Two-way coupled MHD-PIC simulations of magnetic reconnection in magnetic island coalescence

Abstract

Abstract. We present simulations of magnetic reconnection with a newly developed coupled MHD-PIC code. In this work a global magnetohydrodynamic (MHD) simulation receives kinetic feedback within an embedded region that is modeled by a kinetic particle-in-cell (PIC) code. The PIC code receives initial and boundary conditions from the MHD simulation, while the MHD solution is updated with the PIC state. We briefly describe this coupling mechanism. This method is suitable for simulating magnetic reconnection problems, as we show with the example of reconnection in the coalescence of magnetic islands. We compare the MHD, Hall-MHD, fully PIC and coupled MHD-PIC simulations of the magnetic island coalescence. We find that the kinetic simulations are very different from the MHD and Hall-MHD results, while the coupled MHD-PIC simulations can remedy this discrepancy while saving computing time. The diffusion region is well resolved in the kinetic simulations, which is also captured by the coupled MHD-PIC model. The coupled simulation also reproduces the kinetic Hall magnetic fields correctly. We calculate the reconnection rates and find differences between the MHD and kinetic results. We find that the coupled MHD-PIC code can reasonably reproduce the kinetic reconnection rate when a larger PIC feedback region is used, while still saving significant computing time. IntroductionSimulating plasmas is a very challenging task because plasma processes are multi-scale as well as multi-physics in nature. For example, turbulence can be driven at large scales by fluid processes, like solar flares or some magnetohydrodynamic (MHD) instabilities. The nonlinear interactions at the high Reynolds and Lundquist numbers in space and astrophysical plasmas give rise to energy transfer to multiple scales, going right down to the ion and electron scales, which are several orders of magnitude smaller [1, 2] than the driving scales. In solar corona MHD processes operate at 10 9 m while electron scales lie at 10 −1 m [3]. Similarly in Earth's magnetosphere the solar wind driver operates at 10 9 m while electron scales lie at 10 3 m [4]. Simulating this range of scales is not possible even with the computing facilities of foreseeable future. However, an even greater challenge is that while the plasma can be treated as a fluid at the largest scales, the kinetic, particulate nature of plasma becomes critical at the small scales. MHD models are fluid models which work at scales larger than the ion gyroradius or skin depth [5] and are computationally ideal for global simulations. However, they do not capture the kinetic physics that results from the particulate nature of plasma. The Maxwell-Vlasov equations are typically used to describe a plasma kinetically and many advanced particle-in-cell (PIC) techniques have been developed to simulate them. However, these are significantly more

Grad-Shafranov equation: MHD simulation of the new solution obtained from the Fadeev and Naval models

“…Fadeev's model in an MHD simulation shows that initially the only place where particles could diffuse is the X-type point through magnetic reconnection (Makwana et al, 2018). On the other hand, excluding the x-axis from our model, in each region (z < 0 and z > 0) there are two X-points instead of one.…”

Rotation and Confined Eruption of a Double Flux-rope System

“…Moreover, it is noted that the two adjacent flux ropes have the same sign of the parallel electric current and helicity at the beginning of the eruption, which is prone to trigger the coalescence of two flux ropes (Linton et al 2001;Makwana et al 2018). However, such an interaction is not evident in our simulation for the following reasons.…”

Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. II. Test Particles in Electromagnetic Fields and GRMHD

“…Ultimately, the true nature of microscopic plasma processes in accretion disk environments will have to be studied with kinetic codes, or a combination of MHD and kinetic methods. Coupled PiC-MHD runs have recently been performed in Newtonian setups (Daldorff et al 2014;Markidis et al 2014;Tóth et al 2016;Chen et al 2017;Makwana et al 2018;Markidis et al 2018), where a PiC simulation box is embedded in an MHD calculation, in regions where collisionless physics is supposed to be important. The implementation of test particles in curved spacetimes in a framework such as BHAC is a necessary first step in this direction.…”