Statistical Analysis of Ions in Two-Dimensional Plasma Turbulence

Abstract

The statistical properties of ions in two-dimensional fully developed turbulence have been compared between two different numerical algorithms. In particular, we compare Hybrid Particle In Cell (hybrid PIC with fluid electrons) and full PIC simulations, focusing on particle diffusion and acceleration phenomena. To investigate several heliospheric plasma conditions, a series of numerical simulations has been performed by varying the plasma \(\beta \) – the ratio between kinetic and magnetic pressure. These numerical studies allow the exploration of different scenarios to be performed, going from the solar corona (low \(\beta \)) to the solar wind (\(\beta \sim 1\)), as well as the Earth’s magnetosheath (high \(\beta \)). It has been found that the two approaches compare pretty well, especially for the spectral properties of the magnetic field and the ion diffusion statistics. Small differences among the models have been found regarding the electric field behavior at sub-ion scales and the acceleration statistics, due evidently to the more consistent treatment of the plasma in the full PIC approach.

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Acknowledgements

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 776262 (AIDA). This work is partly supported by the International Space Science Institute (ISSI) in the framework of International Team 405 entitled ‘Current Sheets, Turbulence, Structures and Particle Acceleration in the Heliosphere’, by the US NSF AGS-1156094 (SHINE). We acknowledge PRACE for awarding us access to SuperMUC at GCS@LRZ, Germany. The work by F. Pucci has been supported by Fonds Wetenschappelijk Onderzoek – Vlaanderen (FWO) through the postdoctoral fellowship 12X0319N. We thank the anonymous Referee for the comments and suggestions that helped improve the quality of this work.

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Appendix

Appendix

The statistical convergence study for the hybrid runs has been performed in Servidio et al. (2016). They show that, for a number of particles per cell larger than 400, turbulence statistical properties remain unchanged. Here we report the statistical convergence study performed for the full PIC high-\(\beta \) runs that are those more sensible to statitive noise. We verified the statistical convergence for both the power spectra and the diffusion coefficient. We found that the properties of turbulence remain unchanged for ppc \(\geq 400\). In Figure 6 we show the power spectra of the magnetic field for run7 (ppc \(=400\)) and run8 (K3) (ppc \(=4000\)). The spectra have the same behavior (and inertial range slope) in the two cases. There are small differences, especially at very small (electron) scales, as expected. To test the reliability of the high-\(\beta \) simulations also from the particle point of view, we compared the diffusion coefficient for the full PIC runs. We performed the analysis described in Section 3.3 and measured the diffusion coefficient for each energy interval for the three different runs with \(\beta _{i}=5\). Results are reported in Table 3. The values of particle energy show consistency from one run to another meaning that acceleration and energization mechanisms are not affected by the number of particles per cell used (once convergence has been achieved). Also, the diffusion coefficients are comparable among the runs (at the same energy) meaning that neither spatial diffusion is affected by variation in the number of particles used, further proving that convergence has been achieved for this high-\(\beta \) case. This agreement is somewhat expected since the diffusion coefficient depends on the shape of the spectrum in the energy-containing and inertial scales \((k d_{i} \ll 1)\), which are similar as shown in Figure 6.

Figure 6
figure6

Magnetic field power spectra for run7 and run8 (K3) with 400 and 4000 particles per cell, respectively. The spectra show the statistical convergence achieved already at 400 ppc since the large scales are quite similar and the inertial ranges have the same slopes.

Table 3 Particle energy values and the corresponding diffusion coefficient. The energy values do not change by increasing the number of particles from 400 to 4000 meaning that particles are accelerated and energized in the same way. Moreover, the diffusion coefficients are comparable among the runs suggesting that also spatial diffusion is not affected by an increase in the number of particles.

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Pecora, F., Pucci, F., Lapenta, G. et al. Statistical Analysis of Ions in Two-Dimensional Plasma Turbulence. Sol Phys 294, 114 (2019). https://doi.org/10.1007/s11207-019-1507-6

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Keywords

  • Plasma physics
  • Turbulence