1. Structure and Dynamics of Inner Magnetosphere and Their Effects on Radiation Belt Electrons Chia-Lin Huang Boston University, MA, USA CISM Seminar, March 24 th, 2007 Special thanks: Harlan Spence, Mary Hudson, John Lyon, Jeff Hughes, Howard Singer, Scot Elkington, and many more APL

2. 2 Goals of my Research  To understand the physics describing the structure and dynamics of field configurations in the inner magnetosphere  To assess the performance of global magnetospheric models under various conditions  To quantify the response of global magnetic and electric fields to solar wind variations, and ultimately their effects on radial transport of radiation belt electrons.

3. 3 Motivation: Radiation Belts  Discovery of Van Allen radiation belts – Explorer 1, 1958  Trapped protons & electrons, spatial distribution (2-7 R E ), energy (~MeV) outer belt slot region inner belt J. Goldstein

4. 4 Dynamical Radiation Belt Electrons  Why study radiation belt electrons?  Because they are physically interesting  Radiation damage to spacecraft and human activity in space   Goal: describe and predict how radiation belts evolves in time at a given point in space Green [2002]

5. 5 Solar Wind and Magnetosphere  Average picture of solar wind and magnetosphere (magnetic field, regions, inner mag. plasmas)  Variations of Psw, IMF Bz causes magnetospheric dynamics Ring Current

6. 6 Magnetic Storms  Most intense solar wind-magnetosphere coupling  IMF Bz southward, strong electric field in the tail  Formation of ring current and its effect to field configurations  Dst measures ring current development  Storm sudden commencement (SSC), main phase, and recovery phase  Duration: days

7. 7 Magnetospheric Pulsations  Ultra-low-frequency (ULF) MHD waves  Frequency and time scale: 2-7 mHz, 1-10 minutes  Field fluctuation magnitude  First observed in 19 th century  Waves standing along the magnetic field lines connect to ionospheres [Dungey, 1954]  Morphology and generation mechanisms are not fully understood

8. 8 Global Magnetospheric Models  Provide global B and E fields needed for radiation belt study  Data-based: Tsyganenko models  Parameterized, quansi-static state of average magnetic field configurations  Physics-based: Global MHD code  Self-consistent, time dependent, realistic magnetosphere  Importance and applications, validation of the global models Empirical model Global MHD simulation LFM MHD codeTsyganenko model

9. 9 Charged Particle Motion in Magnetosphere  Gyro, bounce and drift motions  Gyro ~millisecond, bounce ~ 0.1-1 second, drift ~1-10 minutes  Adiabatic invariants and L-shell  To change particle energy, must violate one or more invariants  Sudden changes of field configurations  Small but periodic variation of field configurations

10. 10 Highly Structured and Dynamical Relativistic Electrons  Relativistic electron events: magnetic storms, high speed solar wind stream and quiet intervals Reeves et al. [2007]

11. 11 Why is it so Hard? What Would Help?  Proposed physical processes  Acceleration: large- and small-scale recirculations, heating by Whistler waves, radial diffusion by ULF waves, cusp source, substorm injection, sudden impulse of solar wind pressure and etc.  Loss: pitch angle diffusion, Coulomb collision, and Magnetopause shadowing.  Transport  Difficulties to differentiate the mechanisms:  Lack of Measurements  Lack of an accurate magnetic and electric field model  Converting particle flux to distribution function is tricky  Need better understanding of wave-particle interactions  Computational resource

12. 12 The Rest of the Talk  Magnetospheric field dynamics: data & models  Large-scale: Magnetic storms  Small-scale: ULF wave fields  Effects of field dynamics on radiation belt electrons  Create wave field simulations  Quantify electron radial transport in the wave fields

13. 13 Lyon-Fedder-Mobbary Code Lyon-Fedder-Mobbary Code Lyon et al. [2004]  Uses the ideal MHD equations to model the interaction between the solar wind, magnetosphere, and ionosphere  Simulation domain and grid  2D electrostatic ionosphere  Solar wind inputs  Field configurations and wave field validations by comparing w/ GOES data LFM grid in equatorial plane

