PIC Simulation of Magnetic Reconnection with Adaptive Mesh Refinement Keizo Fujimoto National Astronomical Observatory of Japan
Overview Introduction Particle-in-Cell (PIC) model with adaptive mesh refinement (AMR) Wave activities in the reconnection region Electrostatic solitary waves (ESWs) Whistler waves EM waves around the x-line Summary 2
Magnetic Reconnection in Space Auroral Substorms [NASA] Solar Flares 3
Multi-Scale Nature of Reconnection 1km 10km 10 3 km 10 5 km 10 11 km Dissipation Hall effect Topology λ De Full PIC ρ e, λ e ρ i, λ i L L c (Particle-In-Cell) MHD (Magnetohydrodynamics) Coulomb mean free path β i ~ 1 [NASA] 4
Restrictions of Explicit PIC Model Cell size x 3λ De Num of particles per cell N p 10 2 Memory requirement per cell Field (n s, J s, E, B) 14 4 Byte << Particle (x s, v s ) (12 4 Byte) 10 2 5
AMR-PIC Model [Fujimoto, JCP, 2011] x 3λ De n e -1/2 (Adaptive Mesh Refinement Particle-in-Cell) λ De,lobe ~ 6 10 3 m λ De,ps ~ 3 10 2 m Electron scale Removing unnecessary cells. Particle splitting-coalescence 6
AMR-PIC Simulations 7
Data Structure Similar to a fully threaded tree (FTT) structure (Khokhlov, 1998). [Fujimoto & Machida, JCP, 2006] 8
Basic Equations Superparticle S: Shape function Superparticles (Buneman-Boris method) EM Field (Yee-Buneman scheme) Charge Conservation Method [Villasenor & Buneman, 1992] 〇 Local operations Facilitate parallel computing No numerical damping for any wave numbers! 9
Radiation of EM Waves E SM =f SM (E) B SM =f SM (B) 10
Load Balancing Example using 8 nodes Fixed block case * Block = Decomposition domain Adaptive block case 11
Adaptive Block Technique That is similar to Morton order, So that the block surface is as small as possible, Especially in the central current sheet, the surface must be small. [Fujimoto, JCP, 2011] Base-level cells in the entire domain are sorted in an appropriate order: 12
Performance of the AMR-PIC Model [Fujimoto, JCP, 2011] Fujitsu FX1 @Nagaya Univ. Node CPU (4 cores) CPU (4 cores) Memory (32G) CPU (4 cores) Memory (32G) Memory (32G) CPU (4 cores) Memory (32G) Parallel fraction: 99.8% Load balancing Removing Poisson Eq. 13
Examples of the AMR-PIC simulation: Wave activities in the reconnection region 14
Electrostatic Solitary Wave (ESW) ESWs are often observed in the PSBL in the Earth magnetotail (Matsumoto et al., 1994). Magnetic reconnection is closely related to the generation of the ESWs (Deng et al, 2004; Cattell et al., 2005; Viberg et al., 2013). [Matsumoto et al., GRL, 1994] 15
Electrostatic Solitary Wave (ESW) [Fujimoto & Machida, JGR, 2006] 16
Electrostatic Solitary Wave (ESW) [Fujimoto & Machida, JGR, 2006] Wave spectrum + Linear dispersion Electron heating B Consistent with Electron 2-stream instability observations. rather than Buneman. [Shinohara et al., 1998] 17
Whistler Waves Cluster observations [Wei et al., JGR, 2007] High frequency waves with 0.1ω ce ~ ω ce. Right-hand polarizartion 0.1ω ce ~ ω ce Right-hand polarization 18
Whistler Waves [Fujimoto & Sydora, GRL, 2008] Transverse E 19
Whistler Waves [Fujimoto & Sydora, GRL, 2008] Time B ξ B 20
Wave Activities in Separatrix Region Ex Ey 21
EM Waves near the X-line Magnetotail Lab. Exp. ω LH ω LH ω ci [Zhou et al, JGR, 2009] [Ji et al, PRL, 2004] 22
EM Waves in 3D magnetic reconnection [Fujimoto & Sydora, PRL, 2012] # of particles ~ 10 11 Surface: J, Line: Field line Color on the surface: Ey, Cut plane:jy 23
Dissipation Mechanism [Fujimoto & Sydora, PRL, 2012] 3D reconnection 2D reconnection Anomalous effects 24
EM Waves in 3D Magnetic Reconnection ω = ω r + iγ Simulation results ω ci < ω r < ω LH V ph V A ω LH Linear analyses Profiles taken from simulation Electron ω ci [Fujimoto & Sydora, PRL, 2012] Two-fluid equations Ion 25
Summary Adaptive mesh refinement (AMR) has been implemented in the electromagnetic particle-in-cell (PIC) model to achieve large-scale simulations of magnetic reconnection. Main differences from the usual PIC models are Tree-type data structure, Smoothing of the EM fields to avoid the wave reflection, Particle splitting-coalescence to control the number of particles per cell, Adaptive block technique to keep load balancing. 26
Summary2 We found wave activities in the reconnection region of Electrostatic solitary waves (ESWs) generated due to the electron 2-stream instability in the PSBL, Whistler waves excited by the temperature anisotropy in the downstream region, and EM waves maintained by the velocity shear around the x-line in 3D magnetic reconnection. 27