A NEW MODEL FOR REALISTIC 3-D SIMULATIONS OF SOLAR ENERGETIC PARTICLE EVENTS

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1 A NEW MODEL FOR REALISTIC 3-D SIMULATIONS OF SOLAR ENERGETIC PARTICLE EVENTS Nicolas Wijsen KU Leuven In collaboration with: A. Aran (University of Barcelona) S. Poedts (KU Leuven) J. Pomoell (University of Helsinki)

2 OUTLINE Space Weather Solar energetic particle events Solar energetic particle transport The focused transport equation A new particle transport code EUHFORIA (inner heliospheric MHD model) particle transport code + EUHFORIA

3 TEXT-BOOK SPACE WEATHER STORM Solar eruptive events: Solar Flares Coronal Mass Ejections (CME) Timeline at Earth: 8 minutes: EUV and X-ray emission reach earth: Radio frequency (HF)losses, GPS signal disturbed, astronauts endangered 1 hour: energetic particle onset HF loss, GPS signal disturbed, satellites damaged, astronauts endangered 1-4 days: CME arrives at earth Disturbed GPS signal, Radio communication affected, Polar lights

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5 Protons, electrons and ions. Energy ranging from a few tens of kev to GeV SOLAR ENERGETIC PARTICLE EVENTS

6 SEP-ACCELERATION SITES Particle accelerators (not fully understood): 1. gradual events: Shocks in front of CMEs (mobile source) 2. impulsive events: current sheets at solar flare sites 3. Hybrid events: CMEs + flares? Aran (2007)

7 SEP-TRANSPORT Charged particles tend to follow the interplanetary magnetic field (e.g., Parker Spiral) Magnetic turbulence (Alfvén waves, meandering field lines, ) scatters the charged particles. Scattering is mainly in pitch-angle θ, but also field-line hopping is possible (perpendicular diffusion)

8 FOCUSED TRANSPORT EQUATION Particle distribution function with: Gyro-averaged focused transport equation (mixed coordinates): (Roelof et al.,1969; Ruffolo, 1995; Lario et al., 1998; Dröge et al. 2010)

9 FOCUSED TRANSPORT EQUATION From Itô-calculus it follows that the FTE is equivalent to the following five stochastic differential equations (SDEs): where dw i are Wiener processes. Monte-Carlo simulation: integrate the SDEs for >10 6 particles forward in time Output is the differential energy flux: and the particle anisotropy:

10 PARTICLES PROPAGATING IN A PARKER SOLAR WIND Test Case: Parker Solar wind: Constant radial solar wind speed (400 km/s) Spiral Magnetic field Impulsive injection of 4 MeV protons at 0.05 AU Particles are injected in the solar equatorial plane over a 30 longitudinal range. Neglect adiabatic energy losses Diffusion to model effects of turbulence: with P xx the magnetic turbulence power spectrum

11 PARTICLES PROPAGATING IN A PARKER SOLAR WIND

12 PROBLEMS WITH PARKER SOLAR WIND Most SEP forecasting codes assume a steady-state Parker solar wind configuration. In reality, the interplanetary magnetic field can deviate strongly from a Parker-configuration, due to e.g.,: (multiple) CMEs Fast solar wind streams (corotating interaction regions) More realistic solar wind configurations are needed: Particle transport code + 3D MHD code for the solar wind

13 EUHFORIA EUROPEAN HELIOSPHERIC FORECASTING INFORMATION ASSET EUHFORIA is a time dependent 3D MHD model of the inner heliosphere (0.1 AU 5 AU) (Pomoell&Poedts, 2017) Data-driven solar wind model with superposed coronal mass ejections (cf. ENLIL) radial velocity density

14 Flux-rope CMEs Magnetic fields of CMEs are the main driver of geomagnetic storms They may also strongly influence the transport of energetic particles Earth orbit Flux rope CME CME shock (SEP source) Shock from previous CME

15 EUHFORIA+MONTE CARLO SEP MODEL Propagate particles in the solar wind computed by EUHFORIA Synthetic solar wind case: slow solar wind with an imbedded fast solar wind stream 2 injection zones: 1. In the slow solar wind 2. On the boundary between the fast and slow solar wind Delta-injection of 4 MeV protons (flare-like) over 30 longitude range Zone 2 Zone 1

16 Particle Intensity in the slow solar wind

17 Particle Intensity in the Ecliptic ZONE 1: SLOW SOLAR WIND ZONE 2: MIXED SOLAR WIND

18 SUMMARY AND FUTURE PROSPECTS We developed a numerical code to model the anisotropic three-dimensional propagation of SEPs in interplanetary space.. We coupled the SEP model with EUHFORIA, allowing us to propagate particles in realistic solar wind configurations. Future work: use both models to study the transport of SEPs in more complex solar wind configurations to model gradual SEP events.

19 THANK YOU FOR YOUR ATTENTION!

20 DIFFUSION COEFFICIENTS Scattering of the particles due to magnetic turbulence is modelled by diffusion processes: The diffusion coefficients can be computed from the observed turbulence power spectrum. Typical assumptions: Turbulence is stationary in solar wind frame. Slab-turbulence: Non-linear guiding centre theory: Figure: Schematic of the wave number spectrum observed typically in the solar wind.

21 Particle Intensities in the Ecliptic ZONE 1: SLOW SOLAR WIND Protons are adiabatically decelerated in the solar wind. No sharp cut-offs due to perpendicular diffusion and particle drifts.

22 EUHFORIA EUHFORIA = Coronal model + Heliospheric model 1. Coronal model (1 Rs Rs): Potential magnetic field using magnetograms as boundary conditions WSA/DCHB+CSC : semi-empirical model which computes the solar wind parameters at 21.5 Rs 2. Heliospheric model (21.5 Rs - 2 AU): Time dependent 3D MHD code Coronal model is used as boundary conditions CMEs can be injected at the inner boundary Credit: Jens Pomoell

23 DATA-DRIVEN CME MODELS Hydrodynamic cone-model and/or pancake -shaped CME inserted as time-dependent boundary condition at 0.1 AU. Parameters (speed, direction, width) obtained through fits to coronagraph data Mass density and temperature need to be provided by forecaster Problem: neglects internal magnetic field of the CME