Abstract
High-intensity discharge (HID) lamps are highly efficient light sources with many applications. Depending on the dimensions or geometry of the electrode, lamp current, and waveforms, the plasma may attach to the cathode in a diffuse mode that covers the electrode tip surface or a localized mode where heating and current transfer occur in a local region of the electrode surface. The localized mode is often deleterious to lamp operation because the electrode becomes locally overheated. First order perturbation theory is applied to ac operation to determine the stability of the time-dependent cathode diffuse mode in an adiabatic approximation. As a first step towards understanding ac mode changes, we apply the results to study diffuse to localized 2D and 3D mode transitions for a rod electrode with lateral insulating sides. The linear stability theory is compared with simulations using commercial finite-element software. We show that the stability condition can be inferred from time-integrated rate-constants of the unstable eigenmodes over the ac cycle.
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