3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium Ring current models: How well can they be applied for space weather modeling purposes? N. Yu. Ganushkina, T. I. Pulkkinen (Finnish Meteorological Institute, Space Research, Helsinki, Finland), A. Milillo (Istituto di Fisica dello Spazio Interplanetario, Rome, Italy), M. Liemohn (University of Michigan, Space Physics Research Laboratory, USA) J. Geophys. Res., 111, A11S08, doi: /2006JA011609, 2006

Outline  Following the evolution of proton ring current during the GEM IM/S Challenge storm event on April 21-25, 2001 using three ring current models: - the ring current model combined with tracing particles numerically in the drift approximation by Ganushkina et al., Ann. Geophys., 23, , 2005; - the empirical model of proton fluxes in the inner magnetosphere by Milillo et al., J. Geophys. Res., 108, doi: /2002JA009581, 2003; - the kinetic ring current-atmosphere interaction model (RAM) by Liemohn et al., J. Geophys. Res., 106, 10,883-10,904,  Focus on contributions from protons in different energy ranges to the ring current energy during different storm phases (base: Polar CAMMICE/MICS observations).  Study the influence on the model ring current energy of the - choice of magnetic and electric field models, - initial particle distributions, - role of substorm-associated electric fields in particle transport and energization.  Discussion on outputs from different models. 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

April 21-25, 2001: Storm event overview 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium  Shock arrival: small Vx junp of 100 km/s, large density pulse with Psw to 10 nPa, IMF Bz > 0 at 2145 UT Apr 21, SYM-H from 0 to 30 nT, no AE increase, Kp around 3  Cloud arrival: IMF Bz < 0 at 0130 UT Apr 22, Vx from 400 km/s to 300 km/s, Psw fluctuating at 3 nPa, SYM-H negative reaching -100 nT at 1540 UT Apr 22, AE about 450 nT at 0200 UT Apr 22, more activation of 1500 nT with SYM-H decrease, Kp =6 at SYM-H min  Storm recovery: several SYM-H enhancements during cloud passage, AE low, Kp below 2, SW and IMF nominal, SYM-H to 0 after cloud passage

Ring current energy density and total energy calculated from Polar CAMMICE/MICS measurements  Energy density of RC protons j(E, L) – measured flux.  Total proton ring current energy: integrated over RC volume of V=10 23 m 3 (torus with crossection of 2.5 Re, radius of 5 Re), symmetric, no PA corrections  Previous statistical results: - Before storm: main contribution from keV, - Main phase: dominance of keV, - Recovery: dominance of keV.  Difference for April 21-25, 2001 storm: Smaller values, dominance of 1-30 keV. - Polar orbit evolution, ring current fast crossings at high magnetic latitudes, - underestimate of keV 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

Ganushkina et al model description  Drift of protons with 90º±60ºpitch angles, 1st and 2nd invariants = const in time-dependent magnetic and electric fields.  kappa-type initial distribution with the observed parameters (T, n) by LANL MPA at R= MLT in the equatorial plane.  Drift velocity as sum of ExB and magnetic (gradient and curvature) drifts: where E 0 and B 0 are electric and magnetic fields, p is the particle moment, q is the particle charge, τ b is the bounce period, B m is the magnetic field and mirror point S m, ds is the element of magnetic field line length.  Changes in distribution function and flux calculations using Liouville’s theorem (conservation of distribution function along dynamic trajectory of particles) taking into account charge-exchange processes with cross section by Janev and Smith, 1993 and number density of neutrals by thermosphere model MSISE 90 (Hedin, 1991) 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

 kappa-type initial distribution with n and T II and T  by LANL MPA; where n is the particle number density, m is the particle mass, E 0 = k B T(1-3/2k) is the distribution peak particle energy, k B = * J/K is the Boltzmann constant, T = 1/3 (T II + 2T  ), gamma functions computed for k=5.  Time-dependent boundary conditions: - measurements within 4 h around midnight; - values averaged for more than one satellite simultaneously in the region; - linear interpolation of data when no satellite. 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium Ganushkina et al model: Initial boundary conditions for April 21-25, 2001 storm

Electric field models: (1) Kp-dependent Volland-Stern convection electric field with observed Kp  is the magnetic local time,  0 = 0 is the offset angle from dawn-dusk meridian; (2) Boyle et al., 1997 polar cap potential dependent on solar wind and IMF parameters applied to Volland-Stern convection field  IMF is the IMF clock angle. Ganushkina et al model: Models for electric fields for April 21-25, 2001 storm 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

