Transcript Atomistic Mechanisms of rf Breakdown in high

Atomistic Mechanisms
of rf Breakdown in highgradient linacs
Z. Insepov, J. Norem,
Argonne National Laboratory
S. Veitzer
Tech-X Inc
Muon Cooling RF Workshop, 7-8 July, 2009
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
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Unipolar Arc model in tokamaks
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
+
-
kT
M
,
U f   e  ln i
2e  
2me 

D   0 kTe
Ef 
Uf
D
+
,
2ne e 2
-
+
+
 ne kTe   5.12
+
-
+
+
+
e
+
+
e
D~0.1 mm
+
D  1.6  107 m,
D
-
e
+
kTe  18 eV , U f  26.4 V
Uf
+
12
ne  4  1022 m -3
Ef  
-
+
 3.6  1010 V
m
12


  D  2 M i eU 
f 

hot spot
~ 1 ps
surface
Y~10
[Schwirzke, JNM 1984]
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Unipolar Arc in glow discharge
Typical parameters for self-sustained self-sputtering
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
nc ~ 1021 m 3 ,
Jc
vc

Y ji
vc Ze
~ 1025 m 3 ,
 i  ne 1  1 mm
d c  2 0U c ene  ~ 50mm,
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12
~ 10 V
9
2
 E ccr 

 ,
  


E ccr  10 GV/m, necr  5  1019 m 3
2
ne  n  0
eU c
Heating via ion bombardment.
Plasma fueling:
 Evaporation of surface atoms
 Tip explosion by high electric field
nc 
1


   ve e sec   1m m
j

e


 en U 
U
Ec   c    e c 
dc
 2 0 
 ~ 20, U c ~ 2 keV
RF breakdown on Copper surface
cr
e
m
,
( i ~ 10-19 m 2 )
D  2 nm, d c  1.5D .
d c  2 0U c ene  ~ 1  3 nm,
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Ec  
Uc
 5 1010 V .
m
dc
[Insepov, Norem CAARI (2008)]
[A. Anders et al, J. Appl. Phys. (1994)]
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Unipolar Arc model for rf linacs



0
j  jFN
 jChild
 jtherm
 J Sputt
,

1.541 106 E 2 t 2 ( y ) 
j

(1) FN 



3




2
7 

exp 6.831 10
v y , E   E0
E







(2) j Langmuir Child
(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.

Thermoioni c
(3) j
4
 0
9
3
2e V 2
,
2
mi d
 e 
 A0T exp
,
k
T
 B 
2
12
 2kTe 


 ,
j

0
.
43
e
n
0 i
(4) Bohm
 mi 
T
cv
 j 2  kT ,
t
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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 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
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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.
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Bridging the scales
Time, s
Wien2k, Abinit, AMBER
ART
CG-MD
COGNAC
Kinetic models
DSMC
Continuum
Gas-, hydro-, hemodynamics
1
Microstructure
Thermo-chemistry
Mesoscale
Accelerated MD
Hybrid MD/MC
10-3
Kinetic MC
Radiation defects
and damages
10-6
Atom. simulations
Molecular Dynamics/
Monte-Carlo
10-12 El. structure
Ab initio Quant.
Mechanics
1
102
Thermodynamics
Chemical reactions
TST
MD: HyDyn-scale: from nm to tens of mm
MC: Penelope, MC SEE
Length, [Ǻ]
104
Understanding/prediction
106
108
1010
Engineering applications
8
Plasma-model development
plasma
Coulomb explosion
of tips and fragments
d ~ 1.5D
OOPIC and Vorpal need the self-sputtering data as an input
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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
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Sputtering theory and models
 Sigmund’s theory
Y ( E )  FD E ,

3
1
0.0420

,
2
4 NC0U s
NU s
FD E    M 2 M 1 NS n E 
FD E   deposit edenergy,
N  at omicdensit y,
U s - surface binding energy,
S n E   nuclear st oppingpower,
 Eckstein-Bohdansky’s model
  Eth  2 3    Eth  2
Y ( E )  Qsn  1  
  1  
 ,
  E     E 
Q, Eth  adjustable paramet ers,
 E
M2
aL
, ( - reduced energy)
M 1  M 2 Z1 Z 2 e 2

aL  0.4685 Z 12 3  Z 22 3
snTF   

1 2
A
3.441  ln1  1.2288 
.
  0.1728    6.882   1.708


C 0  coefficient .
Not applicable for heavy ions
C0, Us - adjustable parameter.
[P. Sigmund, Phys. Rev. B (1969)]
Not applicable for light ion, high energy ions
(no electronic stopping power).
Needs adjustable parameters.
[Bohdansky, NIMB B (1984)]
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Yamamura’s empirical model
 Yamamura’s interpolation model based on Monte-Carlo code
Y ( E )  0.042
Eth 
FD E  
1 

NU s 
E 
 M 2 M 1 S n E  
Eth 
1 

NU s
E 

N  atomicdensity,U s - surface binding energy,
0.042
S n E   nuclear stoppingpower,
  adjustable parameter,
Eth 
 M 2 M 1  S n E sn   
Y ( E )  0.042
 1 
 ,
Us
sn    S n E  
E 
s
 6.7
  ,
Eth  
1  5.7M 1 M 2 

,



M1  M 2 ,
M1  M 2.
4 M 1M 2
.
M 1  M 2 2
No temperature dependence
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Why atomistic simulation?
Atomistic simulations of breakdown triggers: progress report
Flyura Djurabekova and Kai Nordlund, University of Helsinki
  1.5
  3.6
Background 2
Argonne showed that nanobump +
high electric field can lead to the
cluster evaporation
 6
[Insepov et al, PRST-AB 7 (2004)]
CLIC RF Breakdown Workshop, CERN 2008
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MD model for energetic collisions
Cu+ 
v
Central red area are evaluated by atomistic
MD simulation method.
Thermal balance is maintained by finitedifference 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
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MD model of Cu self-sputtering
Sputtering Model
MD simulations T=300-1300K
Plasma
 Lattice parameter depends on T
 Energy absorbing boundaries
 The number of ions: 102-106
Yield 
N atoms
N ions
MD gives the positions, energies and the
probabilities of various processes: sticking,
sputtering, back-scattering, energies.
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MD movies
Ei=170 eV, T=300K
Ei=100 keV, T=300K, Yield=9
Ei=8 keV, T=300K
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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
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T-dependence of Sputter Yield
Ei=50 ev
Ei=100 ev
Ei=150 ev
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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
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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 20100K
Gas ion
 ≈ 98.6
jet
HV
FIM
[G. Taylor, Proc.R.Soc.1964]
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Comparison with experiment
time: 1ps
Em=10GV/m
f=1.25 GHz
T=800K
time: 185 ps
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Coulomb explosion (CE) model
 A bell-shaped Cu tip on the surface and a cubic fragment in vacuum
 Charge density defined from  ~ 200
E0 = 10 GV/m; D = 55 - 125Å
S = D2/4 = (0.2-1.2)×10-16
m2
N+ =  S/e = 0 E S/e
Nq  10 - 100
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Energies of exploded atoms
time=0
time=200 ps
time=0
time=40 ps
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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 plasmasurface interaction in rf linacs and we can mitigate the RF
breakdown.
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