7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Statistical and structural properties of Hall MHD turbulence

Hideaki Miura1, Sharad Kumar Yadav2, Keisuke Araki3, Rahul Pandit4, Toshiyuki Gotoh51National Institute for Fusion Science, 2 Sardar Vallabhbhai National Institute of Technology,
3Okayama University of Science, 4Indian Institute of Science, 5 Nagoya Institute of Technology
e-mail (speaker) : miura.hideaki@nifs.ac.jp
Hall magnetohydrodynamics (MHD) model is one ofextended MHD models which incorporate effects of theion skin-depth (or ion inertia scale) to the resistive MHD
model. The Hall MHD model has three importantparameters: ion skin-depth di, viscosity , and the current
resistivity . An important nature of the Hall MHD
model is that the ion skin-depth (the Hall) effects divide
the spatial scale into the macroscopy range (MHD scale)where the ion skin-depth effects are assumed being notvery important, and a high wavenumber region (subionicscale) where the Hall effects are pronounced. Hall MHD
turbulence is extensively studied in contexts of solar
wind studies as well as in the context of more
fundamental framework of turbulence studies.
We study homogeneous and isotropic Hall MHD
turbulence by means of numerical simulations [1-7]. A
typical influence of the Hall term can appear in a scale
smaller than the ion skin depth di. We carry out
simulations for some values of di =1/ki where the symbol
ki is the wave- number of the ion skin depth. The
numerical results are analyzed in views of the formationof energy flow in the wave-number space [1,2,6] as well
as of coherent structures and their contributions
statistical quantities [3-5,7]. More specifically, we areinterested in the scale-to-scale interactions in themagnetic and velocity fields. To study the scale-to- scaleinteraction, we carry out numerical simulations of themagnetic Prandtl number PrM= unity as well as ahigh PrM and compare differences between them.

compared among simulations of various PrM and ion skindepth di.
Spatial structure and intermittency in our numericalsimulations are discussed in the context of studies ofsolar wind turbulence and other kind of turbulence.
References[1] H. Miura and K. Araki, Phys. Plasmas 21, 072313(2014).
[2] K. Araki and H. Miura, Plasma Fusion Res. 10,3401030 (2015).
[3] H. Miura, K. Araki, and F. Hamba, J. Comput.
Physics 316, 385-395 (2016).
[4] H. Miura, Fluids 4, No.4 (2019).
[5] K. Araki and H. Miura, Plasma Fusion Res. 15,2401024 (2020).
[6] S.K.Yadav, H.Miura, R.Pandit, Phys. Fluids 34,095135 (2022) .
[7] H. Miura and T. Gotoh, IUPAP Conference ofComputational Physics 2023 (4-8 August 2023, Kobe,Japan).

In Fig.1, structure function of the velocity field in HallMHD turbulence with PrM=100 [7],where 𝑢 is the i-th component of the velocity field.
The structure functions represent two-scaling regimes,characterizing its intermittent spatial structure. Structure
functions, especially of the 3rd-order, are closely relatedwith the von Karman-Howarth equation for homogeneous and isotropic turbulence in hydrodynamic
turbulence, and with that for MHD and Hall MHD
turbulence as well. We will present analysis of ournumerical data (both PrM=1 and PrM=100) in the contextof turbulence theory related with the vKH equation.
The intermittency nature of turbulence is considered tooriginate from localized spatial structures of both themagnetic and velocity fields. Spatial structures are

Figure 1: Structure function 𝑆 (𝑙) of the velocity fieldin Hall MHD turbulence with PrM=100.

Figure 2: Isosurface of the enstrophy density 𝜔 /2 inthe Hall MHD simulation with PrM=1.