14. 14 Data/Model Case Study  24-26 September 1998 major storm event (Dst minimum -213 nT)  LFM inputs: solar wind and IMF data  Geosynchronous orbit Sep98 event: solar wind data and Dst  Compare LFM and GOES B-field at GEO orbit

15. 15 Statistical Data/Model Comparisons  9 magnetic storms; 2- month non-storm interval  LFM field lines are consistently under- stretched, especially during storm-time, on the nightside  Predict reasonable non- storm time field  Improvements of LFM  Increase grid resolution  Add ring current Field residual  B = B MHD – B GOES

16. 16 Statistical comparison of Tsyganenko models and GOES data  52 major magnetic storm from 1996 to 2004  TS05 has the best performance in all local time and storm levels Under-estimate Perfect prediction Over-estimate Field residual  B = B GOES – B Tmodel T96 T02 TS05

17. 17 Consequence of field model errors  Inaccurate B-field model could alter the results of related studies  Example: radial profiles of phase space density of radiation belt electrons  Discrepancies between Tsyganenko models using same inputs  Model field lines traced from GOES-8’s position (left)  Pitch angles at GOES-8’s position and at magnetic equator (right) ~15% error between T96 and TS05

18. 18 ULF Waves in Magnetosphere  Wave sources: shear flow, variation in the solar wind pressure, IMF Bz, and instability etc.  Previous studies: integrated wave power, wave occurrence  Next, calculate wave power as function of frequency using GOES data; wave field prediction of LFM and T model. NASA

19. 19 Power Spectral Density (PSD)  Calculate PSD using 3- hour GOES B-field data  Procedures: 1.Take out sudden field change 2.De-trend w/ polynomial fit 3.De-spike w/ 3 standard deviations 4.High pass filter (0.5 mHz) 5.FFT to obtain PSD [nT 2 /Hz]

20. 20 GOES B-field PSDs in FAC  9 years of GOES data (G-8, G-9 and G-10 satellites)  Field-aligned coordinates  Separate into 3-hour intervals (8 local time sectors)  Calculate PSDs  Median PSD in each frequency bin Noon Midnight Dawn Dusk CompressionalAzimuthal Radial

21. 21 Sorting GOES B b PSD by SW Vx PSD B [nT 2 /Hz]

22. 22 Sorting GOES B b PSD by IMF Bz PSD B [nT 2 /Hz] Bz southward Bz northward

23. 23 ULF Waves in LFM code Direct comparisons of ULF waves during Feb-Apr 1996 in field-aligned coord. PSD B [nT 2 /Hz] Local Time LFM output GOES data B b compressional B n radial B φ azimuthal Much better than expected!

24. 24 Dst and Kp effects on ULF wave power High Kp interval Kp ≥ 4 Low Kp interval Kp < 4 High Dst interval Low Dst interval Dst ≤ -40 nT Dst > -40 nT  ULF wave power has higher dependence on Kp than Dst  Even though LFM does not reproduce perfect ring current, it predicts reasonable field perturbations

25. 25 ULF wave prediction of Tsyganenko model TS05 model LFM code GOES data  Underestimates the wave power at geosynchronous orbit  Field fluctuations are results of an external driver  Lack of the internal physical processes

26. 26 Summary of Model Performance  Use LFM’s wave fields during non-storm time to study ULF wave effects on radiation belt electrons  Such conditions exist during high speed solar wind streams.

