Unipolar Plasma Model of RF Breakdown Z. Insepov, J. Norem 1) - PowerPoint PPT Presentation

Unipolar Plasma Model of RF Breakdown Z. Insepov, J. Norem 1) Purdue University, 2) Nanosynergy Inc Feb 12, 2014 "RF breakdown physics" sprint

Outline  Motivation - RF breakdown in cavities  Calculation of electric field for real surfaces  Experimental enhancement factor for dark current  Cluster field evaporation in high electric field  Unipolar (Schwirzke) plasma model development  Surface sputtering by ions  Atomistic model of non-Debye plasma  Plasma model of RF BD  Conclusions 2

RF Breakdown examples Severe damage Moderate damage CLIC CERN, Izquierdo, 2008 NLC NLC [From the 2001 Report on the Next Linear Collider]

Calculation of electric field for real surfaces

FE m ulti-physics sim ulation • Comsol simulation : Solving Laplace’s equation for arbitrary geometry ∆ φ = 0 φ =  1 V  el ⋅ = E n 0 φ = 0 V  E  φ = 0 V ⋅ n = g 0 g φ = 1 V 2 µ m el

Field Enhancem ent by tips  Comsol simulation vs analytical theory of field enhancement 2 µ m 1 µ m ρ =1nm ρ =10nm ρ =100 nm

Field Enhancem ent by cones • Comsol simulation of field enhancement at sharp cones G. Arnau Izquierdo, 2008 β ~ 1000 1 µ m

Enhancem ent at crack’s edges • Sharp tips, edges and corners of the cracks More exotic cracks can enhance the electric • can significantly enhance the electric field field too β ~ 100

Triple junction E-fields • We have been modeling, cracks, junctions, edges and other shapes  Comsol simulation of field enhancement at triple crack junction 1 µ m β =140 9

Experim ental enhancem ent factor obtained from dark current m easurem ents: β = 1 8 4

Comparison with experiment X rays show that cavities break [Norem, PR STAB (2003)] down at E local ~ 7–10 GV/m Fowler-Nordheim field emission (1928) ( )   β 3 2 φ A ( E )  2  B = − A FN surf FN i ( E ) exp ,   φ β 2 surf m E   surf = × 6 2 A 1 . 54 10 eV A/(MV) FN 3 = 2 B 6830 MV/m(eV) FN φ = 4.6eV β – Local Field Enhancement β =184 11

Cluster field evaporation – a result of a high local electric field

W hy atom istic sim ulation? Flyura Djurabekova and Kai Nordlund, University of Helsinki β = β = 1.5 3.6 β = 6 CLIC RF Breakdown Workshop, CERN 2008

Cluster field evaporation [Miller, Atom Probe Tomography (2000)] 14 12 Voltage (KV) 10 7.6 nm, 30×10 3 19 nm, 450×10 3 8 9.3 nm, 50×10 3 6 4 1×10 5 2×10 5 4×10 5 6×10 5 8×10 5 1×10 6 Single ion field evaporation : Ecr = 30 GV/m Figure shows abrupt discontinuities in the voltage vs. number of ions in a DC- field evaporation system and evidence for large clusters produced at field ion microscope tips. [Insepov Norem, Phys Rev STAB (2004)]

Electric field initiates breakdow n • Surfaces contain grain boundaries, tips, oxides, dust particles • A strong electrostatic field enhancement can be generated • Maxwell stress includes electric forces acting on the tip • The chunks fill the near region of the vacuum Ionization by FN-electrons and • Coulomb explosion form plasma • Unipolar plasma model can explain triggering of the breakdown

Crater form ation via field evaporation • A new mechanism of crater formation – pulling out a large area of the surface S. Yip, MIT 2014 (private communication)

Unipolar ( Schw irzke) Plasm a m odel developm ent

Double electric layer in plasm a Tokamak F. R. Schwirzke, SEM image of plasma damaged metal surface: Superposition of “younger” (10 µ m) and “older” IEEE Trans. on Plas. Sci., 19 , 690 (1991) craters (30-40 µ m).

Unipolar arc breakdow n m odel Unipolar Arc Model Plasma   k T M   = B e i V ln , Plasma potential   π pl   2 e 2 m e Dark space V = Surface field pl E , λ s d 1 ε   2 V   λ = 0 pl Debye length   d 2   n e e Cavity surface V pl V pl ~ 100 V φ BD triggered by impact ionization • Neutrals accumulated in the dark space plasma sheath • Ionization of neutrals by FN-current • Percolation of dark space via ionization 0 z ~ 1-2 n m d • Crater formation via explosion

