Electron temperature anisotropy instabilities: Whistler, electrostatic and z mode

An electron temperature anisotropy T ⊥ e / T ‖ e > 1 leads to excitation of three distinct instabilities in collisionless plasmas at frequencies below the electron cyclotron frequency |Ω e | (Here ⊥ and ‖ denote directions relative to the background magnetic field B 0 .). Linear Vlasov theory is used to study these growing modes, with emphasis on the scaling of the temperature anisotropy at instability threshold. If the electron plasma frequency ω e is greater than |Ω e | and electrons are sufficiently hot, the whistler is the unstable mode with smallest anisotropy threshold; this electromagnetic mode has maximum growth rate at propagation parallel to B 0 . At ω e > 0.5|Ω e |, an electrostatic electron anisotropy instability can arise at propagation oblique to B 0 ; this mode may have the smallest threshold for sufficiently cool electrons and ω e ∼ |Ω e |. And T ⊥ e / T ‖ e > 1 drives the z mode unstable at ω e < |Ω e |; this electromagnetic mode also has maximum growth rate at parallel propagation and is the persistent instability at ω e ≲ 0.5|Ω e |. The results are discussed in connection with observations from the polar and auroral regions of the terrestrial magnetosphere.