Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 1

Multiscale modelling of sparking in CLIC components

We are developing a multiscale model to

understand the electrical breakdown in CLIC

components Pursuing three activities in parallel:

Investigation of possible scenarios to initiate a growth

of asperities on the surface under an electric field

Developing a concurrent molecular dynamics and

electrodynamics code for dynamic simulation of

effect of electric field on metal surface combined with

electron dynamics

Simulation of the plasma development and surface

damage during the breakdowns

F. Djurabekova, K. Österberg, H. Timko, A. Ruzibaev, A. Pohjonen, S. Parviainen, K. Nordlund, HIP; in close collaboration with Walter Wuensch and Sergio Calatroni (CERN)

[Walter Wuensch, CERN]

6

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 2

Dislocations as source of tip growth

We have shown that a void below a surface can act as a source for growth of protrusions and ejection of material

[Pohjonen, Djurabekova, Nordlund, Fitzgerald, Phys. Rev. B (2010) submitted)]

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 3

Dislocations as source of tip growth

The growth can be understood in terms of the void emitting a series of prismatic dislocation loops that glid to the surface and cause growth there

[Pohjonen, Djurabekova, Nordlund, Fitzgerald, Phys. Rev. B (2010) submitted)]

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 4

Algorithm for finding the charge on metal atoms due to the electric field.

Gauss law = 0Eloc as a source of a

charge estimation where Eloc is a

local field near the atom surface. Since the atoms belong to the

surface they can be only partially

ionized.

ELOC

In the present algorithm: the atoms are rectangular grid points, which are part of the

same grid as for a Laplace solver• Problem: the discreteness of the Laplace solver ->

presence of the tangential component of electric field. • Solution: only perpendicular to the atom surface

components are taken into account. the change of local density of atoms also affects the

distribution of charge

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 5

Verifying algorithm for finding the charge on metal atoms due to the electric field, part 1.

The accuracy of the discretization of the

Laplace solution has been tested against an

exactly solvable case -> agreement within a

few %!

EL

OC

[Djurabekova, Parviainen, Nordlund, Phys. Rev. E (2010) submitted)]

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 6

Verifying algorithm for finding the charge on metal atoms due to the electric field, part 2.

Accuracy of the interatomic potential energy has

been tested again quantum mechanical (DFT)

calculations of the case of a single adatom on a

tungsten surface Very good agreement!

Agrees with experimental value for the critical field

for field evaporation in W of about 50 GV/m!

EL

OC

[Djurabekova, Parviainen, Nordlund, Phys. Rev. E (2010) submitted)]

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 7

Field increase at protrusions

Our model also reproduces the increase of the field strength around a hemispherically capped cylinder in excellent agreement with previous Finite Element Method calculations Field strength increases less than linearly, in agreement

with the literature

Aspect ratio of tip

Elec

tric

fiel

d en

hanc

emen

t

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 8

Heating depends on several electronic effects

Heat conduction

Electron screening

Escreened

Electronic effects in MD

Electric current (resistive heating)

2 2

2V V

T(x,t) K T(x,t) (T(x,t))Jt C x C

At the moment a 1D equation to handle the temperature raise due to the Joule heating is implemented into the parcas MD code

K K KP e

K ( )

( )eLTTT

2 2 8 -2L ( / 3)( ) 2.443 10 W KBk

Here electron thermal conductivity introduced explicitly according to the Wiedemann-Franz law

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 9

Resistive heating leads to necking in tips

Starting from a cylindrical tip, the Joule heating and desire of material to minimize surface energy (Rayleigh instability) leads to necking (thinning) below the maximum First stage for atom or cluster emission that is needed for

onset of plasma!

[Parviainen, Djurabekova, Timko, Nordlund, Comput. Mater. Sci. (2010) submitted)]

Kai Nordlund and Flyura Djurabekova, HIP, University of Helsinki 10

Outlook

The validated ED-MD will be used in the electronic heating and

dislocation dynamics simulations to use a realistic surface force

model in them Dislocation dynamics: the effect of temperature on the emission

of dislocation and surface growth due to voids will be determined Finite-size effects are studied to estimate a realistic time range

for the melting of surface asperities Study includes both cylinders on surfaces and isolated

nanowires 2D PIC model under development The effect of the spatial and velocity distribution of bombarding

ions on the surface damage as a result of plasma interaction

with the cathode is being studied