Stormtime plasmasheet access to the inner magnetosphere: evidence for an internal source S. R. Elkington LASP, University of Colorado, Boulder A. A. Chan, B. Yu Rice University, Houston, TX M. Wiltberger HAO/NCAR, Boulder, CO Rarotonga Energetic Particle Workshop Cook Islands August 2007

Stochastic transport: Fick’s law Diffusion (in any coordinate) will act to smooth out gradients in that variable. The net “current” G of particles diffusing across a position is given by Fick’s Law:

Does radial diffusion act as a source or a loss? The net effect of radial diffusion depends on the phase space gradient in L: High f at outer boundary, acts as a source Low f at outer boundary, may act as a loss

Energization through radial transport: a plasma sheet source? Simplistic considerations put r 0 ~20 R E for M corresponding to a 1 MeV geosynchronous electron Simplistic considerations put r 0 ~20 R E for M corresponding to a 1 MeV geosynchronous electron Conversely, W for r 0 =6.6R E is 50 keV. Conversely, W for r 0 =6.6R E is 50 keV. Does diffusion always act as a loss process? Does diffusion always act as a loss process? N. Tsyganenko os/data-based/modeling.html

MHD/particle simulations of plasmasheet access Previous simulations have indicated that the plasmasheet may serve as a direct source of radiation belt electrons by transporting and heating particles from the plasmasheet. What conditions in the plasmasheet must prevail for the particles to have access? What is the contribution of plasmasheet particles to the trapped population? Does the ‘size’ of an event matter? Does the stage of an event matter? A storm: 01/28/1995 HSSW event, B Z fluctuates N-S D ST ~ -60 nT A bigger storm: 09/24/1998 Prolonged B Z <10 nT D ST < -200 nT A really, really big storm: 03/31/2001 Prolonged B Z <-40nT D ST < -380 nT

Simple picture of electron drift Electron drift paths in the T96 model Electron drift paths in the T96 model Electron  =.002 MeV/nT Electron  =.002 MeV/nT Energy=~ 1MeV at geo Energy=~ 1MeV at geo E convection=2 mV/m E convection=2 mV/m Electrons that can diffuse radially onto closed drift paths come from dusk flanks. Electrons that can diffuse radially onto closed drift paths come from dusk flanks. electron source region Trapped orbits J. Green, S. Elkington

Duskward flows in the plasmasheet During some parts of the main phase, all three storms exhibit significant duskward flows in the plasmasheet. However, the January 1995 event shows fewer and less-frequent duskward injections of plasma.

Tracking phase space density in a test particle simulation Q3 We calculate phase space densities using a method suggested by D. Nunn [J. Comput. Phys., 1993]. In this technique, conservation of phase space density along a trajectory is enforced a priori. The contribution of each test particle (“trajectory marker”) is calculated on a grid using an areal weighting technique: The flux at each grid point is the usual Q1 Q4 Q2 A1 A3 A2 A4 e-e-

Plasmasheet/Radiation belts phase space density Taylor et al. [JGR 2004]Asnes et al. [2006] Cluster-RAPID data provides a valuable view of the distribution function in the plasmasheet [Taylor et al., 2004; A. Asnes, 2006]. Statistical efforts have cataloged the phase space density as a function of solar wind conditions, K P, plasmasheet , etc.

Phase space density: 03/31/06 Initially trapped population assigned a phase space density f 0. Plasmasheet population assigned a normalized phase space density 5 f 0. Phase space density calculated according to Nunn [1993].

PSD calculations for other storms… January 1995September 1998 (final) The (big) September 1998 storm shows a significant change in trapped PSD as a result of coupling to the plasmasheet. The more moderate storm of January 1995 showed almost no coupling with the plasmasheet.

Alfven Layers in the MHD During periods of less-strong magnetospheric driving, well-defined Alfven Layers are observed to form in all the storms thus far studied. During these times, there is no access for equatorial plasmasheet particles to the inner magnetosphere.