Magnetic field models: (1) dipole; (2) Tsyganenko T89 model parameterized by Kp, Kp observed; (3) Tsyganenko T01s model with the observed input parameters such as Dst index, solar wind dynamic pressure Psw, IMF By and IMF Bz, functions G1 and G2, which depend on IMF Bz and Vsw and take into account the history of solar wind. Ganushkina et al model: Models for magnetic fields for April 21-25, 2001 storm 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

Ganushkina et al model results for April 21-25, 2001 storm : Influence of electric and magnetic field models 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium No initial distribution in the inner magnetosphere

Ganushkina et al model: Electric field pulse model Time varying fields associated with dipolarization in magnetotail, modeled as an electromagnetic pulse (Li et al., 1998; Sarris et al., 2002):  Perturbed fields propagate from tail toward the Earth;  Time-dependent Gaussian pulse with azimuthal E;  E propagates radially inward at a decreasing velocity;  decreases away from midnight. Time-dependent B from the pulse is calculated by Faraday’s law. In spherical coordinates (r, ,  ): - location of the pulse maximum, r I determines pulse arrival time - pulse front velocity, d - width of pulse, c 1, p describe LT dependence of E amplitude, largest at  0, - delay of pulse from  0 to other LTs, c 2 - delay magnitude, v a - longitudinal propagation speed 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

Ganushkina et al. model: Addition of pulsed electromagnetic field for April 21-25, 2001 storm 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

Ganushkina et al model results for April 21-25, 2001 storm : Role of smaller-scale electric fields 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium No initial distribution in the inner magnetosphere

Ganushkina et al model: Initial distribution in the inner magnetosphere for April 21-23, 2001 storm Initial energy density distribution Final ED map while tracing with empty magnetosphere 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium  Available observational data not sufficient to reconstruct the prestorm initial proton distribution in the inner magnetosphere.  As initial distribution - model distribution obtained at the end of Apr 25, 2001 after tracing with empty inner magnetosphere.

Ganushkina et al model results for April 21-25, 2001 storm : Effects on the initial distribution 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium Initial distribution in the inner magnetosphere

Ganushkina et al model results for April 21-25, 2001 storm : Effects on the initial distribution and smaller-scale fields 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium Initial distribution in the inner magnetosphere

Milillo et al. model description  Based on AMPTE/CHEM data of 90  PA H+ fluxes at L=3-9.3 for keV.  Gives ion distributions as a function of L, energy, MLT.  Functional form of model distribution consists of: (1) Gaussian in L added to a continuum with a Gaussian shape in energy for proton flux at intermediate energies of 5-80 keV – CONVECTION/INJECTION POPULATION (2) Gaussian for high energy population (> 40 keV) – DIFFUSION POPULATION  For April 21-25, 2001 storm LANL MPA data for 3-45 keV and SOPA data for keV added.  Set of 6 time-evolving parameters (intensity, energy position and width of two populations) applied to the model, model gives storm evolution of two populations.  Total energy is calculated by integrating energy density. 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

Liemohn et al. model description 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium  Kinetic ring current-atmosphere interaction model (RAM) - solves the gyration and bounce-averaged Boltzmann equation inside of geostationary orbit; - uses second-order accurate numerical schemes to determine hot ion phase space distribution as a function of time, equatorial plane location, energy, and equatorial pitch angle.  Initial conditions from Sheldon and Hamilton [1993].  Sources specified by LANL MPA and SOPA data across the nightside outer boundary.  Loss mechanisms include - flow of plasma out the dayside outer boundary, - precipitation of particles into the upper atmosphere, - pitch angle scattering and drag from Coulomb collisions (plasmaspheric model of Ober et al. [1997]), - charge exchange with neutral hydrogen geocorona (Rairden et al. [1986]).

Milillo et al., Liemohn et al. and Ganushkina et al. model results for April 21-25, 2001 storm : Comparison 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

Modelling of April 21-25, 2001 storm event by three ring current models All models predict - high-energy protons dominate before the storm, - the low and medium energy protons are rapidly enhanced during the main phase of the storm, - slowly decline in energy content throughout the recovery phase of the storm. - main difference between the models is in the contribution from the high-energy protons during the storm.  Ganushkina model predicts a low contribution from these protons, unless an extra electric field is included to replicate substorm injections.  The Milillo model predicts that the high-energy protons dominate throughout the storm.  The Liemohn model predicts a constant contribution from the high-energy protons during the late recovery phase. Summary 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

General Summary 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium  Changing from dipole to more realistic magnetic field decreased the RC energy content by 30%.  Details and strength of convection electric field cause only small changes in time-evolving RC energy content.  Time-dependent and localized electric fields are the only means to provide preferential increase of high-energy particles.  Role of diffused processes is rather small in bringing RC ion during main phase.  Relative contributions from diffusion and convection to RC energy content are equal during recovery phase.  Initial populations in the inner magnetosphere and boundary conditions have significant effects on model results.

