muon cooling rf workshop, 7-8 july, 2009 atomistic mechanisms of rf breakdown in high- gradient...
Post on 21-Dec-2015
213 views
TRANSCRIPT
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.