Transcript All Particle Simulation of a Cathodic Arc Plasma I. J. Cooper

All Particle Simulation of
a Cathodic Arc Plasma
I. J. Cooper
D. R. McKenzie
Tim Ruppin and Andrew Rigby
Traces left by an arc on tungsten cathode
Vacuum Arc
• High Current, Low
Voltage discharge in
vacuum ambient
• Current conducted
in metal vapor
plasma produced by
discharge itself from
evaporated
electrode material
Usually plasma production concentrated at cathode spots
3
Ion flow 
rapid heating
of microprotrusion 
shock wave
traveling to
base 
explosion of
microprotrusion
Time Evolution of Cathode Spot Cell
Liquid drops,
energetic
electrons, ions
and atoms
ejected from
cathode
leaving a
micro-crater
Atoms
ionized by
electron
impact or if
density
sufficient,
self
ionization
Expanding hot
dense plasma
cell in nonthermal
equilibrium
layer
Micro-protrusions on cathode surface
Ion flow
to anode
New ion
flow to
cathode
Cathodic arc plasma

Subspots (fragments)

Cells

Initial confinement of plasma
L = 1×10-8 m
V = 1×10-24 m3
Hot e- Te =3x104 K
Cold ions
Number of ions 10 to 100
Densitymax ~ 1026 ions.m3
All particle N body simulation
Coulomb forces between electrons and ions
 q (i ) q ( j )  x (i, j )
Fx (i )   

3
4


r
(
i
,
j
)
o 
j i 
2
 q (i ) q ( j ) 1  K 
1
m
(
i
)
v
(
i
)
  K (i )
2
U  

i
i
j  i  4  o r (i, j ) 
Up > 0 Ue > 0 Upe < 0
E U  K
x(i, t  t )
 2 x(i, t )  x(i, t  t )
q( j )  x(i, t )  x( j, t ) 
q(i ) t


3
4 o m(i) j i
r (i, j , t )
2
r(i, j, t) small  problems
r(i, j, t)

r(i, j, t) + 
Problem: Lots of particles – lots of calculations
Can modify equations to include
external electric and magnetic fields
xj(t+1): qj Ex t2
FB = q v x B
Bx =0, By = 0, Bz vz = 0
x(t+1):
G2[2x(t) + (G12-1)x(t-1) + 2G1y(t) – 2G1y(t-1)]
G1 = t Bz /2m G2 = 1 / (1+G12)
Motion of a proton: B = 0.8 T and E = 0 V/m
0.04
0.03
0.02
y (m)
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.04 -0.03
-0.02
-0.01
0
x (m)
0.01
0.02
0.03
0.04
Software MATLAB
slow need to remove loops by using array operations
For each time step t ~ 1x10-18 s Nsteps ~ 107:
xx = meshgrid(x_1,x_1);
yy = meshgrid(y_1,y_1);
zz = meshgrid(z_1,z_1);
xd = xx - xx';
yd = yy - yy';
zd = zz - zz';
Sx = (qq.*xd) ./rd3;
Sy = (qq.*yd) ./rd3;
Sz = (qq.*zd) ./rd3;
SSx = -A2 .* sum(Sx');
SSy = -A2 .* sum(Sy');
SSz = -A2 .* sum(Sz');
rd = sqrt(xd.^2 + yd.^2 + zd.^2);
rd = rd + rdMin;
rd3 = rd.^3;
xfp = 2.*x_1 - x_2 + SSx;
yfp = 2.*y_1 - y_2 + SSy;
zfp = 2.*z_1 - z_2 + SSz;
qq = meshgrid(q,q)
SIMULATIONS
single, multiple and mixed charged states
10 ps
50 Ti+ 50 e-
H C Ti
10 ps
100 Ti+
100 e-
10 ps
100 Ti+
100 e-
0.10 ps
50 Ti+
50 e-
10 ps
50 ions
50 e-
10 ps
100 Ti+
100 e-
10 ps
100 Ti+ 100 e-
10 ps
100 Ti+
100 e-
10 ps
1026 ion.m-3  Kavg ~ 3.8 eV
Kavg(real) ~ 60 eV  1028 ion.m-3
Initial
Volume
(m3)
1.0×10-24
1.0×10-24
1.0×10-24
1.0×10-24
Initial
Ion
density
(ion.m-3)
No. of
e
100×1024
100
100 Ti+
3.8  0.5
30×1024
30
30
Ti+
1.7  0.6
30×1024
60
30
Ti2+
9.6  1.2
60
10
10
10
Ti+
Ti2+
Ti3+
1.8  0.6
8.2  1.2
11.8  1.6
30×1024
No. of Ti
ions
Average ion
KE (eV)
10 ps
R = Ti2+ / Ti+