Wave particle Interactions in the Inner Magnetosphere

1. R. Friedel ISR-1, Los Alamos National Laboratory, USA Plus many community contributions… Wave particle Interactions in the Inner Magnetosphere

2. Contents • Motivation • “Once upon a time in the radiation belts” • Brief History • Current Status • Dynamics • Inner radiation Belt WP modeling approaches • Classes of Models • Diffusion coefficient calculations • Limits of pure diffusion codes • Role of Proxies • Background electron density proxy • LEO Wave proxy • Substorm injection proxy • Summary/Conclusion

3. Motivation • This talk looks at wave particle interactions from the point of view of how they are modeled in inner radiation belt MeV electron models, looking at current limitations. • I am NOT reviewing here the detailed micro-physics of wave particle interactions – that would be presumptuous in the presence of experts in the field (some present here) – Danny Summers, Jay Albert, the three Richards (Thorne, Horne, Denton), Yoshiharu Omura, Jacob Bortnik, plus many others! • I ask the question: What do we need to do better to increase the fidelity of inner radiation belt wave particle interaction modeling? With our current approaches, are we on the right path? Are we getting lost in detailed physics that while “interesting”, may not play an important part in global inner radiation belt modeling?

4. Brief History (1)From Friedel et al. 2002 review Initially observed as dropout followed by a delayed increase of relativistic electrons at geosynchronous orbit during recovery phase of storm. Up to 3 orders of magnitude increase of ~2 MeV electrons (blue line) Initially a zoo of proposed mechanisms (See review, Friedel et.al, 2002): external source, recirculation, internal source, MeV electrons from Jupiter… For a more recent review see Shprits et al 2008a, b; JGR

5. Brief History (2)Results form Reeves et al. 2003 Difficulty in understanding dynamics of system: Wide range of responses for similar geomagnetic storms – Increase / Decrease / Shift of peak / No change - are all possible responses Many processes operate simultaneously that cannot be separated observationally Response thought to be result of a delicate balance of loss, transport and internal energization processes.

6. Quick Question:Why can’t current models reproduce observed range of dynamics? We have a range of quite sophisticated modelling approaches for the inner radiation belts, that include transport, acceleration, losses. What’s missing? I would hold that our current models DO include the major physical processes, but that we are driving these models with broad statistical inputs (DLL, wave statistics driving DEE and Dαα, simple density models, badly constrained boundary conditions) Simply: Average inputs in -> average behaviour out

7. Current Status (1) – Internal/External SourceResults from Yue Chen et al. (Nature Physics, 2007) Strongly suggestive of internal source

8. Current Status (1) – Internal/External SourceResults from Geoff Reeves et al. (Science, submitted, 2013) μ = 3433 MeV/G K =0.11 Re G1/2 Final proof of internal source?

9. Current Status (2) – The wave picture(or: no talk on waves is complete without this graphic from Danny Summers) Plasmasheet: Source of seed population (convection&impulsive injection) Magnetopause: Possible loss mechanism, shadowing + outward diffusion Waves: Drifting electrons encounter several possible wave regions Hiss (loss) inside plasmasphere/plumes, Chorus (energization) outside plasmasphere, and EMIC (strong loss) at edge of plasmasphere / plumes. New: magnetosonic waves near equator

10. Current Status (3) - Characteristics of Fast Waves

11. Current Status (3) - Characteristics of Slow Waves ULF waves from MHD simulations Bz relative to a dipole field in LFM (left); and in a coupled LFM-RCM simulation, from Pembroke et al. (2012). Also numerous studies on ULF observations from spacecraft (GOES, CRRES, etc) – used to calculate DLL, drift resonance interactions

12. Radiation Belt Dynamics (1) The intensity and the structure of the relativistic electron belts is controlled by a balance of: • acceleration • transport • & losses

13. Radiation Belt Dynamics (2) Earthward Radial Diffusion produces betatron acceleration as electrons move to regions of higher B. Perpendicular energy gain enhances the flux of 90° pitch angles. Magnetic moment, µ, is conserved

14. Radiation Belt Dynamics (3) Substorm Injections will produce similar effects to diffusion and are critical for moving particles from open to closed drift orbits. -> source particles for energization processes -> free energy for waves -> NOT included in current modeling efforts!

15. Plasmapause position seems to control the inner edge of the outer electron belt. Radiation Belt Dynamics (4) Whistler mode Hiss inside the plasmasphere produces electron loss through precipitation.

16. Radiation Belt Dynamics (5) EMIC Waves are produced when hot ring current ions stream through the dense plasmasphere/ plasmaspheiric plumes EMIC waves can produce strong MeV pitch angle scattering leading to electron precipitation and isotropization.

