Negative energy waves and quantum relativistic Buneman instabilities

The quantum relativistic Buneman instability is investigated theoretically using a collective Klein-Gordon model for the electrons and a cold fluid model for the ions. The growth rate and unstable wave spectrum is investigated in different parameter regimes corresponding to various degrees of relativistic and quantum effects. The results may be important for streaming instabilities involving ion dynamics in very dense plasmas.

Figure 1

Characteristic function $F=F(\omega ,k)$ from Eq. (8) in the nonquantum case, showing a generic unstable equilibrium when $F_{\min }>1$.

Figure 2

Characteristic function $F=F(\omega ,k)$ from Eq. (21) in the nonrelativistic case, showing a generic stable equilibrium when $F_{\min }<1$. In the graphic, ${\omega }_{\pm }=kv\pm \hslash k^2/\left(2m\right)$.

Figure 3

Functions ${\theta }_{\pm }$ from Eq. (27). Bottom, line: ${\theta }_{+}$. Upper, dashed: ${\theta }_{-}$.

Figure 4

The filled area shows the allowable values of the quantum parameter $H$ in terms of $\beta =v/c$, as found from Eq. (45).

Figure 5

Functions ${\zeta }_{\pm }(H,\gamma )$ from Eq. (47). In all plots, the dashed curve is ${\zeta }_{-}(H,\gamma )$, while ${\zeta }_{+}(H,\gamma )$ is the other one. Parameters are (a) upper left, $\gamma =1.5$; (b) upper right, $\gamma =2.0$; (c) bottom left, $\gamma =2.5$; (d) bottom right, $\gamma =3.0$.