On the influence of environmental parameters on mixing and reconnection caused by the Kelvin-Helmholtz instability at the magnetopause Matthieu H.J. Leroy CmPA, KU Leuven October 11 216 FNRS Contact Group, Planetarium of the Royal Observatory of Belgium
Outline Motivation Introduction Parameters exploration Initial density jump Shear layer width Hall-term Resolution Simulated spacecrafts Conclusion
M. Leroy Kelvin-Helmholtz instability at the magnetopause 3 / 22 Motivation Understanding the mechanisms underlying the solar wind entering Earth s magnetosphere is one of the biggest goals of magnetospheric physics as it forms the basis of space weather phenomena such as magnetic storms and auroras (Hasegawa, Fujimoto et al., Nature, 24) Observations Solar wind matter regularly enters the magnetosphere during southward IMF, solar and geomagnetic fields are anti-parallel reconnection at low-latitude during northward IMF, fields are parallel reconnection should not be efficient Nonetheless plasma boundary layer gets thicker during northward IMF solar wind is still penetrating the magnetopause.
M. Leroy Kelvin-Helmholtz instability at the magnetopause 4 / 22 Motivation Several hypothesis Simultaneous northern and southern cusps reconnections KH instability in non-linear stage enhancing mixing Double reconnection at mid-latitude The in-situ data by various spacecrafts (Cluster, THEMIS) support the KHI hypothesis (Hasegawa, Fujimoto et al., Nature, 24). But how does it works, and is it sufficient?
M. Leroy Kelvin-Helmholtz instability at the magnetopause 5 / 22 Previous studies and state of the art : 2D simulations Settings Most studies until now focused on 2D simulations of KHI in (Hall-)MHD frame Initial v B, both sheared KHI stabilized Initial v B, both sheared KHI enhanced Homogeneous density, single KHI vortex Conclusions KHI can cause reconnection on KH scale (Nykyri & Otto, 21) Possible fast anomalous ion mixing, efficiency mitigated by inhomogeneity (Terasawa, 1992 & 1994) Hall-MHD has various effects depending on initial configuration, but usually enhance instability, reconnection and transport Matsumoto and Seki (27) showed existence of secondary 3D KHI 2.5D simulations exhibited important z-component development Structure of Hall term and nature of the situation studied points to 3D
M. Leroy Kelvin-Helmholtz instability at the magnetopause 6 / 22 Previous studies and state of the art : 3D simulations Settings Angle between v and B not only or Initial density jump Large slab encompassing high to low latitudes Conclusions Various orientation influence growth of KHI and thickness of boundary layer Density jump add competition with Rayleigh-Taylor instability Large simulation to encompass field lines as far as possible due to frozen-in properties, local phenomenon can reflect at a distance along field lines : double mid-latitude magnetic reconnection (Faganello et al. 212)
M. Leroy Kelvin-Helmholtz instability at the magnetopause 7 / 22 Initial and boundary conditions Box size : L x = 7, L y = 188, L z = 377 (ion inertial lengths), resolution N 3 = 2 3, periodic in y and z-directions, x-direction continuous extrapolation. Solution of Grad-Shafranov equation with ignorable y-direction: ( 4x A y (x, z) =.5 3 + Lx 2π sinh ( 2πx L z ) cos ( 2πz B x = Ay Ay, By =, Bz = z x, Vx =, Vy = M ( A 2 tanh Ay L u ( ) Ay ρ =.5(ρ c + 1) +.5(ρ c 1) tanh. L u δa y = ɛ ( 6 2πmx/Ly + φ(m) m=1 cos m L z )). ), V z =. ) ( ) x 2 ( ) z 2 exp exp 2L u 2L u Domain large enough for two pairs of KH vortices. high-latitude conditions relaxed not KHI unstable. Alfvén Mach number M A =1,the sonic Mach number M c=1, β =.7, L u = 3, η = 1e 3, ρ c=4.7
M. Leroy Kelvin-Helmholtz instability at the magnetopause 8 / 22 Initial and boundary conditions
M. Leroy Kelvin-Helmholtz instability at the magnetopause 9 / 22 Reproduction of Faganello et al. Figure : Snapshots of the evolution of the reference run Motivation Introduction Parameters exploration Simulated spacecrafts Conclusion
M. Leroy Kelvin-Helmholtz instability at the magnetopause 1 / 22 Parameters exploration Aim of the study Value of several initial physical quantities modified to assert their influence on growth rate and topological development of the KHI. Label ρ M A L u shn Ref 4.7 1 3 ρ 7 1 3 M A =1/2 4.7.5 3 M A =2 4.7 2 3 L u 4.7 1 1 ρ +L u 7 1 1 ρ +L u +shn= 1 7 1 1 1
M. Leroy Kelvin-Helmholtz instability at the magnetopause 11 / 22 Parameters exploration 2.5e-4 Ref 2e-4 ρ=7 Ma=1/2 t9 1.5e-4 Ma=2 t6 Vx 2 Lu=1 1e-4 5e-5 ρ+lu ρ+lu+shn=+1 t2 2 4 6 8 2.5 Ref 2 ρ=7 Ma=1/2 t9 1.5 Ma=2 Jmax Lu=1 1 ρ+lu t5 ρ+lu.5 +shn=+1 2 4 6 8 ρ=7 similar values of < Vx 2 >, higher values of J max. Ma=1/2 does not develop KHI. Ma=2 starts later, but higher < V 2 x >. L u=1 lower < V 2 x >, higher J max. ρ+l u starts faster, highest values of < V 2 x > and J max.
