Pavel Ozhogin, Paul Song, Jiannan Tu,and Bodo W. ReinischCenter for Atmospheric Research,University of Massachusetts Lowell, MA 01854

AGU Fall 2012San Francisco, CA, USA

3-7 December 2012SM41C-2228

Introduction Variations of Diffusive Equilibrium Models 2-D Density Distributions

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Evaluating the Diffusive Equilibrium Models: Comparison with the IMAGE RPI Field-aligned Electron Density Measurements

Since it was proposed by Angerami and Thomas in 1964, the diffusive equilibrium model and its variations have been extensively used by the scientific community to determine the plasma densities in the Earth’s plasmasphere, particularly for ray tracing of wave propagation and wave particle interaction. However, up until the IMAGE mission in 2000, all the measurements, by which these models could be evaluated, were made either in situ or from ground whistler wave measurements. As a result, they could not provide independent validation of the field-aligned distribution of plasma.

The data from the Radio Plasma Imager (RPI) instrument onboard the IMAGE satellite allowed us to determine almost instantaneous plasma density distribution along a magnetic field line [Huang et al., 2003]. Using more than 700 measurements obtained between June 2000 and July 2005, we developed an empirical model (RPI model) of the plasmaspheric densities, which determined the electron density as a function of L-shell and magnetic latitude [Ozhogin et al., 2012]:

NB and ηi – reference electron density and ion composition at the base of diffusive equilibrium model RB; i=1, 2, 3 for H+, He+, O+; TDE – temperature; Hi – scale height. We omit the lower ionosphere and plasmapause terms, since we only compare with plasmaspheric data in this study.

Acknowledgements

This work was supported by the NSF grants ATM-0902965 and AGS-0903777 to the University of Massachusetts Lowell. Product ID for RPI plasmagram data is http://spase.info/VWO/DisplayData/IMAGE/RPI/IMAGE_RPI_PNG_PGM_PT5M

References

Angerami, J.J. and Thomas, J.O. (1964), Studies of planetary atmospheres, 1. The distribution of electrons and ions in the earth's exosphere, J. Geophys. Res., 69, 4537-60 Bortnik, J., L. Chen, W. Li, R. M. Thorne, and R. B. Horne (2011), Modeling the evolution of chorus waves into plasmaspheric hiss, J. Geophys. Res., 116, A08221 Huang, X., B. W. Reinisch, P. Song, P. Nsumei, J. L. Green, and D. L. Gallagher (2004), Developing an empirical density model of the plasmasphere using IMAGE/RPI observations, Adv. Space Res., 33, 829-832 Inan, U. S., and T. F. Bell (1977), The Plasmapause as a VLF Wave Guide, J. Geophys. Res., 82(19), 2819–2827 Kimura, I. (1966), Effects of ions on whistler-mode ray tracing, Radio Sci., 1, 269–283 Ozhogin, P., J. Tu, P. Song, and B. W. Reinisch (2012), Field-aligned distribution of the plasmaspheric electron density: An empirical model derived from the IMAGE RPI measurements, J. Geophys. Res., 117, A06225 Sonwalkar, V. S., A. Reddy, and D. L. Carpenter (2011), Magnetospherically reflected, specularly reflected, and backscattered whistler mode radio-sounder echoes observed on the IMAGE satellite (Part 2), J. Geophys. Res., 116, A11211

The main advantage of measurements from RPI is the ability to obtain almost instantaneous plasma density distribution along the magnetic field line. When there are several measurements obtained along a segment of the orbit, we can construct and study 2-D density distribution. 6 measurements on February, 24th 2005 were obtained to create a 2-D plot displayed on panel (a). The variation of equation (1) from Ozhogin et al., (2012) was used to derive the 4 coefficients through the least squares fit of the model to multiple field-aligned density profiles (relative error less than 8%). This 2-D distribution is best represented by the average RPI model [panel (b)]. The DE-B* model [panel (c)] produces slightly lower densities that decrease more slowly with radial distance than the measurements. The field-aligned distribution is somewhat different, but it qualitatively consistent with the data. The diffusive equilibrium models are unable to reproduce the data [panels (d-e)].

Errors

Conclusions

• None of the diffusive equilibrium models are able to reproduce the L-shell dependence of density in equatorial plane. Nor do they have the variation of density with L-shell/magnetic latitude for a fixed geocentric distance. As a result, the overall performance is unreliable: even for best set of parameters (DE-S2) the average errors of <0.25 are achieved only for less than one third of the cases.• Modified model (DE-B*) improves the overall behavior and results in errors that are comparable with those of the empirical (RPI) model. • However, the number of free parameters doubles to 12, while original parameters loose their physical meaning .• Even the “best-fit” modification of DE-B* shows 40% difference at high latitudes.

Parameter DE-1 DE-2 DE-S2 DE-B / DE-B*

RB (km) 500 1000 1180 1000

TDE (K) 1000 1000 1700 1600

NB (cm-3) 34600 10000 7645 3100

H+ (%) 0.2 15.2 40 8

He+ (%) 1.9 82.3 30 2

O+ (%) 97.9 2.5 30 90

All of the diffusive equilibrium models (except for the modified version DE-B*) produce average errors of <0.25 for less than a third of the cases.

In contrast, the intrinsic variation in the data, which appears as the errors of RPI model, is <0.25 for almost 45% of the cases. The DE-B* model performs slightly below the RPI model.

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Diffusive Equilibrium Model

In addition to the 7(!) original assumptions of Angerami and Thomas (1964), the later implementations added more assumptions:

• no centrifugal force (geopotential height G is independent of latitude)

• ion/electron temperatures are equal to each other, and are constant

This leads to the following equation for the electron densities:

The parameters of different diffusive equilibrium models vary significantly. We have selected 4 different models from very recent and rather dated papers, which have used these models in the ray tracing codes. DE-1 and DE-2 come from Kimura (1966), DE-S2 from Sonwalkar et al. (2011), DE-B is used by Bortnik et al. (2011) and, except, for different value of NB by Inan and Bell (1977). DE-B* is not a diffusive equilibrium model, but an adaptation with additional 6 parameters to modify the plasmaspheric density; for a full description see Bortnik et al. (2011).

Equatorial Densities

The main dependence of equatorial densities in plasmasphere is on L-shell. By comparing the 700 of equatorial density values with the models we can see that none of the diffusive equilibrium models can reproduce the falloff of densities with L-shell, except for the modified version of DE-B* in which the additional 6 parameters that created this modification were selected such that it reproduces the equatorial model of Carpenter and Anderson (1992) and is rather close to the RPI measured values beyond L=3. Densities from DE-S2 are close to the data within L=3, while DE-B, DE-1, and DE-2 extremely underestimate.

Off-equator densities distribution

One of the principal differences between diffusive equilibrium models and measured data is the dependence of densities on L-shell and magnetic latitude for a fixed geocentric distance R. Here we compare the models to the measurements along the R=2.5 RE line within ±38° magnetic latitude (within the L=4 shell). Since all of them (except for DE-B*) depend only on R and not L-shell or magnetic latitude, the resulting disagreement of data and models is very evident. The DE-B* model performs better than the diffusive equilibrium models. Diamonds indicate binned averages of the RPI measurements.

Model Differences