300K 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 104.3 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.