A Kinetic Alfvén Wave Cascade Subject to Collisionless Damping Cannot Reach Electron Scales in the Solar Wind at 1 AU

Abstract

Turbulence in the solar wind is believed to generate an energy cascade that is supported primarily by Alfvén waves or Alfvénic fluctuations at MHD scales and by kinetic Alfvén waves (KAWs) at kinetic scales k _bottomρ _i >~ 1. Linear Landau damping of KAWs increases with increasing wavenumber and at some point the damping becomes so strong that the energy cascade is completely dissipated. A model of the energy cascade process that includes the effects of linear collisionless damping of KAWs and the associated compounding of this damping throughout the cascade process is used to determine the wavenumber where the energy cascade terminates. It is found that this wavenumber occurs approximately when |γ/ω| ~= 0.25, where ω(k) and γ(k) are, respectively, the real frequency and damping rate of KAWs and the ratio γ/ω is evaluated in the limit as k _bottom Gt k _par. For plasma parameters typical of high-speed solar wind streams at 1 AU, the model suggests that the KAW cascade in the solar wind is almost completely dissipated before reaching the wavenumber k _bottomρ _i ~= 25. Consequently, an energy cascade consisting solely of KAWs cannot reach scales on the order of the electron gyro-radius, k _bottomρ _e ~ 1. This conclusion has important ramifications for the interpretation of solar wind magnetic field measurements. It implies that power-law spectra in the regime of electron scales must be supported by wave modes other than the KAW.