Consider the following closed set of MHD equations in the so-called Chew, Goldberger, and Low approximation,

In the equations of this set, involving the pressure tensor P, it is considered that

(a) Taking the equilibrium mean velocity equal to zero, show that the dispersion relation for the magnetohydrodynamic waves can be written as

where θ is the angle between k and B₀, and where p_∥ , p_⊥, and B₀ stand for the unperturbed quantities.

(b) Show that these waves are unstable for all values of θ less than a critical angle θ_c, which satisfies the equation

Transcribed Image Text:

apm + V. (Pmu) = 0 Ət Pm Du = PE - (P₁ +2²) + (B-v) [(-__-_P₁-P¹) B] Dt B² PIB² ) = D Dt Pm a) ² PL D()=0 Dt Pm B. V x B = μοJ VXE = - = 0 V.E = ƏB Ət P €0 E+ux B=0