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Register a new userThe Theory of Heating of the Solar Corona and Launching of the Solar Wind by Alfven Waves
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Authors
A. M. Varonov
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State-of-the-art MHD calculations reveal acceptable agreement with observational data for the height profile of the temperature $T(h)$ in the transition region of solar corona. Simultaneously, the velocity of the solar wind $U(h)$ has also been calculated. The developed method gives the possibility at given frequency dependent spectral density of Alfven waves (AW) coming from chromosphere $mathcal{W}(omega)$ to calculate both height profiles $T(h)$ and $U(h)$. In agreement with the concepts of the self-induced opacity of plasma with respect of AW, the narrow width $lambda$ of the transition region is determined by the fast temperature increase of the viscosity $eta(T,B)$. After more than 70 years of development of Solar physics, the Alfven hypothesis of heating of the solar corona by AW has remained without alternatives; none of other mechanisms can explain $ab$ $initio$ the value of $lambda$. The performed MHD analysis explains the height dependence of the non-thermal broadening of the chromospheric spectral lines and predicts angular dependence of this broadening with respect of position in solar disc. One can expect significant impact of MHD analysis in the interpretation of the long expected data from Parker Solar Probe.
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A three-dimensional MHD model for the propagation and dissipation of Alfven waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100 km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfven waves using the reduced MHD approximation. The increase of Alfven speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheric and chromospheric parts of the flux tube. Part of the wave energy is transmitted through the TR and produces turbulence in the corona. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfven wave turbulence, provided the small-scale footpoint motions have velocities of 1-2 km/s and time scales of 60-200 s. The heating rate per unit volume in the chromosphere is 2 to 3 orders of magnitude larger than that in the corona. We construct a series of models with different values of the model parameters, and find that the coronal heating rate increases with coronal field strength and decreases with loop length. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfvenic turbulence.
We perform 2.5D hybrid simulations with massless fluid electrons and kinetic particle-in-cell ions to study the temporal evolution of ion temperatures, temperature anisotropies and velocity distribution functions in relation to the dissipation and turbulent evolution of a broad-band spectrum of parallel and obliquely propagating Alfven-cyclotron waves. The purpose of this paper is to study the relative role of parallel versus oblique Alfven-cyclotron waves in the observed heating and acceleration of minor ions in the fast solar wind. We consider collisionless homogeneous multi-species plasma, consisting of isothermal electrons, isotropic protons and a minor component of drifting $alpha$ particles in a finite-$beta$ fast stream near the Earth. The kinetic ions are modeled by initially isotropic Maxwellian velocity distribution functions, which develop non-thermal features and temperature anisotropies when a broad-band spectrum of low-frequency non-resonant, $omega leq 0.34 Omega_p$, Alfven-cyclotron waves is imposed at the beginning of the simulations. The initial plasma parameter values, such as ion density, temperatures and relative drift speeds, are supplied by fast solar wind observations made by the textit{Wind} spacecraft at 1AU. The imposed broad-band wave spectra is left-hand polarized and resembles textit{Wind} measurements of Alfvenic turbulence in the solar wind. The imposed magnetic field fluctuations for all cases are within the inertial range of the solar wind turbulence and have a Kraichnan-type spectral slope $alpha=-3/2$. We vary the propagation angle from $theta= 0^circ$ to $theta=30^circ$ and $theta=60^circ$, and find that the minor ion heating is most efficient for the highly-oblique waves propagating at $60^circ$, whereas the protons exhibit perpendicular cooling at all propagation angles.
We solve numerically the ideal MHD equations with an external gravitational field in 2D in order to study the effects of impulsively generated linear and non-linear Alfven waves into isolated solar arcades and coronal funnels. We analyze the region containing the interface between the photosphere and the corona. The main interest is to study the possibility that Alfven waves triggers the energy flux transfer toward the quiet solar corona and heat it, including the case that two consecutive waves can occur. We find that in the case of arcades, short or large, the transferred fluxes by Alfven waves are sufficient to heat the quiet corona only during a small lapse of time and in a certain region. In the case of funnels the threshold is achieved only when the wave is faster than 10 km/s, which is extremely high. We conclude from our analysis, that Alfven waves, even in the optimistic scenario of having two consecutive Alfven wave pulses, cannot transport enough energy as to heat the quiet corona.
The solar corona is a complex system, with nonisothermal plasma and being in the self-gravitating field of the Sun. So the corona plasma is not only a nonequilibrium system but also a nonextensive one. We estimate the parameter of describing the degree of nonextensivity of the corona plasma and study the generalization of the solar wind speed theory in the framework of nonextensive statistical mechanics. It is found that, when use Chapmans corona model (1957) as the radial distribution of the temperature in the corona, the nonextensivity reduces the gas pressure outward and thus leads a significant deceleration effect on the radial speed of the solar wind.
To properly describe heating in weakly collisional turbulent plasmas such as the solar wind, inter-particle collisions should be taken into account. Collisions can convert ordered energy into heat by means of irreversible relaxation towards the thermal equilibrium. Recently, Pezzi et al. (Phys. Rev. Lett., vol. 116, 2016, p. 145001) showed that the plasma collisionality is enhanced by the presence of fine structures in velocity space. Here, the analysis is extended by directly comparing the effects of the fully nonlinear Landau operator and a linearized Landau operator. By focusing on the relaxation towards the equilibrium of an out of equilibrium distribution function in a homogeneous force-free plasma, here it is pointed out that it is significant to retain nonlinearities in the collisional operator to quantify the importance of collisional effects. Although the presence of several characteristic times associated with the dissipation of different phase space structures is recovered in both the cases of the nonlinear and the linearized operators, the influence of these times is different in the two cases. In the linearized operator case, the recovered characteristic times are systematically larger than in the fully nonlinear operator case, this suggesting that fine velocity structures are dissipated slower if nonlinearities are neglected in the collisional operator.
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