# High-Intensity Discharge Lamp and Duffing Oscillator - Similarities and Differences

## TL;DR

This paper models the nonlinear behavior of high-intensity discharge lamps using finite element simulations, revealing hysteresis and jump phenomena similar to a Duffing oscillator but with notable differences such as a stiffening effect at large amplitudes.

## Contribution

It provides a detailed nonlinear simulation model of HID lamps and compares their dynamic behavior to that of a Duffing oscillator, highlighting key similarities and differences.

## Key findings

- HID lamps exhibit hysteresis and jump phenomena similar to Duffing oscillators.
- The nonlinear behavior includes a stiffening effect at large amplitudes.
- Differences between HID lamps and Duffing oscillators are discussed.

## Abstract

The processes inside the arc tube of high-intensity discharge lamps are investigated by finite element simulations. The behavior of the gas mixture inside the arc tube is governed by differential equations describing mass, energy and charge conservation as well as the Helmholtz equation for the acoustic pressure and the Navier-Stokes equation for the flow driven by the buoyancy and the acoustic streaming force. The model is highly nonlinear and requires a recursion procedure to account for the impact of acoustic streaming on the temperature and other fields. The investigations reveal the presence of a hysteresis and the corresponding jump phenomenon, quite similar to a Duffing oscillator. The similarities and, in particular, the differences of the nonlinear behavior of the high-intensity discharge lamp to that of a Duffing oscillator are discussed. For large amplitudes the high-intensity discharge lamp exhibits a stiffening effect in contrast to the Duffing oscillator.