GLYPH<Minus> 10 GLYPH<Minus> 5 5 10 GLYPH<CapOmega> GLYPH<Minus> 4 GLYPH<Minus> 2 2 4 $^{Ε}$GLYPH<LParen1>$^{GLYPH<CapOmega>}$GLYPH<RParen1> GLYPH<LParen1> a GLYPH<RParen1> , K GLYPH<Equal> 2 GLYPH<Minus> 6 GLYPH<Minus> 4 GLYPH<Minus> 2 2 4 6 GLYPH<CapOmega> GLYPH<Minus> 2 GLYPH<Minus> 1 1 2 $^{Ε}$GLYPH<LParen1>$^{GLYPH<CapOmega>}$GLYPH<RParen1> GLYPH<LParen1> b GLYPH<RParen1> , K GLYPH<Equal> 3 GLYPH<Minus> 10 GLYPH<Minus> 5 5 10 GLYPH<CapOmega> GLYPH<Minus> 4 GLYPH<Minus> 2 2 4 $^{Ε}$GLYPH<LParen1>$^{GLYPH<CapOmega>}$GLYPH<RParen1> GLYPH<LParen1> c GLYPH<RParen1> , K GLYPH<Equal> 4 FIG. 3: Dispersion function according to Eq. (8) H = 0 . 6, θ = π/ 6 and K = 2 (a), K = 3 (b) and K =4 (c). 0.5 1.0 1.5 2.0 2.5 3.0 Kz 0.5 1.0 1.5 Kx FIG. 4: Plot of K ∗ (yellow), K − (blue) and K + (purple) given by Eqs. (12–13). K − = K + for θ $_{= arccos}$√$_{H}$$_{. Wave vectors between the two frontiers are unstable.}$ K − ( θ ) are unstable. The unstable domain defined by Eqs. (12–13) is graphically summarized in Figure 4 when one recognizes immediately the domain outlined in Figs. 1. It turns out that the dispersion equation from Eq. (8) is biquadratic and can be solved exactly for any parameter set. In terms of Ω $^{2}$, the two roots are, Unstable modes clearly arises from Ω 2 $_{1}$, since Ω 2 $_{2}$> 0 for any parameters. Of course, the sign analysis of Ω 2 1 yields the unstable domain already explained. Analytic results are acessible not only in the electrostatic approximation. Indeed, allowing for magnetic field perturbations and following the steps outlined in Section II, the exact Ω 2 1 = 1 4 [ 2 + 4 K 2 z + H 2 ( K 2 x + K 2 z ) 2 − 2 √ 1 + 4 K 2 z [ 2 + H 2 ( K 2 x + K 2 $_{z}$) $^{2}$] ] , Ω 2 2 = 1 4 2 + 4 K 2 z + H 2 K 2 x + K 2 z 2 + 2 1 + 4 K 2 z 2 + H 2 ( K 2 x + K 2 $_{z}$) . (14) IV. GROWTH RATE ANALYSIS 7