Particle injection vs. IMF conditions January 1995September 1998March 2001 Calculations of the total particle number in the simulation (top frame) suggest that effective trapping of plasmasheet particles may only occur when strong magnetospheric convection is being driven by extended periods of southward IMF. i.e., the flux increases observed to occur in the 1-2 days following storm main phase must result from either redistribution of previously-injected and trapped populations, or from an internal acceleration source.

January 1995 storm, trapped particle dynamics Hilmer et al., [JGR, 2000] examined energetic electrons at geosynchronous and GPS altitudes for the January 1995 event, concluding that the observations were consistent with a source at/beyond geosynchronous. Can we reconcile these observations with our simulation results, which show no Plasmasheet source of particles?

Simulation Result I : the January 1995 storm Event Simulated (red) and observed (blue) phase space density of the energetic electrons (M=2100 MeV/G). Here model uses a free outer boundary condition and infinite lifetime of electrons.

Simulation Result II : the January 1995 storm Event Simulated (red) and observed (blue) phase space density of the energetic electrons. Here model uses the the dynamic outer boundary conditions from the observations and infinite lifetime of electrons.

Incorporating losses and VLF interactions Interactions with non-MHD waves may be accounted for in an ad hoc way by appropriately adjusting the phase space density along each trajectory when the particles pass through regions where such waves occur (e.g. the plasmapause).

Simulation Result III : the January 1995 storm Event Simulated (red) and observed (blue) phase space density of the energetic electrons. Here model uses the dynamic outer boundary condition and decay lifetime of electrons based on Shprits et al loss formula.

Summary/conclusions Plasmasheet access to the inner magnetosphere dictates whether radial transport (convection/ diffusion) will act as a source or loss of radiation belt particles. Plasmasheet access to the inner magnetosphere dictates whether radial transport (convection/ diffusion) will act as a source or loss of radiation belt particles. We have used MHD/particle simulations to investigate plasmasheet access during three different storms of varying size. We have used MHD/particle simulations to investigate plasmasheet access during three different storms of varying size. Equatorial plasmasheet particles have access during the main phase of the larger storms Equatorial plasmasheet particles have access during the main phase of the larger storms Phase space density calculations indicate the plasmasheet may be a significant source of particles during the main phase of a storm. Phase space density calculations indicate the plasmasheet may be a significant source of particles during the main phase of a storm. Simple analytic models indicate injected plasmasheet particles must originate from the dusk flank. Simple analytic models indicate injected plasmasheet particles must originate from the dusk flank. MHD simulations often show duskward flows as convecting plasma breaks in the inner magnetosphere during main phase, particularly for the larger storms. MHD simulations often show duskward flows as convecting plasma breaks in the inner magnetosphere during main phase, particularly for the larger storms.

Summary/conclusions (cont) During the recovery phase (IMF-N), all three storms show well- developed Alfven layers, and no plasmasheet access to the inner magnetosphere. During the recovery phase (IMF-N), all three storms show well- developed Alfven layers, and no plasmasheet access to the inner magnetosphere. Diffusion acts predominantly as a loss during this time. Diffusion acts predominantly as a loss during this time. Suggests phase space density increases observed during recovery phase is a result of trapped particle redistribution and local acceleration of keV particles. Suggests phase space density increases observed during recovery phase is a result of trapped particle redistribution and local acceleration of keV particles. The GEO/GPS increase in flux observed by Hilmer et al. during January 1995 can be reproduced by the MHD particle simulations iff: The GEO/GPS increase in flux observed by Hilmer et al. during January 1995 can be reproduced by the MHD particle simulations iff: Boundary conditions at GEO are set to match observations. Boundary conditions at GEO are set to match observations. Finite lifetime of particles included. Finite lifetime of particles included. The lack of a plasmasheet source for January 1995, coupled with better agreement using observed BC, strongly suggests a local source near geosynchronous during main phase of this event. The lack of a plasmasheet source for January 1995, coupled with better agreement using observed BC, strongly suggests a local source near geosynchronous during main phase of this event.