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All Particle Simulation of a Cathodic Arc Plasma I.J. Cooper D. R. McKenzie Tim Ruppin and Andrew Rigby

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Traces left by an arc on tungsten cathode

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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

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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

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Cathodic arc plasma Subspots (fragments) Cells Initial confinement of plasma L = 1×10 -8 m V = 1×10 -24 m 3 Number of ions 10 to 100 Density max ~ 10 26 ions.m 3 Hot e - T e =3x10 4 K Cold ions

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All particle N body simulation Coulomb forces between electrons and ions U p > 0 U e > 0 U pe < 0

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r(i, j, t) small problems r(i, j, t) r(i, j, t) + Problem: Lots of particles – lots of calculations

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Can modify equations to include external electric and magnetic fields x j (t+1): q j E x t 2 F B = q v x B B x =0, B y = 0, B z v z = 0 x(t+1): G 2 [2x(t) + (G 1 2 -1)x(t-1) + 2G 1 y(t) – 2G 1 y(t-1)] G 1 = t B z /2m G 2 = 1 / (1+G 1 2 )

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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 N steps ~ 10 7 :

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SIMULATIONS single, multiple and mixed charged states H C Ti 10 ps 50 Ti + 50 e -

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10 ps 100 Ti + 100 e -

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10 ps 100 Ti + 100 e -

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0.10 ps 50 Ti + 50 e -

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10 ps 50 ions 50 e -

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10 ps 100 Ti + 100 e -

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10 ps 100 Ti + 100 e -

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10 ps 100 Ti + 100 e -

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10 ps 10 26 ion.m -3 K avg ~ 3.8 eV K avg(real) ~ 60 eV 10 28 ion.m -3

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Initial Volume (m 3 ) Initial Ion density (ion.m -3 ) No. of e - No. of Ti ions Average ion KE (eV) 1.0×10 -24 100×10 24 100100 Ti + 3.8 0.5 1.0×10 -24 30×10 24 3030 Ti + 1.7 0.6 1.0×10 -24 30×10 24 6030 Ti 2+ 9.6 1.2 1.0×10 -24 30×10 24 60 10 Ti + 10 Ti 2+ 10 Ti 3+ 1.8 0.6 8.2 1.2 11.8 1.6

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10 ps R = Ti 2+ / Ti +

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