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\label{eqn:spectrum}  \frac{d \dot{E}_0(\omega)}{d\omega} \sim \frac{\dot{E}_0}{\omega_c} \left(\frac{\omega}{\omega_c}\right)^{-a},  \end{equation}  where $a$ is the slope of the frequency spectrum, which is somewhat uncertain. As in F14, we expect a spectrum slope in the range $3 \lesssim a \lesssim 7$. 7$, and we use a value of $a=4.5$ in our calculations.  Lower frequency waves have shorter wavelengths and slower group velocities, making them more prone to both radiative and non-linear damping. Thus, as waves propagate inwards, low frequency waves may damp out, and increasing the wave frequency $\omega_*$ of waves that dominate AM transport. F14 show that radiative damping leads to   \begin{equation}