Study of electric and magnetic field fluctuations from lower hybrid drift instability waves in the terrestrial magnetotail with the fully kinetic, semi-implicit, adaptive multi level multi domain method

Abstract

The newly developed fully kinetic, semi-implicit, adaptive multi-level multi-domain (MLMD) method is used to simulate, at realistic mass ratio, the development of the lower hybrid drift instability (LHDI) in the terrestrial magnetotail over a large wavenumber range and at a low computational cost. The power spectra of the perpendicular electric field and of the fluctuations of the parallel magnetic field are studied at wavenumbers and times that allow to appreciate the onset of the electrostatic and electromagnetic LHDI branches and of the kink instability. The coupling between electric and magnetic field fluctuations observed by Norgren et al. [“Lower hybrid drift waves: Space observations,” Phys. Rev. Lett. 109, 055001 (2012)] for high wavenumber LHDI waves in the terrestrial magnetotail is verified. In the MLMD simulations presented, a domain (“coarse grid”) is simulated with low resolution. A small fraction of the entire domain is then simulated with higher resolution also (“refined grid”) to capture smaller scale, higher frequency processes. Initially, the MLMD method is validated for LHDI simulations. MLMD simulations with different levels of grid refinement are validated against the standard semi-implicit particle in cell simulations of domains corresponding to both the coarse and the refined grid. Precious information regarding the applicability of the MLMD method to turbulence simulations is derived. The power spectra of MLMD simulations done with different levels of refinements are then compared. They consistently show a break in the magnetic field spectra at k⊥di∼30, with di the ion skin depth and k⊥ the perpendicular wavenumber. The break is observed at early simulated times, Ωcit<6, with Ωci the ion cyclotron frequency. It is due to the initial decoupling of electric and magnetic field fluctuations at intermediate and low wavenumbers, before the development of the electromagnetic LHDI branch. Evidence of coupling between electric and magnetic field fluctuations in the wavenumber range where the fast and slow LHDI branches develop is then provided for a cluster magnetotail crossing.

Rippled Electron‐Scale Structure of a Dipolarization Front

“…For E ⊥ we observe a power law spectrum in the frequency range with the exponent α E =−3. Similar slopes have been reported for LHDI turbulence in particle‐in‐cell simulations and Cluster data (Innocenti et al, ). At the front layer, LHDI develops quickly to saturation and becomes turbulent at nonlinear stage (Divin, Khotyaintsev, Vaivads, André, Markidis, & Lapenta, ).…”

“…This suggests a quarter wavelength difference between MMS2 and MMS3, corresponding to wavelength λ ≈120 km. This corresponds to the wave number k ρ e ≃0.4, which is consistent with quasi‐electrostatic LHDI (Graham et al, ; Innocenti et al, ). From the time delay between the spacecraft we find that the distortion propagates in the − M direction at a speed of V ph =120 km/s.…”

Lower hybrid waves in the ion diffusion and magnetospheric inflow regions

“…To calculate the phase velocity v ph of the lower hybrid waves, we fit the potential calculated by integrating δ E (for f > 10 Hz), . The phase speed v ph and propagation direction are found by finding the best fit of ϕ E to ϕ B , where v ph is a free parameter [ Norgren et al , ; Graham et al , ; Khotyaintsev et al , ; Innocenti et al , ]. Figures f–i show ϕ B and the best fit of ϕ E to ϕ B for the lower hybrid waves observed by each spacecraft in the diffusion region and near the ion edge.…”

Onset and Evolution of the Oblique, Resonant Electron Firehose Instability in the Expanding Solar Wind Plasma

“…Thanks to the semi-implicit IMM temporal discretization, the temporal and spatial resolution of the code can be adapted to the scale of the processes under investigation rather than being tied to the strict stability constraints of explicit discretizations. This property is massively exploited in the Multi-Level Multi-Domain evolution of iPic3D, where several grid levels are resolved with different spatial and temporal resolutions to catch progressively smaller scale processes (Innocenti et al 2013(Innocenti et al , 2015(Innocenti et al , 2016. Other, non semi-implicit, fully kinetic implementations of similar EB formulations are Sironi & Narayan (2015) and Ahmadi et al (2017), where the compression (rather than expansion) of the plasma mimics collisionless accretion flow and magnetopause compression respectively.…”