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

pseUM

mVU

E

m

VUeVkT

mn

kTnU

E

enkT

mM

ekTU

f

iD

D

ff

D

e

e

eeD

ff

e

eD

e

ief

1~2

106.3

,106.1

4.26 , 18

104

12.5

,2

,2ln2

21

10

7

f

3-22

21

20

+

+

++ +

+

+

+

+

+---

--

-

-

-

-

-

D~0.1 m

hot spot

ee

e+

+

++

Tokamak Plasma

[Schwirzke, JNM 1984]

n ~ 1022 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 dischargeUnipolar Arc in glow discharge

319

2

0

9

21

0

210

1

sec

321

105 GV/m,10

,2

2~,20~

, 10~2

,50~2

1

,10~

mnE

E

eUnn

keVU

mVUen

d

UE

menUd

mmj

ev

mn

cre

cr

cr

c

cree

c

ce

c

cc

ecc

e

e

c

c

c

[A. Anders et al, J. Appl. Phys. (1994)]

Superdense glow discharge in pseudospark (hollow Mo cathode filled with H2)

Heating occurs via ion bombardment.Plasma fueling: Evaporation of surface atoms Tip explosion by high electric field

RF breakdown on Copper surface

.105

,31~2

.5.1, 2

)10~(

1

,10~

10

210

219-

1i

325

mV

d

UE

nmenUd

dnm

m

mn

mZevjY

vJn

c

cc

ecc

DcD

i

e

c

i

c

cc

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 linacsUnipolar 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.

,

,2

43.0

,exp

,2

9

4

,10831.6exp

)(10541.1

,

2

21

0

20

2

23

0

0

23

7

226

0

Tkjt

Tc

m

kTnej

Tk

eTAj

d

V

m

ej

EEyvE

ytEj

Jjjjj

v

i

eiBohm

BcThermoioni

iChildLangmuir

FN

SputtthermChildFN

(1)

(2)

(3)

(4)

6

Plasma model of RF breakdownPlasma 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 interactionsPlasma-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 scalesBridging the scales

Engineering applications

Length, [Ǻ]

Understanding/prediction

Tim

e, s

102 104 1061 108 1010

10-3

1

10-6

10-12 El. structureAb initio Quant.

Mechanics

Atom. simulations Molecular Dynamics/

Monte-Carlo

Kinetic MC

MicrostructureThermo-chemistry

Mesoscale

Continuum Gas-, hydro-, hemo-

dynamics

Accelerated MD Hybrid MD/MC

Kinetic modelsDSMC

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

ARTCG-MD

COGNAC

9

Plasma-model developmentPlasma-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

.708.1882.61728.0

2288.11ln441.3

A4685.0

energy) reduced - (,

,parameters adjustable,

,11)(

213232

22121

2

232

21

TFn

L

L

th

ththn

s

ZZa

eZZ

a

MM

ME

EQ

E

E

E

EQsEY

Eckstein-Bohdansky’s modelSigmund’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)]

t.coefficienC

power, stoppingnuclear

energy, binding surface -

density, atomic

energy, deposited

,0420.01

4

3

,)(

0

12

02

ES

U

N

EF

ENSMMEF

NUUNC

EFEY

n

s

D

nD

ss

D

Not applicable for heavy ionsC0, Us - adjustable parameter.

12

Yamamura’s empirical model Yamamura’s interpolation model based on Monte-Carlo code

.

4

.,7.51

,,7.6

,1042.0)(

parameter, adjustable

power, stoppingnuclear

energy, binding surface - density, atomic

1042.0

1042.0)(

221

21

2121

21

12

12

MM

MM

MMMM

MME

E

E

ESs

sES

U

MMEY

ES

UN

E

E

NU

ESMM

E

E

NU

EFEY

th

s

th

nn

nn

s

n

s

th

s

n

th

s

D

No temperature dependence

13

Why atomistic simulation?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

3.6

6

1.5

CLIC RF Breakdown Workshop, CERN 2008

14

MD model for energetic collisionsMD model for energetic collisions

vCu+

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-sputteringMD model of Cu self-sputtering

MD simulations T=300-1300K

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: 102-106

ions

atomsN

NYield

16

MD moviesEi=170 eV, T=300K

Ei=100 keV, T=300K, Yield=9

Ei=8 keV, T=300K

17

Comparison of yield data @ 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 YieldT-dependence of Sputter YieldEi=50 ev Ei=100 ev Ei=150 ev

19

Cu self-sputtering Yield: T=300-1300KCu 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 formationTaylor 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 tipcooled to 20-100K

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 tensionand 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

Em=10GV/mf=1.25 GHzT=800K

22

Coulomb explosion (CE) modelCoulomb explosion (CE) model

E0 = 10 GV/m; D = 55 - 125ÅS = D2/4 = (0.2-1.2)×10-16 m2

N+ = S/e = 0 E S/e

Nq 10 - 100

A bell-shaped Cu tip on the surface and a cubic fragment in vacuum Charge density defined from ~ 200

23

Energies of exploded atomsEnergies 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.