A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU

(Abridged) Turbulence in the solar wind is believed to generate an energy cascade that is supported primarily by Alfv'en waves or Alfv'enic fluctuations at MHD scales and by kinetic Alfv'en waves (KAWs) at kinetic scales $k_{\perp }{\rho }_i\gtrsim 1$. 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 $\mathrm{\mid }\gamma \mathrm{/}\omega \mathrm{\mid }\simeq 0.25$, where $\omega (k)$ and $\gamma (k)$ are, respectively, the real frequency and damping rate of KAWs and the ratio $\gamma \mathrm{/}\omega$ is evaluated in the limit as the propagation angle approaches 90 degrees relative to the direction of the mean magnetic field.