ABSTRACT
The propagation equation (2) takes the form of the first equation of the system (3). The second equation is the boundary condition ( is a unitary outward pointing vector).
Ap„(r)+ 60
2 p0( 2 _
r)= 0 c,
ii . p„(T)= 0 (3)
This system of equations can be solved only for discrete values of co. This pulsation is consequently written to,„„, with 1,m,n integers. As:
the frequencies fi„. are called eigenfrequencies. This means that the acoustic wave can take place in the plasma only if the excitation frequency corresponds to one of the discrete values of the solutions for co„n . The whole solutions for w can be seen as a spectrum of frequencies depending only on the sound velocity and on the geometrical dimensions of the discharge tube. The system of equations (3) was implemented in a finite element method software, Femlab, with a tube geometry of a 400W mercury lamp. The sound velocity was calculated using a temperature profile from a stationary high pressure mercury lamp model. The computation was limited in frequency to 20kHz and the calculated spectrum of eigenfrequencies is presented in figure 3.