27. 27 ULF Wave Effects on RB Electrons  Strong correlation between ULF wave power and radiation belt electron flux [Rostoker et al., 1998]  Drift resonant theory [Hudson et al., 1999 and Elkington et al., 1999]  ULF waves can effectively accelerate relativistic electrons  Quantitative description of wave-particle interaction Rostoker et al. [1998] Elkington et al. [2003]

28. 28 Particle Diffusion in Magnetosphere  Diffusion theory: time evolution of a distribution of particles whose trajectories are disturbed by innumerable small, random changes.  Pitch angle diffusion (loss): violate 1 st or 2 nd invariant  Radial diffusion (transport and acceleration): violate 3 rd invariant (Radial diffusion coefficient)(Radial diffusion equation), where

29. 29 Radial Diffusion Coefficient, D LL  Large deviations in previous studies  Possible shortcomings  Over simplified theoretical assumptions  Lack of accurate magnetic field model and wave field map  Insufficient measurement  M. Walt’s suggestion: follow RB particles in realistic magnetospheric configurations Walt [1994] Experimental (solid) and theoretical (dashed) D LL values

30. 30 When Does LFM Predict Waves Well?  GOES and LFM PSDs sorted by solar wind Vx bins  LFM does better during moderate activities  Create ULF wave activities by driving the LFM code with synthetic solar wind pressure input XO OO

31. 31 Solar Wind Pressure Variation  Histograms of solar wind dynamic pressure from 9 years of Wind data for Vx = 400, 500, and 600 km/s bins  Make time-series pressure variations proportional to solar wind Vx

32. 32 Synthetic Solar Wind Pressure (Vx)  LFM inputs:  Constant Vx; variation in number density.  Northward IMF Bz (+2 nT), to isolate pressure driven waves.  Idealized LFM Vx simulations using high time and spatial resolutions

33. 33 Idealized Vx Simulations GOES statistical study (9 years data) as function of Vx (“mostly” northward IMF) Drive LFM to produce “real” ULF waves with solar wind dynamic pressure variations as function of Vx (“purely” northward IMF) LFM Vx runs GOES data Vx = 400 Vx = 500 Vx=600

34. 34 Eφ Wave Power Spatial Distributions  Wave power increases as Vx (Pd variations) increases  Wave amplitude is higher at larger radial distance (wave source)

35. 35 Radiation Belt Simulations  Test particle code [Elkington et al., 2004]  Satisfy 1 st adiabatic invariant  Guiding center approximation  90 o pitch angle electron  Push particles using LFM magnetic and electric fields  Simulate particles in  LFM Vx = 400 and 600 km/s runs  Particle initial conditions  Fixed μ = 1800 MeV/G  Radial: 4 to 8 R E  1 o azimuthal direction  ~15000 particles /run

36. 36 Rate of Electron Radial Transport (D LL )  Convert particle location to L * [Roederer, 1970]  Calculate our radial diffusion coefficient, D LL (Vx) D LL increases with L D LL increases with Vx

37. 37 Compare D LL Values I  The major differences between previous studies and this work  Amplitude of wave field  IMF Bz  Magnetic field model  Particle energy  Calculating method  Theoretical assumption  Differences make it impossible for a fair comparison  Highlight: Selesnick et al. [1997]  B ~10 nT  B ~1 nT  B ~2 nT

38. 38 Compare D LL Values II  D LL ~ dB 2 [Schulz and Lanzerotti, 1974]  After scaling for wave power  Compare to Selesnick et al. [1997] again  Match well with Vx=600 km/s interval (L-dependent)  Average Vx of Selesnick et al. [2007] and IMF Bz effect  This suggests that radial diffusion is well-simulated, can differentiate from other physical processes  D LL (Vx, Bz,  P dyn, Kp etc.)

39. 39Summary  TS05 best predicts GEO magnetic fields in all conditions  LFM has good predictions of quiet time fields, but not for storm time  ULF wave structures and amplitudes at GEO sorted by selected parameters  ULF wave field predictions: LFM is very good, but not TS05  Radial diffusion coefficient derived from MHD/Particle code

40. 40 Conclusions and Achievements  Most comprehensive, independent study of state-of-the-art empirical magnetic field models  Most quantitative investigation of global MHD simulations in the inner magnetosphere  Most comprehensive observational ULF wave fields at geosynchronous orbit dedicated to outer zone electron study  First exploration on ULF wave field performance of global magnetospheric models  First D LL calculation by following relativistic electrons in realistic, self-consistent field configurations and wave fields of an MHD code