Unipolar Arc m odel in linac Linac Plasma Heating occurs via ion bombardment. Plasma fueling: n ~ 10 25 m -3  Evaporation of surface atoms -  Tip explosion by high electric field + + + - + Plasma potential - - - - - -     - + + kT M + + =     U e ln i , + π -     f 2 e 2 m + e ε kT λ = 0 e , 2 D 2 n e e + e U ( ) λ D ~2 nm ≈ ≈ × + f 1 2 e E n kT 5 . 12 e + λ f e e D ≈ × 25 - 3 n 1 10 m + e ≈ ≈ kT 18 eV , U 50 V e f − λ ≈ × 9 2 10 m , D ≈ × λ d 1 . 5 c D hot spot Y ~10 U ≈ β ≈ × f V 10 E 5 10 λ f m surface D [Insepov, Norem, 2012] • Schwirzke model

Self-sputtering by plasm a Coulomb explosion plasma of tips and fragments d ∼ 1.5λ D Self-sputtering is the main mechanism of plasma fueling

Surface sputtering by ions  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 – good for known materials  Molecular dynamics – time consuming but no limit for energies, ion masses, temperatures, dense cascades, thermal properties - can verify the OOPIC/VORPAL simulations

Sputtering theory and m odels • Eckstein-Bohdansky’s model • Sigmund’s theory ( ) = Λ   2 Y ( E ) F E , 2 3       ( ) E E D = ε − −       th th Y ( E ) Qs 1  1  , n       3 1 0 . 0420   E E   Λ = = , π 2 − 4 NC U NU Q , E adjustable parameters , 0 s s th ( ) ( ) ( ) = α F E M M NS E M a ε = ε D 2 1 n 2 L E , ( - reduced energy) ( ) + − 2 M M Z Z e F E deposited energy, 1 2 1 2 D { } − − 1 2 = + 2 3 2 3 N atomic density, a 0 . 4685 Z Z A L 1 2 ( ) U - surface binding energy, ε + ε ( ) 3 . 441 ln 1 1 . 2288 s ε = ( ) TF ( ) s . − n ε + ε + ε ε − S E nuclear stopping power, 0 . 1728 6 . 882 1 . 708 n − C coefficien t. 0 Not applicable for light ion, high energy ions Not applicable for heavy ions (no electronic stopping power). C 0 , U s - adjustable parameter. Needs adjustable parameters. [P. Sigmund, Phys. Rev. B (1969)] [Bohdansky, NIMB B (1984)]

Yam am ura’s em pirical m odel  Yamamura’s interpolation model based on Monte-Carlo code ( )  −  F E E = = D  th  Y ( E ) 0 . 042 1 NU  E  s ( ) ( )  −  α M M S E E 2 1 n  th  0 . 042 1 NU  E  s − N atomic density, U - surface binding energy, s ( ) − S E nuclear stopping power, n α − adjustable parameter, ( ) ( ) ( )  −  s α ε M M S E s E = × 2 1 n n  th  Y ( E ) 0 . 042 1 , ( ) ( ) ε + U s S E E   s n n  6 . 7 ≥ , M M ,   γ 1 2 =  ( ) E + th 1 5 . 7 M M  ≤ 1 2 , M M .  γ 1 2  4 M M γ = 1 2 . ( ) + 2 M M 1 2 No temperature dependence

MD sim ulation of Copper self-sputtering at high T and E [Insepov et al, NIMB, 2010] • Self-sputtering is the mechanism for fueling unipolar surface plasma. • Unipolar model requires Y > 10 typical at low ion energies. MD predicts very high sputtering yields for high surface T and E . • • Erosion rates on the order of ~ 1 m/s. 25

Atom istic m odel of non-Debye near-surface plasm a

n-T Diagram for plasmas 0 1 2 10 3 4 5 6 10 7 8 Nonideality 10 10 10 10 10 10 10 28 28 parameter for 10 10 θ = 1 n e, cm -3 electrons 26 26 Quantum gas 10 10 π 1/3   2 = ε 4 n e 2 / Γ =  e a 24 24 e  10 10 F   3 kT 22 22 10 10 MD Number of 20 20 10 10 electrons in the 18 18 Debye sphere 10 10 π 3 ionization 4 r 16 16 = 10 10 D N n D e Classical gas 3 14 14 10 10 Γ = 1 12 12 Degeneracy 10 10 = N 10 parameter 10 10 D 10 10 T e , K θ = ε F kT / 8 8 10 10 0 1 2 10 3 4 5 6 10 7 8 10 10 10 10 10 10 10

Density-Temperature Diagram Nonideality 0 1 2 10 3 4 5 6 10 7 8 10 10 10 10 10 10 10 parameter for 28 28 10 10 θ = electrons 1 n e, cm -3 26 26 Quantum gas π 1/3   10 10 2 4 n e Γ =  e  = ε 2   e / a 24 24 3 kT 10 10 F 22 22 MD 10 10 Number of 20 20 10 10 electrons in the 18 18 Debye sphere 10 10 π 3 ionization 4 r 16 16 = 10 10 D N n D e Particle-in-cell 3 14 14 10 10 = 12 12 N 100 10 Degeneracy 10 D parameter 10 10 10 10 T e , K θ = ε F kT / 8 8 10 10 0 1 2 10 3 4 5 6 10 7 8 10 10 10 10 10 10 10