May 2005 Campaign Event: Introducing Turbulence

1. 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

2. 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.

3. 2008 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.

4. 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.

5. 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.

6. 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

7. 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

8. 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.

9. 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: Itot = I+ +I- I+ = Itot I-= (1 - )Itot 0< <1

10. 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.

11. Simulation Outline Magnetogram - driven steady-state solution of the solar corona (up to 24 Rs). Free parameters of the model and the uncertainties are: • Mass density at solar surface. • Magnetogram scaling factor. Spectrum: • fmin= 1x10-4Hz • fmax = 100 Hz (in accordance with Pontieu et. al. 2007) Roe solver scheme, adaptive mesh refinement. Initial grid resolution: 0.001 Rs near the Sun Currently the advection in frequency space is not presented.

12. Results - CR2029

13. Results - CR2029

14. 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 .

15. 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.