Effect of Differential Flow of Alpha Particles on Proton Pressure Anisotropy Instabilities in the Solar Wind

In the solar wind, when the effects of proton–proton Coulomb collisions are negligible, alpha particles usually flow faster than the protons in such a way that the differential alpha–proton flow velocity V d = V α − V p is on the order of the Alfvén speed, is directed away from the Sun, and is nearly aligned with the local mean magnetic field. When this differential flow is taken into account, solutions of the hot plasma dispersion relation show that for the parallel propagating electromagnetic ion cyclotron (EMIC) instability driven by the proton temperature anisotropy T ⊥ p > T ∥ p , the maximum growth rate occurs in the + V d direction and for the parallel firehose instability driven by the opposite proton temperature anisotropy T ∥ p > T ⊥ p , the maximum growth rate occurs in the − V d direction. Thus, the EMIC instability preferentially generates left circularly polarized Alfvén-ion-cyclotron waves propagating away from the Sun and the parallel firehose instability preferentially generates right circularly polarized magnetosonic-whistler waves propagating toward the Sun with the maximum growth rates occurring for frequencies on the order of the proton cyclotron frequency and wavenumbers on the order of the proton inertial length. Because of the Doppler shift caused by the motion of the solar wind, both types of waves are left circularly polarized in the spacecraft frame for observations taken when the local mean magnetic field is collinear with the solar wind flow velocity. Theoretical investigation of these instabilities also shows that regions of parameter space exist where the unstable waves are generated propagating unidirectionally such as, for the EMIC instability for example, when the temperature anisotropy is small |( T ⊥ p / T ∥ p ) − 1| < 1. Taken together, the above properties can explain the origin of parallel propagating electromagnetic waves recently observed near the proton inertial length in high-speed solar wind. The observed waves are most likely produced in situ by these instabilities. A remarkable property of the proposed mechanism that may be of practical importance is that the magnetic helicity of the unstable waves has the same sign no matter whether the proton temperature anisotropy ( T p ⊥ / T p ∥ ) − 1 is positive or negative.