Modelling Electron Radiation Belt Variations During Geomagnetic Storms with the new BAS Global Radiation Belt Model Richard B. Horne Sarah A. Glauert Nigel P. Meredith Mai M. Lam British Antarctic Survey Cambridge UK Sixth European Space Weather Week, Brugge, Belgium, 20th Nov 2009

Radiation Belts - The Problem How do you produce >1 MeV electrons? What causes the variations?

Horne, Nature Physics [2007]

Global Models Several models are based on ‘simple’ 1d radial diffusion But – it omits flux increases due to wave-particle interactions (wpi) New results show conclusively that acceleration and loss due to wpi is key for radiation belt dynamics Need a 3d model which includes radial diffusion and wpi Need good models for many types of waves ULF, chorus, plasmaspheric hiss, EMIC, magnetosonic, lightning Loss term

Basic Equations Electron motion has 3 components –drift, bounce, gyration Each motion has an associated adiabatic invariant Use this fact to describe radiation belt variations by a diffusion equation f is the phase space density J i are the 3 adiabatic invariants D JJ are diffusion coefficients J i is not an easy coordinate system to work in Difficult to specify boundary conditions in terms of J i Electron flux is usually measured in energy, pitch angle, position Diffusion coefficients are calculated in terms of energy, pitch angle, not J i and therefore must be transformed

New Variables Change from invariants ( J 1, J 2, J 3 ) to (  E, L* )  - Equatorial pitch-angle E - Energy L* - Roederer L * (denoted simply by L from here) Phase space density, f ( , E, L, t ), is now given by The diffusion coefficients depend on , E, L and magnetic activity

Simplifications Omit cross diffusion terms such as D aE D EL Some of these terms (e.g. D aE ) may be important We have transformed completely to (  E, L ), so radial derivatives are with constant (  E ) not constant ( J 1, J 2 ) pitch-angle diffusion energy diffusion radial diffusion Losses – e.g. Loss cone , E, L All diffusion coefficients depend on , E, L and magnetic activity

Initial and Boundary Conditions 6 boundary conditions At  = 0 o and  = 90 o df/d  = 0 At  E = E min f from data (CRRES) At  E = E max f = 0 ( E max large) At  L = L min and L = L max f from data CRRES data Converted to L*. Too sparse to provide good coverage at all equatorial pitch angles At each L*, energy and time fit flux with A sin n  eq Interpolate fitted data for initial and boundary conditions. Convert from flux to phase-space density Day of 1990

Diffusion Coefficients D LL Driven by ULF waves Drives radial diffusion (transport) across the magnetic field Function of magnetic activity (Kp), pitch-angle, energy and L shell From [Brautigam & Albert, JGR,2000] D   and D EE Driven by wave-particle interactions Drive acceleration and loss Function of magnetic activity (AE*), pitch-angle, energy and L shell Calculated by PADIE [Glauert & Horne, JGR,2005] Current model includes diffusion due to Hiss and Chorus

Plasmaspheric Hiss hiss plasmapause f uh r f ce f lhr Occurs in high-density regions Electron loss to the atmosphere

BAS Hiss Model [Meredith et al, JGR, 2006, 2007, 2009] Model construction: Identify hiss in the CRRES wave data Bin wave data and fpe/fce by activity level (Kp and AE), 0.5L shell and 1 hr MLT Calculate average frequency spectrum from the data Use the spectra to calculate diffusion coefficients at all energies Create tables of f pe /f ce and B w at every 0.1 L and 1 hour MLT To use the data: For a given activity level (kp) and L shell For each MLT bin, look up f pe /f ce from the table, select the diffusion coefficient and scale by B w Add diffusion coefficients for each MLT bin

Quiet-time Decay Test for hiss model Period of quiet time decay Start at day 340 (6 Dec.) 1990 Following active period flux decays and slot region reforms Want to reproduce decay 90 o flux (cm -2 s -1 ster -1 MeV -1 ) Data – 510 keV

Hiss - effect of wave-normal angle Data Model

Data Model Hiss - effect of wave-normal angle

Data Model Hiss - effect of wave-normal angle

Diffusion by chorus waves chorus plasmapause f uh r f ce f lhr To simulate storms we need chorus acceleration Generally observed outside the plasmapause Frequency range 0.1 f ce < f < 0.8 f ce

BAS Chorus Wave Model Based on [Glauert & Horne, JGR, 2005] Driven by AE* Frequency & wave-normal distributions independent of L-shell CRRES database provides f pe /f ce and B w for given activity, L and MLT Diffusion coefficients for each 1 hour of MLT Equatorial (0< <15 o ) and mid-latitude (15 o < <30 o ) chorus treated separately Energy (keV) Pitch angle ( o ) D EE D αα AE* < 100nT 100nT <AE*< 300nT AE* > 300nT

9 October 1990 CME storm Data 90 o flux (cm -2 s -1 ster -1 MeV -1 ) Model

9 October 1990 CME storm Model : Radial diffusion Data 90 o flux (cm -2 s -1 ster -1 MeV -1 )

9 October 1990 CME storm Data Model : Chorus + Radial diffusion 90 o flux (cm -2 s -1 ster -1 MeV -1 )

9 October 1990 CME storm Radial diffusion + Chorus diffusion

9 October 1990 CME storm Radial diffusion + Chorus + Hiss diffusion

Model : Chorus + Radial diffusion 20 June 1991 CIR Storm Data

June 1991 CIR storm Radial diffusion + Chorus diffusion

June 1991 CIR storm Radial diffusion + Chorus + Hiss diffusion

Conclusions First results from BAS global radiation belt model Includes wave-particle interactions and radial diffusion Wave propagation direction makes a big difference to losses – slot region CME driven storm Radial diffusion alone underestimates the increase in flux > 0.5MeV Chorus gives flux increase Addition of hiss and chorus gives best fit to data Reproduce flux drop-out but minimum flux is too high CIR driven storm Reproduce the persistance of the radiation belt Do not reproduce flux drop out Model gives too much outward transport Suggests outer trapping boundary has moved inwards

Research to SW forecasting Many issues How can we adapt research models to forecast ahead? What type of models should we use? How far in advance can we forecast ? Data availability and access time?

Research to SW forecasting Drive diffusion coefficients by solar wind data - ACE Provides ~ 1 hour forecast Assuming the solar wind remains constant thereafter provides longer forecast – up to 1-2 days, but less reliable Note, even if sw is constant, the radiation belt flux will change in time If we can forecast the SW, we can forecast the radiation belts further ahead –Longer term goal

Boundary conditions Research models use data as a boundary condition, e.g. at L=6.6 We want to forecast the data, not use it as a boundary condition Difficult for 1d models Flows naturally from 3d physics based models

Research to SW forecasting Chen et al. [2007] Need 3d models Wpi provides a source in the inner region Radial diffusion gives outward (inward) transport Provides whole radiation bet modelling Galileo/GPS orbits

Difficulties – Coupling models Losses can be large at low energy boundary Assumed that this is balanced by inward transport of low energy electrons Need to couple different models and incorporate different physical processes Radial Diffusion Convection Wave-particle interactions

Data Assimilation Methods Use in meteorology Needs data in real time for RB work Needs physic based models Quantify improvements in the physical modelling Natural partnership Geoff Reeves and the next talk

Summary Forecasting requires –3d physics based models –Real time data access ACE GEO GPS/Galileo –Large modelling effort Coupling of models Model improvements Data assimilation –International collaboration