  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.
