Download CLIC_meeting270209

CMS
Multiscale modelling of
electrical breakdown
HIP
Flyura Djurabekova, Helga Timkó,
Aarne Pohjonen, and Kai Nordlund
Helsinki Institute of Physics and Department of Physics
University of Helsinki
Finland
Outline
 What is the problem?
 Plasma onset by the external electric field
 Electrodynamics
+ Molecular Dynamics (ED+MD )
code (benefits/drawbacks)
 Plasma burning
 Surface cratering
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
2
Detecting the problem…
Click!
Click!
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
3
The scale of the problem
About 50 km length?
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
4
Electrical Breakdown in
multiscale modeling approach
Stage 1: Charge distribution @ surface
Method: DFT with external electric
field
N
Stage 2: Atomic motion & evaporation
Method: Hybrid ED&MD model
Classical MD
~few fs
~few ns
F
Solution of Laplace
equation
Stage 3: Evolution of surface
morphology due to the given charge
distribution
Method: Kinetic Monte Carlo
N
~ sec to
hours
P
L
A
S
M
A
O
N
S
E
T
Feedback: Electron & ion & cluster emission ions
Stage 4: Plasma evolution, burning of arc
Method: Particle-in-Cell (PIC)
F
Feedback: Energy & flux of bombarding ions
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
~10s ns
Stage 5: Surface damage due to the
intense ion bombardment from plasma
Metod: Arc MD
~100s ns
F
5
or
How does all start???
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
6
How do we introduce the external
electric field?
Macroscopic field to…
Gauss law states
Q
su
rfa
c
e

0E
A
su
rfa
c
e
Due to the external electric field the
surface attains charge
Two electric forces modify the motion
of charged atoms:
FL  Eq
Fcoulomb
Fa
+
Fb
+
a +
+ b
 Fb
 Fa
qa qi
FC 
rˆ

2 0i
4 0 i r0i
1
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
…the atomic level:
G
V
E 0
.0
1
1
m
+ + + + + + + +
7
Simulation approach
 Now ElectroDynamics+Molecular Dynamics
(ED+MD) code to simulate the effect of the electric
field WORKS!
The distribution of the field near
the surface is the solution of
Laplace’s equation
  0
2
with mixed boundary
conditions
E

