Zero beta limit

If we set all the thermal pressure terms in $E_{12}$ and $E_{22}$ to be zero (this is equivalent with setting $\gamma = 0$), the sound wave will be removed from the system. This approximation is called zero beta limit in literature[6]. Numerical results indicate the zero beta limit will remove all the sound continua. Compared with the slow sound approximation, the zero beta limit will make the frequency of the Alfven continua a little lower, and make the zeroth continua gaps (BAE gaps) disappear[7].