Model for designing planar magnetron cathodes

Planar magnetron cathodes have arching magnetic field lines which concentrate plasma density to enhance ion bombardment and sputtering. Typical parameters are: helium at 1 to 300 milli-torr, 200 to 2000 gauss at the cathode, 200 to 800 volts, and plasma density decreasing by up to ten times within 2 to 10 cm from the cathode. A 2D, quasineutral, fluid model yields formulas for the plasma density: n(x,y), current densities: j(x,y), j{sub e}(x,y), j{sub +}(x,y), the electric field: E{sub y}(y), and the voltage between the cathode surface and a distant plasma. An ion sheath develops between the cathode and the quasineutral flow. The thickness of this sheath depends on processes in the quasineutral flow. Experiments shows that T{sub e} (3 {yields} 8 eV) adjusts to ensure that {alpha}{sub 0}{tau} {approx} 2.5 in helium, for ionization rate {alpha}{sub 0} (10{sup 4} {yields} 10{sup 5} s{sup -1}), and electron transit time to the unmagnetized plasma {tau} (10 {yields} 100 {micro}s). Helium glow discharge cathode fall {alpha}{sub 0}{tau} is about 2.5, though this occurs at much higher voltage