Linear and Nonlinear Effects of Proton Temperature Anisotropy on Proton-beam Instability in the Solar Wind

Solar wind observations have shown that the drift velocity of the proton beam relative to the background proton is of the order of the local Alfvén velocity. The proton-beam instability has been suggested to play an important role in decelerating proton beams. Most existing studies examined the kinetic properties of the proton-beam instability in simple Maxwellian or drift-Maxwellian plasmas. In this paper, we systemically investigate the effects of the proton temperature anisotropy on the growth rates of proton-beam instabilities using linear Vlasov equations and the nonlinear evolution of these instabilities at different propagation angles using 1D and 2D hybrid simulations. The results show that the real frequencies, growth rates, and threshold conditions strongly depend on the proton temperature anisotropy Ti⊥/Ti∣∣ and the parallel proton beta βi∣∣ . The parallel magnetosonic/whistler (M/W), backward M/W, and oblique Alfvén/ion-cyclotron (A/IC) instabilities are likely to grow in the regime of Ti⊥/Ti∣∣<1 , whereas the parallel M/W, oblique A/IC, parallel A/IC, and mirror instabilities tend to be excited in the regime of Ti⊥/Ti∣∣>1 . Moreover, the oblique A/IC instability with a linear wave growth phase can quickly reduce the proton-beam drift velocity when Ti⊥/Ti∣∣<1 , while the nonlinear wave–particle interaction for the parallel A/IC and mirror instabilities tends to gradually reduce the drift velocity when Ti⊥/Ti∣∣>1 . The linear and nonlinear evolution of the proton-beam instability associated with the proton temperature anisotropy can be used to explain the observed dependence of the proton-beam drift velocity on the plasma beta and temperature anisotropy in the solar wind.

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