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All Particle Simulation of a Cathodic Arc Plasma J. Cooper D. R. McKenzie

All Particle Simulation of a Cathodic Arc Plasma J. Cooper D. R. McKenzie. Tim Ruppin and Andrew Rigby. Traces left by an arc on tungsten cathode. Usually plasma production concentrated at cathode spots. Vacuum Arc. High Current, Low Voltage discharge in vacuum ambient

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All Particle Simulation of a Cathodic Arc Plasma J. Cooper D. R. McKenzie

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

  2. Traces left by an arc on tungsten cathode

  3. Usually plasma production concentrated at cathode spots Vacuum Arc • High Current, Low Voltage discharge in vacuum ambient • Current conducted in metal vapor plasma produced by discharge itself from evaporated electrode material 3

  4. Time Evolution of Cathode Spot Cell 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 Expanding hot dense plasma cell in non-thermal equilibrium layer Atoms ionized by electron impact or if density sufficient, self ionization Ion flow to anode New ion flow to cathode Micro-protrusions on cathode surface

  5. Cathodic arc plasma  Subspots (fragments)  Cells  Initial confinement of plasma L = 1×10-8 m V = 1×10-24 m3 Number of ions 10 to 100 Densitymax ~ 1026 ions.m3 Hot e-Te =3x104 K Cold ions

  6. All particle N body simulation Coulomb forces between electrons and ions Up > 0 Ue > 0 Upe < 0

  7. r(i, j, t) small  problems r(i, j, t)  r(i, j, t) +  Problem: Lots of particles – lots of calculations

  8. Can modify equations to include external electric and magnetic fields xj(t+1): qjExt2 FB = q vxB 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 /2mG2 = 1 / (1+G12)

  9. 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'; 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; qq = meshgrid(q,q)

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

  11. 10 ps 100 Ti+ 100 e-

  12. 10 ps 100 Ti+ 100 e-

  13. 0.10 ps 50 Ti+ 50 e-

  14. 10 ps 50 ions 50 e-

  15. 10 ps 100 Ti+ 100 e-

  16. 10 ps 100 Ti+ 100 e-

  17. 10 ps 100 Ti+ 100 e-

  18. 10 ps 1026 ion.m-3 Kavg ~ 3.8 eV Kavg(real) ~ 60 eV  1028 ion.m-3

  19. 10 ps R = Ti2+ / Ti+

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