Negative Differential Resistance, Oscillations and Constrictions of Low Pressure, Low Current Discharges

Period doubling cascade in glow discharges: Local versus global differential conductivity

“…There is no systematic way to reduce this model to a simpler one [4,[15][16][17][18][19][20][21][22] with two scalar parameters such as voltage U and current J. We draw this conclusion both from direct analysis and from the occurence of period doubling in the numerical solutions.…”

“…(ii) A glow discharge in a simple electric circuit shows more complex behavior than can be expected from the proposed reaction-diffusion models [4,[15][16][17][18][19][20][21][22] for voltage U and current J with (global) negative differential conductivity dU / dJ Ͻ 0.…”

“…As a consequence of the differential equation (20) and the boundary condition (18), the electron current at position z now can be completely expressed by the instantaneous ion density at the boundary L and the field E between z and L as…”

“…Similar oscillations have been observed in Refs. [19,20,25,26], and similar effective models for current J and voltage U of the general form (1) have been proposed in Refs. [15,[19][20][21][22].…”

“…Negative differential conductivity of the glow discharge should then be the driving force of pattern formation. A number of authors [4,[15][16][17][18][19][20][21][22] actually have aimed at deriving such models from gas discharge physics, but not in a systematic manner.…”