R. Oran csem.engin.umich.edu SHINE 09 May 2005 Campaign Event: Introducing Turbulence Rona Oran Igor V. Sokolov Richard Frazin Ward Manchester Tamas I. Gombosi CSEM, University of Michigan Ofer Cohen HSCA

R. Oran csem.engin.umich.edu SHINE 09 Summary of Results from SHINE 2008 Out of equilibrium flux rope model superposed on a steady state MHD corona. The dynamical solution presented had good agreement with the shock arrival time to earth.

R. Oran csem.engin.umich.edu SHINE Results Revisited However… Steady state solution highly criticized for use of variable polytropic index. The polytropic model, although it achieved good agreement with ambient solar wind observed at 1AU, is not self - consistent and distort the physics, especially at shocks. Work done on thermodynamic MHD models, most prominently by the SAIC group (see Lionello, Linker and Mikic, 2009) inspire further attempts at a self - consistent model which will improve the physical basis for our solution.

R. Oran csem.engin.umich.edu SHINE 09 Introducing Alfven Waves Turbulence Turbulent MHD waves have been suggested in the past as a possible mechanism both to heat the corona and to accelerate the solar wind. Hinode observations suggest energy input is sufficient to drive the solar wind acceleration and heating (e.g. Pontiue et. al. 2007). Heating : Alfven wave dissipation at cyclotron frequency ( likely intensified by the energy cascade process). Wind acceleration : work done by wave pressure gradient force.

R. Oran csem.engin.umich.edu SHINE 09 MHD - Wave Turbulence Model We employ a wave kinetic approach for describing the transport of MHD waves in a background MHD plasma. The wave transport equation for narrow band wave trains is given by: here I is the wave energy spatial and spectral density and  is a specific wave mode. Advantage: describes the spectral evolution.

R. Oran csem.engin.umich.edu SHINE 09 Modified MHD Equations Background momentum equation: Background energy equation: Where P  is the wave stress spectral density. wave stress gradient force Work done by wave stress wave energy dissipation

R. Oran csem.engin.umich.edu SHINE 09 WT Equation - Low Frequency Alfven Waves In this limit the wave stress spectral density becomes: Thus the pressure is scalar and the total wave pressure is: The WT equation takes the form: 2-way coupling of the WT equation to the MHD equations : Wave pressure acts on the background flow, while background solution determines wave propagation and spectral evolution. Advection in space Advection in frequency Dissipation

R. Oran csem.engin.umich.edu SHINE 09 Computational Model The WT equation is fully coupled to the BATSRUS code in the SWMF. The spatial grid is a 3D block adaptive Cartesian grid. In each spatial cell we construct a uniform frequency grid whose range / resolution is defined by the user. Both parallel and anti-parallel propagating waves are considered (currently share the same grid). Solution of WT equation is performed by Strang splitting of the spatial and frequency operators. The solution in 2nd order accurate in space, time and frequency.

R. Oran csem.engin.umich.edu SHINE 09 Model Inputs Magnetogram driven potential field extrapolation. Spectrum: Can be defined by the user. This allows the testing of various theories by comparing results to observations. In the current work, we assume a Kolmogorov spectrum as the initial condition, i.e. I  k -5/3 (in accordance with observations of mean-free-path of protons in the heliosphere). The initial distribution in space can be rather arbitrary, since it quickly advects according to the MHD state. Level of imbalance: I tot = I + + I - I + =  I tot I - = (1 -  )I tot 0<  <1

R. Oran csem.engin.umich.edu SHINE 09 Inner Boundary Conditions Radial magnetic field - high resolution MDI magnetogram data provided by Y. Liu, Stanford. Specify Alfven waves Poynting vector at 1Rs: Solar wind expansion factors WSA model terminal velocity at 1AU Impose conservation of energy along flux tubes (Suzuki, 2006) In-going waves which reach the inner boundary are absorbed.

R. Oran csem.engin.umich.edu SHINE 09 Magnetogram - driven steady-state solution of the solar corona (up to 24 R s ). Free parameters of the model and the uncertainties are: Mass density at solar surface. Magnetogram scaling factor. Spectrum: f min = 1x10 -4 Hz f max = 100 Hz (in accordance with Pontieu et. al. 2007) Roe solver scheme, adaptive mesh refinement. Initial grid resolution: R s near the Sun Currently the advection in frequency space is not presented. Simulation Outline

R. Oran csem.engin.umich.edu SHINE 09 Results - CR2029

R. Oran csem.engin.umich.edu SHINE 09 Results - CR2029

R. Oran csem.engin.umich.edu SHINE 09 Conclusions First calculations in the SWMF of a steady state solar corona/ solar wind which is entirely driven by Alfven wave pressure and the boundary conditions fully driven by the WSA model. Fast solar wind speeds are too high - conversion rate of wave energy into heating is too low. This might be solved when we take the wave dissipation into account. Compared to the previous polytropic model, we can now describe the corona self - consistently without distorting the physics, especially shock wave compression ratio which depend on .

R. Oran csem.engin.umich.edu SHINE 09 Future Work Repeat our dynamical simulation of the CME with the emphasis on more realistic shock wave: Full implementation of spectral evolution Extend the model to the Inner Heliosphere (IH) model to enable comparison of results to observations at 1AU.