Stormtime plasmasheet Stormtime plasmasheet access to the inner access to the inner

magnetosphere: magnetosphere: evidence for an internal evidence for an internal

sourcesourceS. R. ElkingtonS. R. ElkingtonLASP, University of Colorado, BoulderLASP, University of Colorado, Boulder

A. A. Chan, B. YuA. A. Chan, B. YuRice University, Houston, TXRice University, Houston, TX

M. WiltbergerM. WiltbergerHAO/NCAR, Boulder, COHAO/NCAR, Boulder, CO

Rarotonga Energetic Particle Workshop

Cook IslandsAugust 2007

Stochastic transport: Stochastic transport: Fick’s lawFick’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:

x

fDG

Does radial diffusion act as Does radial diffusion act as a source or a loss?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 Energization through radial transport: a plasma sheet transport: a plasma sheet

source?source? Simplistic considerations put Simplistic considerations put rr00~20 ~20

RREE for for MM corresponding to a corresponding to a 1 MeV1 MeV geosynchronous electrongeosynchronous electron

Conversely, Conversely, W for rW for r00=6.6R=6.6REE is 50 keV. is 50 keV. Does diffusion always act as a loss Does diffusion always act as a loss

process?process?

N. Tsyganenkohttp://nssdc.gsfc.nasa.gov/space/model/magnetos/data-based/modeling.html

4

1

0

30

00 ||

3

Eq

RBRLr EE

MHD/particle simulations MHD/particle simulations of plasmasheet accessof 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, BZ fluctuates N-S•DST ~ -60 nT

A bigger storm: 09/24/1998•Prolonged BZ<10 nT•DST < -200 nT

A really, really big storm: 03/31/2001•Prolonged BZ<-40nT•DST < -380 nT

Simple picture of electron Simple picture of electron driftdrift

Electron drift paths in the T96 modelElectron drift paths in the T96 model Electron Electron =.002 MeV/nT=.002 MeV/nT Energy=~ 1MeV at geoEnergy=~ 1MeV at geo E convection=2 mV/mE convection=2 mV/m

Electrons that can diffuse radially onto closed drift paths Electrons that can diffuse radially onto closed drift paths come from dusk flanks.come from dusk flanks.

electron source region

Trapped orbits

J. Green, S. Elkington

Duskward flows in the Duskward flows in the plasmasheetplasmasheet

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 Tracking phase space density in a test particle simulationa 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:

NN

N

NN

AAA

Af

f/,1

,1,0

1

The flux at each grid point is the usual

fpj 2

Q1

Q4

Q2

A1

A3

A2

A4

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, KP, plasmasheet , etc.

Phase space density: Phase space density: 03/31/0603/31/06

•Initially trapped population assigned a phase space density f0.•Plasmasheet population assigned a normalized phase space density 5 f0.•Phase space density calculated according to Nunn [1993].

PSD calculations for other PSD calculations for other storms…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 MHDAlfven 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 Particle injection vs. IMF conditionsconditions

January 1995 September 1998 March 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 January 1995 storm, trapped particle dynamicsparticle 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 noPlasmasheet 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 Incorporating losses and VLF interactionsVLF 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 anddecay lifetime of electrons based on Shprits et al loss formula.

Summary/conclusionsSummary/conclusions Plasmasheet access to the inner magnetosphere dictates Plasmasheet access to the inner magnetosphere dictates

whether radial transport (convection/ diffusion) will act whether radial transport (convection/ diffusion) will act as a source or loss of radiation belt particles.as a source or loss of radiation belt particles.

We have used MHD/particle simulations to investigate We have used MHD/particle simulations to investigate plasmasheet access during three different storms of plasmasheet access during three different storms of varying size.varying size. Equatorial plasmasheet particles have access during the main Equatorial plasmasheet particles have access during the main

phase of the larger stormsphase of the larger storms Phase space density calculations indicate the plasmasheet may Phase space density calculations indicate the plasmasheet may

be a significant source of particles during the main phase of a be a significant source of particles during the main phase of a storm.storm.

Simple analytic models indicate injected plasmasheet Simple analytic models indicate injected plasmasheet particles must originate from the dusk flank.particles must originate from the dusk flank. MHD simulations often show duskward flows as convecting MHD simulations often show duskward flows as convecting

plasma breaks in the inner magnetosphere during main phase, plasma breaks in the inner magnetosphere during main phase, particularly for the larger storms.particularly for the larger storms.

Summary/conclusions Summary/conclusions (cont)(cont)

During the recovery phase (IMF-N), all three During the recovery phase (IMF-N), all three storms show well-developed Alfven layers, and no storms show well-developed Alfven layers, and no plasmasheet access to the inner magnetosphere.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 Suggests phase space density increases observed during

recovery phase is a result of trapped particle redistribution recovery phase is a result of trapped particle redistribution and local acceleration of keV particles.and local acceleration of keV particles.

The GEO/GPS increase in flux observed by The GEO/GPS increase in flux observed by Hilmer Hilmer et al.et al. during January 1995 can be reproduced by during January 1995 can be reproduced by the MHD particle simulations the MHD particle simulations iff: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, The lack of a plasmasheet source for January 1995, coupled with better agreement using observed BC, coupled with better agreement using observed BC, strongly suggests a local source near strongly suggests a local source near geosynchronous during main phase of this event.geosynchronous during main phase of this event.