17. Radiation Belt Dynamics (6) VLF Chorus is produced by injected hot electrons. Doppler-shifted cyclotron resonance can produce both pitch angle diffusion (losses) and energy diffusion (acceleration).

18. Current Status (4) – Chorus = internal source? Evidence from Meredith et al. 2003 CRRES data: October 9th 1990 Storm Recovery phase associated with: • prolonged substorm activity. • enhanced levels of whistler mode chorus. • gradual acceleration of electrons to relativistic energies.

19. Current Status (4) – ULF drift resonance = internal source? Evidence from Rostoker et al. [1998] ULF wave power observed by a ground magnetometer plotted together with energetic electron fluxes observed at geosynchronous orbit.

20. Current Status (4) – Main Phase Losses? From Green et al., Ukhorisky et al., Chen et al, Shprits et al., Turner et al … Magnetopause: Chen computes last closed drift shell from T01s model and shows that this boundary is often near GEO, down to L*=4.5 for major storms. This plus outward diffusion due to negative gradients (Chen, Shprits) can lead to significant losses (Shprits, Turner). Waves: EMIC for strong diffusion losses proposed (Summers, Horne, Thorne). Recent data (Friedel, Chen) point to this NOT to be a major loss process (but it probably happens, data from NOAA [Søraas]). Whistler/lightning induced losses play a role (Rogers) as do ground based transmitters (Abel &Thorne, Starks). Microburst / Precipitation bands Observations from Sampex (O’Brien). Co-located with Chorus region. With some assumptions, could explain all relativistic electron losses on their own. Also observations from balloons (Milan). Alex Crew estimates 10/20% for main phase/recovery phase max loss contribution (at this meeting).

21. Current Status (4) – Observation of fast losses From Morley et al, 2010 – new RBSP observations at this meeting! Loss of MeV electrons down to L=4 within 1-2 hours Superposed epoch (Morley 20111) study shows these dropouts are a consistent signature of High Speed Solar wind Interactions with the magnetosphere.

22. Inner Radiation belt modeling Approaches (1)Modeling the effect of wave particle interactions on trapped electrons • Main classes of models: • Diffusion models based on Fokker-Planck Equation. • Uses diffusion coefficients to model the effects of waves on radial, pitch angle, energy and cross diffusion • Simple lifetimes to model pitch angle diffusion loss • RAM-type drift physics codes • Uses DLL in static fields or calculates drifts in self consistent magnetic and electric fields • Simple lifetimes to model pitch angle diffusion loss • Uses DEE and Dαα + cross terms) with statistic wave amplitudes or with calculated growth rates -> wave amplitudes • MHD codes with particle tracers • Radial diffusion from self-consistent fields • Traced particles use DEE and Dαα with statistic wave amplitudes • Hybrid codes • Can treat self-consistent EMIC / whistler growth & interaction • Limited coupling to global codes • PIC codes • Once these do the global magnetosphere we may all be able to go home…

23. Inner Radiation belt modeling Approaches (2)What limits current wave particle interaction modeling the most? For ULF wave / magnetic+electric field fluctuation driven radial diffusion global, coupled MHD codes (e.g. LFM + RCM or variants of coupled codes in the SWMF are maturing and may be able to soon replace statistic DLL formulations. For the faster wave modes (EMIC, Chorus, Hiss, Magnetosonic) we may need to rely on diffusion coefficients for some time yet. Required inputs: Background plasma density, ion composition, background magnetic field, wave fields. For bounce/drift averaged quantities, these need to be known globally. -> Many approximations, many degrees of freedom. Additional limitations are all the approximations of quasi-linear theory. Strong non-linear effects are not yet taken into account - these may be able to be included using additional advection terms (Albert).

24. Inner Radiation belt modeling Approaches (3)Diffusion coefficient calculation (Glauert et al, Summers et al, Albert etc) Diffusion coefficient calculations based on quasi-linear theory are computationally expensive and the community has spent a lot of effort to perform these calculations with varying degrees of approximations: For background environmental conditions: • Dipole magnetic field • Some dynamic field models • Simple background density models • Simple ion composition models For the waves: • First order resonances only • Parallel propagation of waves only • Assumed k-distribution of waves (guided by data) • Assumed frequency distribution of waves (guided by data) • Fixed K-distribution along field lines • No feedback of particles on waves, no damping • Currently parameterized by wave power only For global wave power distribution: • We never have global in-situ wave data • Simple statistics based on geomagnetic activity indices • Assumes instantaneous MLT distribution = statistical MLT distribution

