Magnetically Self-Consistent Simulations of Ring Current

with Implications for Diffuse Auroraand PIXIE Data Interpretation

Margaret W. Chen1 and Michael Schulz2

1The Aerospace Corporation, Los Angeles, CA

2Lockheed Martin Advanced Technology Center, Palo Alto, CA

2007 The Aerospace Corporation

Fig 12 of Chen et al. [JGR, 110, A03210, 15 March 2005]

Previously we have simulated diffuse aurora by using a static axisymmetric B-field model with no ring current. We have studied effects of convective transport and variations in plasmasheet distributions for various scattering models.

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Solar-wind dynamic pressure was very low during the main phase of this storm.

We use AMIE model results (courtesy of G. Lu) to specify total potential drop V across the polar cap.

19 October 1998 Storm (min Dst ~ –110 nT)

from Fig 1 of Chen et al. [JGR, 110, A03210, 15 March 2005]

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Hamiltonian: H = MBm + qVE(L, ; t)

M = first adiabatic invariant, Bm = mirror-point field, q = particle charge, and VE = electrostatic scalar potential

Euler Potentials: = E/La ; =

Geomagnetic Dipole Moment: E = 0.305 G-RE3

Drift Equations: d/dt = H/; d/dt = + H/

Ring Current Particle Dynamics

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from Figs 2 & 3 of Chen et al. [JGR, 111, A11S15, 23 Nov 2006]

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from Figs 2 & 4 of Chen et al. [JGR, 111, A11S15, 23 Nov 2006]

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Kinetic Energy:

E = [2/(MBm

p2 = 2m0 MBm

Particles gain energy less efficiently from inward radial transport when the magnetic field produced by the ring current itself is taken into account.

Fig 7 of Chen et al. [JGR, 111, A11S15, 23 Nov 2006]

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from Figs 2 & 6 of Chen et al. [JGR, 111, A11S15, 23 Nov 2006]

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Magnetic perturbation B(0) at “center of Earth”

B(0) from self-consistent model is about 75% of B(0) from non-self-consistent model during main phase of 19 Oct 1998 storm.

Fig 9 of Chen et al. [JGR, 111, A11S15, 23 Nov 2006] 10

Comparison of Simulated and

Observed Proton Energy Flux

At ring current energies the simulated energy flux agrees better (especially so at E = 57 keV) with measured (Polar/CAMMICE) energy flux when model is magnetically self-consistent.

Fig 10 of Chen et al. [JGR, 111,

A11S15, 23 Nov 2006]

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Fig 12 of Chen et al. [ JGR, 110, A03210, 15 March 2005]

Application to plasmasheet electron transport (previously based on static axisymmetric B-field model with no ring current) for comparison with UVI and PIXIE data

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Plasmasheet Electron Dynamics

Fourth Adiabatic Invariant: p3

Flux-Tube Volume: (1/B) ds

Hamiltonian:

H = [(/)2/3c2 + m02c4]1/2 m0c2 + qVE(L, ; t)

Strong-Diffusion Lifetime: = 2Bh (1 – )(m/p)

where Bh is the magnetic intensity at altitude h = 128 km, (= 0.25) is a backscatter coefficient, and p/m is the particles’ common speed.

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B(r, ) = [(E/r2) cos (E/b3) r cos ] r = La [1 + (r3/2b3)] sin2 r0 = La [1 + (r0

3/2b3)]

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0 = (2L4a4/E){(16/35) F(r0

3/b3) ln[1 (r0/b)3]} x (r0/b)3 F(x) 1.0225 + 0.5225x + 0.0475x2 + 0.0375x3 error < 0.12% in [Schulz, JGR, 103, 61 67, 1998]

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To simulate ring current, let b depend on r0 and : B = = (E/r) [1 + (r3/2b3)] sin2 Br = + (r2 sin ) 1(/)

B = (r sin ) 1(/r)

=

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Fig 1 of Chen et al. [JGR, 111, A11S15, 23 Nov 2006]

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Schulz & Chen [JASTP, in press, 2007]

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Fig 1 of Schulz [JGR, 102, 14149 –14154, 1997]

Model [based on Søraas and Davis, NASA Report GSFC X-612-68-328, 1968] of equatorial magnetic-field perturbation produced by ring current

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Fig 3 of Schulz [JGR, 102, 14149 –14154, 1997]

Asymptotic radius of tail lobe, scaled radius of equatorial neutral line, and angular radius of boundary between closed and open mag-netic field lines on Earth’s surface as func-

tions of B01 = (2/3)Dst.

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SUMMARY

• Use of self-consistent magnetic field (produced by ring current) in simulations “stretches” field lines outward and mitigates particle energization associated with inward radial transport.

• Particular intensities of diffuse auroral precipitation thus occur at lower latitudes than in Dungey’s model magnetosphere as the stormtime ring current develops.

• As an example, self-consistency reduced the latitude of the midnight mapping from geosynchronous altitude to the ionosphere by about 2 during the main phase of the storm that began 19 Oct 1998.

• A magnetically self-consistent model thus yields significant effects for the diffuse aurora, even though L values of diffuse auroral features are typically almost twice as high as the L values at which the ring current is most intense.

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