1. 3D Modelling of Heavy Ion SEP Propagation
S. Dalla, T. Laitinen, M. Battarbee
University of Central Lancashire, Preston, UK
M.S. Marsh
Met Office, Exeter, UK

2. Heavy ion SEPs
An important probe into m/q-dependent acceleration and transport processes
Assumption that heavy ions propagate in 1D is a key foundation of interpretations
This talk: propagation of heavy ion SEPs is 3D

3. Time variation of Fe/O ratio
Tylka et al, 2012

4. O at double average E
Mason et al, 2006

5. Fe/O: O at double average E
Mason et al,

6. Fe/O decay interpretation
Mason et al (2006) concluded that Fe/O decay is a result of interplanetary transport, and not a signature of acceleration process
1D modelling with a rigidity dependent mean free path can reproduce the effect (Scholer et al 1978, Cohen et al 2005, Mason et al 2006)
Exponent a related to turbulence power spectrum

7. Energy dependent charge states
Möbius et al, 1999

8. Fe charge states
Within a 1D model, measured Q at 1 AU reflect source properties
Popecki et al, 2003

9. <Q> vs E interpretation
Increase in <Q> with E as signature of acceleration process (Barghouty & Mewaldt 1999, Ostryakov et al 2000)
Energy dependent escape from acceleration region
Barghouty & Mewaldt, 1999

10. 3D full orbit propagation code
Integrate test particle trajectories in specified magnetic and electric fields (Dalla et al 2005, Marsh et al 2013)
Effect of small scale turbulence implemented as ‘ad-hoc scattering’ according to mean free path l

11. Simulation 1: Fe ions with multiple Q
1.4 million Fe ions
Power law spectrum in [10,400] MeV/nuc
Unipolar Parker spiral
Constant l=1 AU (rigidity independ.) – no scattering across field
6°x6° source at latitude=20°

12. Fe propagation
Q=20 Q=16
Q=12 Q=8 z y
rxy x

13. Guiding centre drifts
Sum of Parker spiral gradient & curvature drifts:
q =colatitude
Complex dependence on r and q
Dalla et al, 2013

14. Fe intensity profile at 1 AU
MeV/nuc

15. Fe intensity profiles
MeV/nuc

16. Energy distribution of charge states
Dalla et al, ApJ, in press, 2016

17. Conclusions from Simulation 1

18. Simulation 2: Fe and O ions

19. Fe and O intensity profiles
Fe and O both at MeV/nuc

20. Fe/O ratio Fe and O both at 10-30 MeV/nuc
Dalla et al, A&A, in press, 2016
Fe and O both at MeV/nuc

21. O at double average E compared to Fe
Fe at MeV/nuc; O at MeV/nuc

22. Fe/O for O at double energy
Fe at MeV/nuc; O at MeV/nuc
Behaviour observed experimentally by Mason et al (2006)

23. Conclusions from Simulation 2
Within a 3D propagation model, drift to a not well-connected observer produces Fe/O decaying in time
The effect disappears when the comparison and ratio calculations are done for O at double the average energy of Fe (as observed by Mason et al (2006))
Within our simulation this results from the dependence of drift velocity on mE/q

24. Shock-like injection region
Effect of variation of SEP acceleration efficiency along shock front
Latitude dependence of drift velocity
Overall 3D propagation will ‘process’ the injection properties

25. Conclusions
Propagation of heavy ions is 3D, due to drift and deceleration effects (Dalla et al 2015)
3D drift-associated propagation qualitatively reproduces two key heavy ion observations: energy dependence of <Q> and time dependence of Fe/O ratio

26. Fe locations at t=20 hr y
Q=20 Q=16
Q=12 Q=8 z
rxy x
rxy

27. SPARX SPARX: Solar PArticle Radiation swX (Marsh et al, 2015)
SPARX outputs: SEP flux profiles for E>10 MeV and E>60 MeV
E20
W20
W60

28. SEP propagation in Parker spiral
l=0.3 AU
l=1 AU
l =10 AU

29. SEP Fe propagation Fe at 100 Mev/nuc t=100 hrs Q=20 Q=15
Marsh et al, 2013

30. 1 AU view Map of fluence through 1 AU sphere Marsh et al, ApJ 2013;
Dalla et al , JGR 2013

31. Energy change
Inject monoenergetic populations with initial kinetic energy K0=1, 10, 100 MeV and 1 GeV
Strong deceleration observed after 4 days
Dalla et al, 2015

32. Time dependence Fast deceleration during the first ~20 hours
Deceleration is present also in the scatter-free case
Dalla et al, 2015

33. Dependence on mean free path
Dalla et al, A&A,
2016