All Particle Simulation of a Cathodic Arc Plasma I.J. Cooper D. R. McKenzie Tim Ruppin and Andrew...
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Transcript of All Particle Simulation of a Cathodic Arc Plasma I.J. Cooper D. R. McKenzie Tim Ruppin and Andrew...
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
3
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
Ion flow rapid heating of micro-protrusion shock wave traveling to base explosion of micro-protrusion
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
Time Evolution of Cathode Spot Cell
Expanding hot dense plasma cell in non-thermal equilibrium layer
New ion flow to cathode
Ion flow to anode
Micro-protrusions on cathode surface
Cathodic arc plasma Subspots (fragments) Cells
Initial confinement of plasmaL = 1×10-8 mV = 1×10-24 m3
Number of ions 10 to 100Densitymax ~ 1026 ions.m3
Hot e- Te =3x104 K
Cold ions
3
( ) ( ) ( , )( )
4 ( , )x
oj i
q i q j x i jF i
r i j
All particle N body simulation
Coulomb forces between electrons and ions
( ) ( ) 1
4 ( , )oj i
q i q jU
r i j
212
( ) ( ) ( )i i
K m i v i K i
E U K Up > 0 Ue > 0 Upe < 0
2
3
( , )
2 ( , ) ( , )
( ) ( , ) ( , )( )
4 ( ) ( , , )o j i
x i t t
x i t x i t t
q j x i t x j tq i t
m i r i j t
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)
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04Motion of a proton: B = 0.8 T and E = 0 V/m
x (m)
y (
m)
Software MATLAB slow need to remove loops by using array operations
qq = meshgrid(q,q)
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';
rd = sqrt(xd.^2 + yd.^2 + zd.^2);
rd = rd + rdMin;
rd3 = rd.^3;
Sx = (qq.*xd) ./rd3;
Sy = (qq.*yd) ./rd3;
Sz = (qq.*zd) ./rd3;
SSx = -A2 .* sum(Sx');
SSy = -A2 .* sum(Sy');
SSz = -A2 .* sum(Sz');
xfp = 2.*x_1 - x_2 + SSx;
yfp = 2.*y_1 - y_2 + SSy;
zfp = 2.*z_1 - z_2 + SSz;
For each time step t ~ 1x10-18 s Nsteps ~ 107:
SIMULATIONS single, multiple and mixed charged states H C Ti
10 ps 50 Ti+ 50 e-
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 ps1026 ion.m-3 Kavg ~ 3.8 eV
Kavg(real) ~ 60 eV 1028 ion.m-3
Initial Volume
(m3)
Initial Ion
density (ion.m-3)
No. of
e-
No. of Ti ions
Average ion KE (eV)
1.0×10-24 100×1024 100 100 Ti+ 3.8 0.5
1.0×10-24 30×1024 30 30 Ti+ 1.7 0.6
1.0×10-24 30×1024 60 30 Ti2+ 9.6 1.2
1.0×10-24 30×1024 6010 Ti+
10 Ti2+
10 Ti3+
1.8 0.68.2 1.211.8 1.6
10 ps
R = Ti2+ / Ti+