Summary: Model results to Dst 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium Converting peak energy values to magnetic perturbations at the Earth’s surface DPS formulation:  B = 3.98 * E RC Ganushkina model, E RC = 4*10 14 J,  B = 10 nT Milillo and Liemohn models, E RC = 14*10 14 J,  B = 35 nT Observations: 100 nT - Models significantly underestimate the total energy in the ring current region - DPS relation does not account for contributions of other current systems to Dst Include of acceleration processes into models, which are significant in producing high-energy populations (can affect humans and/or technological systems in space) Need for realistic electric field models!

References (1) Boyle, C. B., P. H. Reiff, and M. R. Hairston (1997), Empirical polar cap potentials, J. Geophys. Res., 102, Ganushkina, N. Yu., T. I. Pulkkinen, T. Fritz (2005), Role of substorm-associated impulsive electric fields in the ring current development during storms, Ann. Geophys., 23, Hedin, A. E. (1991), Extension of the MSIS thermosphere model into the middle and lower atmosphere, J. Geophys. Res., 96, Janev, R. K. and J. J. Smith (1993), Cross sections for collision processes of hydrogen atoms with electrons, protons, and multiply-charged ions, in: Atomic and Plasma-Material Interaction Data for Fusion, Int. At. Energ. Agency, 4. Li, X., D. N. Baker, M. Temerin, et al. (1998), Simulation of dispersionless injections and drift echoes of energetic electrons associated with substorms, Geophys. Res. Lett., 25, Liemohn, M. W., J. U. Kozyra, M. F. Thomsen, et al., Dominant role of the asymmetric ring current in producing the stormtime Dst (2001), J. Geophys. Res., 106, 10,883-10,904. 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

References (2) Milillo A., S. Orsini, and I. A. Daglis (2001), Empirical model of proton fluxes in the equatorial inner magnetosphere. 1. Development, J. Geophys. Res., 106, Milillo A., S. Orsini, D. C. Delcourt, A. Mura, S. Massetti, E. De Angelis, and Y. Ebihara (2003), Empirical model of proton fluxes in the equatorial inner magnetosphere: 2. Properties and applications, J. Geophys. Res., 108, doi: /2002JA Ober, D. M., J. L. Horwitz, and D. L. Gallagher (1997), Formation of density troughs embedded in the outer plasmasphere by subauroral ion drift events, J. Geophys. Res., 102, 14,595. Orsini, S., A. Milillo, A. Mura (2004), modeling of the Inner Magnetospheric Time- Evolving Plasma: an empirical approach based on proton distribution, J. Geophys. Res., 109, A11216, doi: / 2004JA Rairden, R. L., L. A. Frank, and J. D. Craven (1986), Geocoronal imaging with Dynamics Explorer, J. Geophys. Res., 91, 13,613. Sarris, T. E, X. Li, N. Tsaggas, and N. Paschalidis (2002), Modeling energetic particle injections in dynamic pulse fields with varying propagation speeds, J. Geophys. Res., 107, 1033, doi: /2001JA d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

References (3) Sheldon R. B., and D. C. Hamilton (1993), Ion transport and loss in the Earth's quiet ring current 1. Data and standard model, J. Geophys. Res., 98, Stern, D. P. (1975), The motion of a proton in the equatorial magnetosphere, J. Geophys. Res., 80, Tsyganenko, N. A. (1989), A magnetospheric magnetic field model with a warped tail current sheet, Planet. Space Sci., 37, Tsyganenko, N. A. (2002a), A model of the near magnetosphere with a dawn-dusk asymmetry: 1. Mathematical structure, J. Geophys. Res., 107, 1179, doi: /2001JA Tsyganenko, N. A. (2002b), A model of the near magnetosphere with a dawn-dusk asymmetry: 2. Parameterization and fitting to observations, J. Geophys. Res., 107, 1176, doi: /2001JA Volland, H. (1973), A semi-empirical model of large-scale magnetospheric electric field, J. Geophys. Res., 78, 171. Wilken, B. et al. (1992), Magnetospheric ion composition spectrometer onboard the CRRES spacecraft, J. Spacecraft and Rockets, 29, d European Space Weather Week – November 13-17, 2006, Brussels, Belgium

Contributions to RC energy from protons with different energy ranges: 27 storms’ statistics 3d European Space Weather Week – November 13-17, 2006, Brussels, Belgium