The Role of Cold Plasma Density in Radiation belt Dynamics

1. R. Friedel1, A. Jorgensen2, R. Skoug1 and C. Kletzing3 LANL1, U. Iowa3, NM Tech2 Plus many community contributions… The Role of Cold Plasma Density in Radiation belt Dynamics

2. Contents • “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 • Summary • Simulation example using proxies (Oct 2012 Storm

3. Brief History 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

4. Brief HistoryResults 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.

5. 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

6. Radiation Belt Dynamics The intensity and the structure of the relativistic electron belts is controlled by a balance of: • acceleration • transport • & losses • The plasma background density in these regions controls many of the critical processes!

7. Current Status - Characteristics of Fast Waves

8. Current Status - 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

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

10. Current Status – 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. • source population • gradual acceleration of electrons to relativistic energies.

11. Current Status – 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.

12. 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 • Use 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…Coarse global PIC is evolving (Lapenta)

13. 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 (e.g. Brautigam & Albert). 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).

14. 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 – affect resonance conditions and wave propagation • 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

15. 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

16. 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.

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

18. 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

19. Van Allen Probes Mission: EMFISIS Density • Density is determined from the upper hybrid line or continuum cutoff depending on region. • Standard cadence is one measurement every six seconds. • Process is being automated, but still requires significant manual checking. • Level 4 public is expected to be available in the next few months on a regular basis. • Requests for density data should be sent to Bill Kurth with copy to Craig Kletzing. • Have constructed a list of of PLASMON whistler station data during conjunctions with RBSP spacecraft which is being submitted to EMFISIS team.

20. Example from Oct 9, 2012 For this example, standard models give n=12/cc, but measurement is only 4/cc Data courtesy of Craig Cletzing

21. 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

22. 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

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

24. Summary • 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 seems 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, boundary conditions) in order to increase the fidelity of modeling. • Ground based / programmatic satellite inputs will be needed for long term operational modeling efforts. • Let me finish off with an example using one of these proxies… The research leading to these results has received funding from the European Union Seventh Framework Program [FP7/2007-2013] under grant agreement n°263218

25. DREAM3D Simulation of the Oct. 2012 event • DREAM3D diffusion model 11 Last closed drift shell L* 9 TS04 7 5 “Event-specific chorus wave and electron seed population models in DREAM3D using the Van Allen Probes” Weichau Tu et al, JGR 2013, submitted Work done at LANL 10-6 PSD data: µ=2000 MeV/G K=0.1 G1/2Re 6 10-7 5 10-8 L* 10-9 4 10-10 20 3 -20 -60 Dst (nT) -100 Oct 10 Oct 11 3D Fokker-Planck Equation: Oct 6 Oct 7 Oct 8 Oct 9 2012

26. DREAM3D Simulation of the Oct. 2012 event • Modeling the dropout: • Lmax=11, magnetopause shadowing: short lifetimes (E-dependent) outside LCDS • Outward radial diffusion 11 Last closed drift shell L* 9 TS04 7 5 6 10-6 10-6 PSD data: µ=2000 MeV/G K=0.1 G1/2Re 6 10-7 10-7 5 5 L* 10-8 10-8 L* 4 10-9 4 10-9 10-10 3 3 RD only 10-10 Oct 10 Oct 11 Oct 6 Oct 7 Oct 8 Oct 9 2012

27. DREAM3D Simulation of the Oct. 2012 event • Modeling the enhancement • Event-specific chorus waves 11 Last closed drift shell L* 9 TS04 7 pT2 5 6 6 10-6 10-6 10-6 PSD data: µ=2000 MeV/G K=0.1 G1/2Re 6 10-7 10-7 10-7 5 5 5 L* L* 10-8 10-8 10-8 L* Empirical model Bw(Mlat) 4 4 10-9 4 10-9 10-9 10-10 3 + 3 3 RD only NOAA proxy model: Bw(MLT,L,time) pT 100 100<AE*<300nT AE*>300nT AE*<100nT 10-10 10-10 RD+chorus 10 Oct 10 Oct 10 Oct 11 Oct 11 1 Lower-band chorus Oct 6 Oct 6 Oct 7 Oct 7 Oct 8 Oct 8 Oct 9 Oct 9 2012 2012

28. DREAM3D Simulation of the Oct. 2012 event • Modeling the enhancement • Event-specific chorus waves • Realistic source population (100s keV) 11 Last closed drift shell L* 9 TS04 7 5 6 6 6 10-6 10-6 10-6 PSD data: µ=2000 MeV/G K=0.1 G1/2Re 6 µ=88 MeV/G K=0.1 G1/2Re 10-7 10-7 10-7 5 5 5 5 L* L* L* 10-8 10-8 10-8 L* 4 4 4 10-9 4 10-9 10-9 10-10 3 3 3 RD only 3 RD only L*=4.2, αeq=50o electron flux data 108 106 10-10 10-10 RD+chorus 104 Oct 10 Oct 10 Oct 11 Oct 11 102 100 Oct 6 Oct 6 Oct 7 Oct 7 Oct 8 Oct 8 Oct 9 Oct 9 2012 2012

29. DREAM3D Simulation of the Oct. 2012 event • Modeling the enhancement • Event-specific chorus waves • Realistic source population (100s keV) 11 Last closed drift shell L* 9 TS04 7 5 6 6 6 10-6 10-6 10-6 PSD data: µ=2000 MeV/G K=0.1 G1/2Re 6 µ=88 MeV/G K=0.1 G1/2Re 10-7 10-7 10-7 5 5 5 5 L* L* L* 10-8 10-8 10-8 L* 4 4 4 10-9 4 10-9 10-9 10-10 3 3 3 RD only 3 RD only L*=4.2, αeq=50o electron flux data 108 106 10-10 10-10 RD+chorus +Seed 104 Oct 10 Oct 10 Oct 11 Oct 11 102 100 Oct 6 Oct 6 Oct 7 Oct 7 Oct 8 Oct 8 Oct 9 Oct 9 2012 2012