25. Inner Radiation belt modeling Approaches (3)Wave Models – Model grid and distribution in one bin L-shell: [3, 12] in step of .2 Local Time: [0, 24]hr in step of 1 hr Mag. Latitude Ranges: [0, 10], [10, 25], [25, 35] and >35 deg AE ranges: <100nT, [100, 300)nT and >300nT

26. Inner Radiation belt modeling Approaches (4)Using diffusion coefficients - challenges • Some basic questions to ponder: • Which of the listed approximations is the “tall pole”? • Particles drift through wave regions repeatedly and integrate the effects of waves over time. How spatially or temporally detailed do we need to make our diffusion coefficients? • Will eliminating the current approximations in calculating diffusion coefficients lead to computationally prohibitive complexity? • Have we reached or will we soon reach the limits of the diffusive approach for modelling the fast wave/particle interaction? • Is our modelling of fast wave particle interactions the “tall pole” in the overall modelling of the inner radiation belt? Compared to, e.g • Specification of boundary conditions • Specification of global magnetic fields • Effects of un-modelled fast transport such as substorm injections

27. Limitation of pure diffusion codes (1)Pitch angle diffusion in realistic fields – drift shell splitting

28. Specifying needed inputs for wave-particle interaction modeling through proxies • Space Physics abounds in the use of proxies, e.g. Dst for the ring current, AE for the electrojet currents, ABI (auroral boundary index from DMSP) for auroral activity, etc… • Advantages: Cheap, often based on simple instrumentation, ground based or based on programmatic missions, can be global and available 24/7, long term availability. Can form a reliable operational input to radiation belt models. • Disadvantages: Often coarse (integrative), may respond to multiple physical processes, mapping to high altitude magnetosphere often problematic.

29. Background electron density Relativistic electron lifetimes from HEO (Joseph Fennell, Aerospace Corporation). Modeled electron lifetimes from Hiss (Chris Jeffery, LANL)

30. PLASMON: Proxies for electron density driving assimilative plasmasphere models Lead by Janos Lichtenberger, Eötvös University, Budapest Uses ground based data from whistlers, field line resonances with in –situ data from LANL MPA, Themis and RBSP with a data assimilative plasmasphere model lead by Anders Jorgensen, NM Tech

31. PLASMON: Automated analyses of whistlers – virtual (whistler) trace transformation [Lichtenberger, JGR, 2009] Whistler Nose frequency related to equatorial electron density and density profile along field line. log10neq=A + B⋅L

32. PLASMON: Automated analyses field line resonances – cross phase method, FLRINV [Berube et al. 2003] Method yields mass density along field line

33. PLASMON: Automated analysis of field line resonances – cross phase method, FLRINV [Berube et al. 2003] Example of automated detection of resonance frequency – example of continuous detection over ~12 hours from European EMMA chain of magnetometer stations

34. PLASMON: data assimilative plasmasphere modeling Data assimilation result with minimal ground-based data set. Observations (red), assimilation result (black), and a reference model (blue). Uses densities inferred from whistlers and field line resonances with a data assimilative DGCPM plasmasphere model [Anders Jorgensen, NM Tech].

35. LEO particle precipitation proxy for high altitude wave distribution and intensity (Y. Chen, LANL) Comparing CRRES wave statistics with NOAA 30 KeV precipitation statistics – deriving model relationship

36. LEO particle precipitation proxy for high altitude wave distribution and intensity Using the statistical wave proxy for near-global, 12hr resolution wave maps during a geomagnetic storm

37. LEO particle precipitation proxy for high altitude wave distribution and intensity Using the statistical wave proxy for real-time wave prediction at RBSP

38. GPS operational dosimeters as a proxy for substorm injection distribution (todo) 100/200 keV – 10 MeV electrons 5/9 MeV – 60 MeV protons

39. GPS high temporal and spatial resolution data November 2003 High Speed Stream event (3hr, 0.10L) GEO GPS 0.15 MeV GPS 1.25 MeV GPS 3 MeV DST SW Speed GEO GPS 0.15 MeV GPS 1.25 MeV GPS 3 MeV DST SW Speed

40. Summary / Conclusion • Coupled MHD codes as a way to “do” radial diffusion is maturing. • For “fast” wave particle interactions the use if diffusion codes for the global problem is likely to be around for some time • Main limitation today seem not to be in the modeling of the physics of wave particle interactions but in the specification of required inputs. • We need to look to other data sources and other methods to specify these inputs (e.g n, BW) in order to increasethe fidelity of modeling. • Ground based / programmatic satellite inputs will be needed for long term operational modeling efforts.