Comment on "Weibel instability in a plasma with nonzero external magnetic field" by O. A. Pokhotelov and M. A. Balikhin, Ann. Geophysicae, 30, 1051–1054, (2012)

Abstract. In the reference (Ann. Geophysicae, 30, 1051–1054, (2012)), the dispersion relation of Weibel modes is explicitly calculated in magnetized plasma. The parameters of Weibel instability which are the Weibel mode frequency, 𝑅𝑒(𝜔), and the growth rate of the Weibel instability, 𝐼𝑚(𝜔) are deduced from the obtained dispersion relation under justified approximations.

Several errors, which affect the results, are identified in this reference (Ann. Geophysicae, 30, 1051–1054, (2012)). We are interested in the present work to correct these errors.

It has been shown that 𝐼𝑚(𝜔) remains the same that in the case of zero external magnetic field. However, 𝑅𝑒(𝜔), is proportional to the electron cyclotron frequency, ~ ∓ 𝜔𝑐 , and to the temperature anisotropy, ~ ∆TT_∥ = T_⊥ − T_∥T _∥ = (T_⊥T_∥ − 1), where T_⊥ and T_∥ are respectively the perpendicular and the parallel temperature.