M. Leroy Kelvin-Helmholtz instability at the magnetopause 12 / 22 Parameters exploration : Initial density jump V 2 x 1.2e-4 1e-4 8e-5 6e-5 4e-5 2e-5 ρ=2 ρ=3.7 ρ=5 ρ=7 ρ=9 2 3 4 5 6 7 8 2.5 ρ=2 2 ρ=3.7 ρ=5 1.5 ρ=7 t9 Jmax ρ=9 1 t6 All ρ similar values of < V 2 x >, but highest for ρ=5. Highest values of J max for largest values of ρ..5 2 3 4 5 6 7 8
M. Leroy Kelvin-Helmholtz instability at the magnetopause 13 / 22 Parameters exploration : Initial density jump
M. Leroy Kelvin-Helmholtz instability at the magnetopause 14 / 22 Parameters exploration : Shear layer width V 2 x 2e-4 1.5e-4 1e-4 5e-5 Ref Lu=2 Lu=1 Lu=1+shn=+1 Lu=1+shn=-1 2 4 6 8 2.5 Ref 2 Lu=2 Lu=1 1.5 Lu=1+shn=+1 Jmax Lu=1+shn=-1 1.5 t8 t7 t6 More complex situation. For < V 2 x > : L u=1 < L u=3 < L u=2. For J max : L u=3 < L u=1 < L u=2. shn=+1 yields highest < Vx 2 > and Jmax. shn=-1 yields lowest < Vx 2 > and Jmax. 2 4 6 8
M. Leroy Kelvin-Helmholtz instability at the magnetopause 15 / 22 Parameters exploration : Influence of the Hall-term V 2 x 2e-4 1.5e-4 Jmax 1e-4 5e-5 Ref η H =.1 η H =.685 η H =1 η H =2 η H =6.25 2 3 4 5 6 7 8 1.5 1.5 Ref η H =.1 η H =.685 η H =1 η H =2 η H =6.25 t8 t8 t6 More complex situation. Similar < V 2 x > for all η H except η H = 6.25 (realistic values) recover usual results from literature. J max decreases regularly as η H increases. 2 3 4 5 6 7 8
M. Leroy Kelvin-Helmholtz instability at the magnetopause 16 / 22 Parameters exploration : Influence of the Hall-term Magnitude and spatial extension of the current sheets decreases as ηh increases. Motivation Introduction Parameters exploration Simulated spacecrafts Conclusion
M. Leroy Kelvin-Helmholtz instability at the magnetopause 17 / 22 Parameters exploration : Influence of the resolution Magnitude of the current increases as resolution increases. Magnetic gradients and secondary instabilities better resolved. Motivation Introduction Parameters exploration Simulated spacecrafts Conclusion
M. Leroy Kelvin-Helmholtz instability at the magnetopause 18 / 22 Simulated spacecrafts.4.2 -.2 -.4 (B x ) 1 15 2 25.6.5.4.3.2 (ρ) P1 P2 P3 P4 P5 P1 P5 1.2 1.8.6 (B z ).4 5 1 15 2 25 6 5 4 3 2 1 (p) P1 P2 P3 P4 P5 P1 P5 First set reproduces Cluster around the interface (P1 to P4). Other located close to the current sheets coordinates..1 5 1 15 2 25 5 1 15 2 25 3 35
M. Leroy Kelvin-Helmholtz instability at the magnetopause 19 / 22 Simulated spacecrafts 6 5 4 ρ 3 2 1 1 15 2 25 1.5 1.5 -.5 Bx(rescaled) By(rescaled) Bz -1 1 15 2 25 1.4 1.2 1 V A.8.6.4.2 1 15 2 25
M. Leroy Kelvin-Helmholtz instability at the magnetopause 2 / 22 Conclusion Double reconnection at mid-latitude recovered. Density jump influence the boundary layer non-mixed blob important for DMLR. Shear layer width influence KHI evolution. Combined with ρ and shn even more complex. Hall-MHD does not modify the phenomenon, but changes the magnitude of current (here inhibition). Higher resolution resolves a lot more secondary instabilities + current magnitude at least 2 s larger. Article to be submitted
M. Leroy Kelvin-Helmholtz instability at the magnetopause 21 / 22 Conclusion Q-maps and diagnostics for reconnection characterization + evaluation of mass entry. Improve simulation of spacecrafts to actually compare with in-situ data. Use parameters value derived from experimental measures correct shear length and magnitude, density jump, Mach and β Implement a more efficient scheme (MHD : 2 3 in 3.5 days (32 proc), Hall-MHD 4 to 8 s longer).
M. Leroy Kelvin-Helmholtz instability at the magnetopause 22 / 22 Thank you for your attention