Magnetic Discontinuities in MHD Turbulence and in the Solar Wind

1. Magnetic Discontinuitiesin MHD Turbulence and in the Solar Wind Vladimir Zhdankin, UW-Madison CMSO, 10/20/2011 Stanislav Boldyrev, Jean Perez, Joanne Mason

2. Recall • Incompressible, forced MHD equations: • Dynamical quantities are magnetic field B and velocity field v

3. Magnetic discontinuities • Qualitatively: a location where magnetic field undergoes rapid spatial variation • Quantitatively: measure by fluctuations in magnetic field direction, i.e. angular shift, • Statistics of discontinuities yield insight to solar wind turbulence and intermittency

4. Possible sources of discontinuities • Flux tubes produced in the solar corona and then passively advected by the solar wind (Borovsky 2008, Miao et al., 2011) • Current sheets dynamically generated by turbulence (Greco et al., 2009) • Combination of these two mechanisms

5. J. Borovsky, J. Geophys. Res., 113, A08110 (2008)

6. Ulysses spacecraft B. Miao et al., Ann. Geophys., 29, 237 (2011)

7. To what extent can MHD turbulence explain these observations? • Analyze simulations of incompressible, forced MHD turbulence with various background magnetic fields, B0 • 5123 resolution, brms ~ 1, Re ~ 2000 • Reduced MHD for strong guide field • Full MHD for weak guide field • Measure angular shifts along lines perpendicular to guide field

8. Probability distribution of angular shifts, B0 = 1 (mesh size)

9. Probability distribution of angular shifts

10. Characteristic angle vs. magnetic field strength Power law fit:

11. Mean angular shift vs. magnetic field strength If P() assumed exponential, would expect

12. Typical fluctuation B0 Characteristic angle is Therefore the form of <> is unsurprising, but the power law form of *is very interesting. θ brms

13. Possible link to solar wind • We found that a population of small  occurs in the regime of large B0, while a population of large  occurs with small B0 • It is known that transition from weakly magnetized to strongly magnetized turbulence occurs near brms/B0 ~ 1/5 (e.g., Mason et al., 2006) • We propose that two populations of discontinuities may exist simultaneously in MHD, corresponding to these two scales

14. What is the relationship between magnetic discontinuities and the velocity field?

15. Velocity jump vs. angular shift

16. J. Borovsky, J. Geophys. Res., 113, A08110 (2008)

17. Structure functions • Structure functions are another statistical tool used to study intermittency • Define angular structure functions of order n, • Determine exponents ζn vs n • Any deviation from linearity indicates intermittency

18. Anomalous scaling of structure exponents

19. Conclusions • Found that probability distributions of angular shifts obey an exponential law, • This is independent of spatial increment, but depends on background magnetic field, • Two populations of angular shifts in the solar wind may correspond to two regimes of MHD • Angular shifts correlate with velocity jumps • MHD turbulence provides a robust explanation of magnetic discontinuities

20. References • J. Borovsky, J. Geophys. Res., 113, A08110 (2008) • B. Miao, B. Peng, and G. Li, Ann. Geophys., 29, 237 (2011) • A. Greco, W. Matthaeus, S. Servidio, P. Chuychai, and P. Dmitruk, Astrophs. J. Lett., 691, L111 (2009) • J. Mason, F. Cattaneo, and S. Boldyrev, Phys. Rev. Lett., 97, 255002 (2006).