Evolution of the poloidal Alfven waves in 3D dipole geometry Jiwon Choi and Dong-Hun Lee School of Space Research, Kyung Hee University 5 th East-Asia School and Workshop on Laboratory, Space, Astrophysical Plasmas August 17 – 22, 2015

Contents  Introduction  Poloidal Alfven waves observed in space  Theoretical background  Model  3D MHD wave simulations in a cold plasma  Results  Summary

Characteristics of poloidal Alfven waves observed in space [Takahashi et al., 1990]  Polarization : Radially polarized (B radial, E east-west )  Azimuthal wave number (m) : ~ 100  Frequency : Pc range (2 – 22 mHz), depending on local conditions  Generation : Internally driven (drift-bounce resonance)  Spatial extent :  Radial : ~ 0.1 R E – 2 R E  Azimuthal : ~ 1 hr – ~ 8 hr MLT

Theoretical approach of poloidal waves  Coupled equations in the dipole coordinates from Lee [1990] where  ν, μ, φ are the orthogonal dipole coordinates; normal to a field line (ν), parallel to a field line (μ), and in the azimuthal direction (φ).  E ν and E represent toroidal and poloidal electric field, respectively.  when m becomes 0 or ∞, above equations decouple to toroidal and poloidal mode equations.

Why are poloidal Alfven waves important?  Electric field perturbation is in east-west direction.  Poloidal waves can interact with drifting (ring current) particles via drift-bounce resonances [Southwood and Kivelson, 1981, 1982].  Various observations show particle flux modulations associated with standing poloidal Alfven waves [Takahashi et al., 1990; Yang et al., 2010].  Poloidal Alfven waves play a role in particle acceleration. [Yang et al., 2010]

Are high-m waves common?  Recently, Le et al. [2011] report radially polarized waves in Pc2-3 range ( mHz) with high occurrence rate (the peak reaches more than 30%) using ST-5 constellation missions. They suggest that these are Doppler shifted Pc4-5 waves in the Earth frame, due to fast traverse speed of the probe. Noon Dusk Midnight  Frequent detection of Doppler shifted Pc2-3 wavesimplys that radially polarized waves are common phenomena in the Earth’s magnetosphere.  Particle acceleration by interacting with ULF waves could be significant.

3D MHD wave model  Wave equation [Lee and Lysak, 1989]  Dipole coordinates  Boundary conditions : Perfect reflecting boundaries  Initial perturbation with various m at L = 3 - 9

Equatorial density and Alfven speed fundamental second Eigenfrequency 13 mHz

2 nd harmonic oscillation along the magnetic field is assumed  Stronger and more localized poloidal mode is formed in high-m regime. 0 [arbitrary unit] [arbitrary unit] freq [mHz] freq [mHz] 0 E BνBν [arbitrary unit] m = 20 m = 80 Radial Distance [R E ]

Mode structure of guided poloidal waves (B ν) m = 20 m = 80 Z [R E ] X [R E ]

Poloidal lifetime (τ)  A period of time during which a wave polarization is dominantly poloidal [Mann et al., 1995].  The larger the m, the longer the lifetime.  The compressional energy density is significant in the low-m case. m = 20 m = s ~ 4.2 period 100s ~ 1.3 period

V A gradient effect on τ L =  Blue: inner magnetosphere ( L = 3, 4 )  Black: outer magnetosphere ( L = 6 – 9 )  L = 5.5 : Plasmapause  We define the length scale of radial inhomogeneity (Lx) : λ φ / Lx

V A gradient effect on τ  Near the region where V A gradient is large (ex. L=5.5)  Poloidal mode vanishes rapidly. L = λ φ / Lx

Summary  High-m poloidal ULF waves are of great importance since they are capable of interacting with particles.  Temporal evolution of the transient poloidal Alfven wave is affected by 1) drift structure (m) 2) inhomogeneity of the medium (B field, density  V A gradient)  Persistent poloidal oscillations with low-m (< ~40) are less likely to be observed unless the waves are continuously driven.  m should be much large in order to maintain poloidal wave near the region where the gradient is steep (ex. plasmapause).