# PSP Bibliography

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An approximate analytic solution to the coupled problems of coronal heating and solar-wind acceleration

 Author Chandran, Benjamin; Keywords astrophysical plasmas; space plasma physics; Astrophysics - Solar and Stellar Astrophysics; Physics - Plasma Physics; Physics - Space Physics; Parker Data Used Abstract Between the base of the solar corona at $r=r_\textrm b$ and the Alfvén critical point at $r=r_\textrm A$, where $r$ is heliocentric distance, the solar-wind density decreases by a factor $\mathop > \limits_∼ 10^5$, but the plasma temperature varies by a factor of only a few. In this paper, I show that such quasi-isothermal evolution out to $r=r_\textrm A$ is a generic property of outflows powered by reflection-driven Alfvén-wave (AW) turbulence, in which outward-propagating AWs partially reflect, and counter-propagating AWs interact to produce a cascade of fluctuation energy to small scales, which leads to turbulent heating. Approximating the sub-Alfvénic region as isothermal, I first present a brief, simplified calculation showing that in a solar or stellar wind powered by AW turbulence with minimal conductive losses, $\dot M ∼eq P_\textrm AW(r_\textrm b)/v_\textrm esc^2$, $U_\infty ∼eq v_\textrm esc$, and $T∼eq m_\textrm p v_\textrm esc^2/[8 k_\textrm B \ln (v_\textrm esc/δ v_\textrm b)]$, where $\dot M$ is the mass outflow rate, $U_\infty$ is the asymptotic wind speed, $T$ is the coronal temperature, $v_\textrm esc$ is the escape velocity of the Sun, $δ v_\textrm b$ is the fluctuating velocity at $r_\textrm b$, $P_\textrm AW$ is the power carried by outward-propagating AWs, $k_\textrm B$ is the Boltzmann constant, and $m_\textrm p$ is the proton mass. I then develop a more detailed model of the transition region, corona, and solar wind that accounts for the heat flux $q_\textrm b$ from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for $q_\textrm b$ by balancing conductive heating against internal-energy losses from radiation, $p \textrm d V$ work, and advection within the transition region. The density at $r_\textrm b$ is determined by balancing turbulent heating and radiative cooling at $r_\textrm b$. I solve the equations of the model analytically in two different parameter regimes. In one of these regimes, the leading-order analytic solution reproduces the results of the aforementioned simplified calculation of $\dot M$, $U_\infty$, and $T$. Analytic and numerical solutions to the model equations match a number of observations. Year of Publication 2021 Journal Journal of Plasma Physics Volume 87 Number of Pages 905870304 Section Date Published 05/2021 ISBN URL https://ui.adsabs.harvard.edu/abs/2021JPlPh..87c9004C DOI 10.1017/S0022377821000052