1. Arianna Ligorini Department of Gamma-ray Astrophysics Institute of Nuclear Physics PAS, Krakow Jacek Niemiec Department of Gamma-ray Astrophysics Institute of Nuclear Physics PAS, Krakow Martin Pohl Institute of Physics and Astronomy, University of Potsdam and DESY
A study of mildly relativistic magnetized perpendicular shocks with PIC simulation
ICRC Busan

2. Astrophysical shocks Shocks in many astrophysical environments
SNRs → non-relativistic shocks
Active Galactic Nuclei, Pulsars, Gamma Ray Burst, Blazars → relativistic shocks

3. Astrophysical shocks: Blazars
AGN with relativistic jets
seen approx head on
Dissipation → Internal
Shock Model
We study the model for mildly relativistic (γ∼2) regime
- perpendicular magnetic field
- total magnetization σ = 0.1
Sikora et al., 2013
Sikora et al., 2016

4. The Synchrotron Maser Instability
A ring of particles gyrating in the shock transition zone breaks up in bunches of charge → they radiate a coherent train of transverse EM waves of the X-mode in the upstream (precursor).
Incoming el.oscillates and their guiding-center velocity decreases → ions keep going.
Difference in bulk → longitudinal E field (wakefield) → this field can boost electrons toward the shock and accelerate them .

5. Recent studies of relativistic shocks with 2D simulations
Sironi&Spitkovsky, Iwamoto et al (2017)
i-e plasma pair plasma
observed precursor waves observed greater amplitude effect for high γ of precursor and more
structures
predicted low effects for predicted possibility of
mildly relativistic case observing effects also at low γ .

6. Particle-In-Cell Simulations
PIC simulations → ab-initio method of solving Vlasov equation:
1. Solving of Maxwell’s equations on a numerical grid
2. Integration of rel. particle eq. of motion in self-consistent EM field

7. Particle-In-Cell Simulations
Large-scale high-resolution PIC simulations must be performed at high-performance supercomputing centers
Prometheus (Poland, Intel Xeon E5-2680v3, 53,568-core, 2.4 Pflop/s)
Main simulations:
→ 1D-like, (1D3V)
→ 2D (2D3V)

8. Ions and electrons cold plasma
Simulation setup
Ions and electrons cold plasma
mi/me = 50, σ = 0.1, λse =15, λsi = 106

9. Shock structure: 1D vs 2D
1. Shock at ~100 (x-xc)/ λsi for both 1D and 2D simulations
2. Precursor waves in Bz and Ey, vel ~ c → X-mode EM waves
3. Wakefield in Ex, λEx ~ 3/ λsi (in accord with Hoshino 2008)
4. Same wavelength but different amplitude → 10 times smaller amplitude in 2D

10. 2D movies: el. dens. and Bz
1. Faint oscillation are visible in Bz and in some measure also in dens.
2. Precursor waves from the SMI

11. Phase space: 1D vs 2D
1. Ring-like feature at the shock in ion ph. sp. in both 1D and 2D
2. Faint downstream oscillations in el. ph. sp.
3. El. upstream ph. sp. is modulated by Ex → precursor waves affect the plasma
4. El. are boosted towards the shock (i.e., in negative x-momentum)
BUT: the level of el. energization by the wakefield seems to be similar in both runs, even if in 1D the waves amplitude is 10 times greater

12. Particle distribution spectra: 1D vs 2D
1. Ions are isotropized around their initial energy
2. El. also thermalize close to their initial energy and are only slightly heated in bulk.
3. Asymmetry in high energies el. may depend on upstr. acceleration by wakefield.
AGAIN 2D and 1D shocks show similar level of electron-ion coupling despite difference in wakefield amplitudes.

13. The role of electron plasma magnetization
Pair plasma, 100 ppc, 2D runs
for a given value of total σ →
σe =(1 + mi/me)σ
exponential decrease of precursor wave amplitude with electron magnetization
Need of further studies to determine the magnetization range allowing for efficient electron-ion coupling in the realistic mi/me case.

14. Summary
1. We presented preliminary results of PIC simulations of a poorly explored regime of mildly relativistic magnetized shocks in ion-electron plasma.
2. We show consistent evidence for SMI (precursor waves, wakefields)
3. Particle-wave interactions in the precursor → plasma thermalization and limited ion-to-electron energy transfer
4. We see similar level of i-e coupling in 2D and 1D → proper interpretation of this result requires further scrutiny

15. Thank you
for your attention