E
0
Multigrid solver is
implemented. The calculation
of the single step speeded up
by 2-3 orders of magnitude!
φ=const
(conducting material)
surface with an arbitrary morphology
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
8
On the positive side…
 What can we benefit from ED+MD code?
 Determine
the charges gained by surface atoms due
to the external electric field
 Estimate
the possible morphologies of surfaces
formed due to the electric field
 Simulate
the field emission of the atoms/clusters at
high gradient electric field, as well as the evaporation
of atoms from the rough features formed on the
surface at the lower fields
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
9
Limits…
 Where are we limited in these simulations?
 Diffusion
process is too long to be treated by MD code.
- Solution: if needed, the other methods for the longer time
span (KMC, for instance) can be applied
 Polycrystal
structures can not be considered at the moment,
since Laplace equation is solved for the uniform surface
(single crystal)
- Solution: we can consider different faces for the surface
and, then, take the statistical average of the field effect
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
10
Stresses due to the field
 The main agreement in the field is that the rapid releasing
of microstresses, which is generally present on grain
boundaries and can be enhanced by any external agents
as mechanical treatment or T-cycling, the migration of
defect complexes is stimulated.
 The strain by the huge
electric field can cause
→
the dislocation motion
E
STRESS
and redistribution
+
+
+ + + +
+ +
=0E2/Y
of the microstress.
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
11
Would it be some Taylor cones?
 It is also known that flat liquid
conducting surfaces form cones
under electric fields
 The tip of the cone emits atoms or
droplets
 This
is industrially used in so
called electrosprays
 Could this happen also on solid
[G. Taylor, Proc. Roy. Soc. London.
Ser. A 280 (1964) 383]
surfaces??
 With
a surface viscosity induced
by a high adatom concentration
due to the electric field, perhaps
 But unlikely this would be large
enough at room temperature
[www.sisweb.com/lc/electrospray-tip.htm]
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
12
Solution of 3d Laplace equation for the surface
with the tip of 20 atomic layers
(color represents the charges)
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
13
Direct current field emission (ED+MD code)
T = 500K
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
14
Activation energy of direct field emission of
atoms
eV
eV
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
15
Adatoms on the surface
We analyzed only two different faces (100) and (111). The difference is
evident. Closer packed face (111) less affected by the field.
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
16
Atom/cluster evaporation from Cu(100)
@ 500 K, E0 = 1 GV/m
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
17
Summary
 ED+MD code is working and giving sensible results!
 We simulated the case of direct field emission, which
corresponds to the experimental data
 At the elevated temperatures the sharp tip of ~300 atoms
emitted atoms/clusters already at 1 GV/m
 The roughening must depend on the surface orientation
(111) the closest pack shows the least respond to the field
effect.
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
18
Arcs or Sparks?
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
19
Background:
Vacuum sparks
 A vacuum spark is an electrical plasma discharge
emerging from a rough surface feature under high electric
field gradients
 Onset
 After
not understood at all (cf. beginning of talk)
that somewhat understood:
[R. Behrisch, in Physics of Plasma-wall Interactions in Controlled fusion, NATO ASI series B 131 (1986) 495]
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
20
How to simulate plasma burning?
 Particle-in-cell
(PIC) simulations of the spark plasma
(will hear more in close future by Helga T.) This part of
project has been started very recently, but we have
some preliminary results by Konstantin Matyash and
Ralf Schneider from Max-Planck Institut für
Plasmaphysik in Greifswald. Their results give us:
- as output e.g. ion and neutral flux and energy
distribution towards surface
- Conditions chosen to be those corresponding to
sparking experiments at CERN for development of
CLIC
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
21
PIC simulations
 The 1D PIC simulations give the plasma
density time evolution above the surface:
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
22
PIC simulation output
 The PIC simulations gave particle flux and energies
Note flux
value !!
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
Note huge
peak
around ion
energy of 8
keV due to
plasma
sheath
potential!
23
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
24
Where these huge fluxes of accelerated
ions go?
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
25
Background: Spark cratering
 The sparking leads to a plasma-wall interactions which
somehow produces a large (~ 0.1 – 100 µm) crater.
 Classical
explanation: surface heating by ions and electrons
=> massive evaporation
[http://www.uni-saarland.de/fak8/fuwe/fuwe_de/Forschung/electroden/Indexi.htm]
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
26
Multiscale modelling of sparks:
Classical MD simulations
 MD simulations of surface bombardment on a given area A
 Ion
flux and energy distribution corresponded exactly to that from
PIC simulations!
- Flux of ~1025 on eg. r=15 nm circle => one ion/20 fs!!
Top view
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
Side view
27
Multiscale modelling of sparks:
Classical MD simulations
 With this huge flux and energy distribution, several
overlapping cascades lead to huge heating and cratering
 This
is not just classical evaporation, but a heat spike!
Simulation time
of 36 hours on
2000 processors
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
28
Multiscale modelling of sparks:
Classical MD simulations
 The end result is cratering
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
29
Multiscale modelling of sparks:
Comparison of materials
Cu
Mo
W
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
30
Comparison with experiments
 Experiments show a wide variety of spark crater sizes
 But
they appear to be self-similar over size scales:
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
31
Comparison with experiments
 Due to the self-similarity over size scales, we can compare
our craters with experiments
Experiment
Simulation
[R. Behrisch, in Physics of Plasma-wall Interactions in
Controlled fusion, NATO ASI series B 131 (1986) 495]
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
32
Conclusion
 Vacuum spark craters are formed by an overlapping heat
spike process (if the electric field is high enough)
 Ions
accelerated in plasma sheath potential to energies ~ 10
times higher than the electric field gradient itself
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
33
Summary & Outlook
 The model comprises the different physical processes
(nature and time wise) probable right before, during and
after an electrical breakdown event.
 All the parts of the general model are started in parallel.
We start, continue and develop intense activities to cover
all possible aspects.
 Nevertheless, currently, there are blocks in model lacking
man-power.
 On filling these gaps too we strongly believe to be
capable to gain comprehensive insight to the puzzle of
electrical BREAKDOWN.
 Effect of rf-field is to be included next.
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
34
Any recommendation?
Flyura Djurabekova, 27.02.09 HIP, University of Helsinki
35