Abstract
In the presence of a strong magnetic field, disturbances travel along magnetic field lines. In most theories for strongly magnetized turbulence, collisions between opposite-traveling wave packets (or ‘eddies’) are essential for energy cascade. In those theories, it is generally assumed that only interactions between similar-size eddies are important. That is, most magnetohydrodynamic (MHD) turbulence models assume scale-locality of energy cascade. In this paper, we show that collisions between different size eddies, especially between outer scale eddies and smaller eddies, are also important and discuss how this non-locality affects energy spectrum. We also discuss dynamics of electron MHD (EMHD) wave packets (a.k.a. whistler wave packets). We show that EMHD wave packets moving in one direction can cascade energy through self-interactions and that they exhibit inverse energy cascade.
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Notes
- 1.
Here ρ is the density and k is the wavenumber. In this paper, we use the following convention: magnetic field B actually means \(\mathbf{B}/\sqrt{4\pi \rho }\). Thus, the field B is in fact the Alfvénic velocity. For Alfvenic perturbations (in ordinary MHD), we have v ∼ b, where \(\mathbf{B} ={ \mathbf{B}}_{0} + \mathbf{b}\) and b is the fluctuating field. For whistler perturbations (in EMHD), we have v ∝ kb.
- 2.
We note that the ratio for MHD gradually decreases as k increases. Although it is not very clear at this moment whether it will continue to drop when we have a very long inertial range, it is likely that the ratio will continue to drop and the non-local effects of the outer scale will ultimately vanish on very small scales. If this is true, we will recover a Kolmogorov spectrum on very small scales (see a related work in [1]).
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Acknowledgements
This research was supported by National R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-0018751).
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Cho, J. (2012). Interaction of Wave Packets in MHD and EMHD Turbulence. In: Leubner, M., Vörös, Z. (eds) Multi-scale Dynamical Processes in Space and Astrophysical Plasmas. Astrophysics and Space Science Proceedings, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30442-2_19
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DOI: https://doi.org/10.1007/978-3-642-30442-2_19
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