INNER MAGNETOSPHERE PLASMA DENSITIES. Bodo W. Reinisch and Xueqin Huang

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1 XA INNER MAGNETOSPHERE PLASMA DENSITIES Bodo W. Reinisch and Xueqin Huang Environmental, Earth, and Atmospheric Sciences Department, Centerfor Atmospheric Research, University of Massachusetts Lowell, MA 01854, USA Abstract: The radio plasma imager (RPI) on the IMAGE satellite performs radio sounding in the magnetosphere, transmitting coded signals stepping through the frequency range of interest and receiving the returned echoes. The measurements provide the echo amplitude as a function of frequency and echo delay time on a so-called plasmagram. A newly developed algorithm inverts THE echo traces on a plasmagram to electron density spatial distributions. Based on these observed density distributions, an empirical model is constructed to describe the twodimensional density distribution in the inner magnetosphere. INTRODUCTION The radio plasma imager (RPI) on the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) satellite (Burch et al., 2001) performs sounding in the frequency range from 3 khz to 3 MHz using three orthogonal antennas, two 500-m long dipoles in the spin plane, and a 20-m dipole along the spin axis. IMAGE is on an elliptical polar orbit with an altitude of 7.2 R E at apogee, and 1,200 km at perigee. When the RPI is sounding inside or close to the plasmapause there are often discrete echo traces with virtual ranges of up to 7 RE The virtual range is the time delay of an echo multiplied by half of the speed of light. Reinisch et al. (2001) have shown that the waves producing these discrete traces have propagated along the magnetic field lines. A newly developed profile inversion algorithm calculates the electron density distribution along the direct path from the spacecraft along the magnetic field line that intersects the spacecraft. The RPI sounding observations of the field aligned propagation echoes make it possible to measure the density profile in a large range of distance along the field line. A single measurement is typically completed within two minutes. This paper first gives a brief description of the inversion technique, then shows examples of the density profiles, and finally presents an empirical model of electron density distribution in the plasmasphere during one pass. PLASMAGRAMS AND INVERSION TECHNIQUE Coded radio signals are transmitted from the RPI into all directions, and they are reflected at places where the wave frequency equals a plasma cut-off frequency. The echo delay

2 106 times are transformed into the so-called virtual ranges by multiplying them with half the speed of light, and the echo amplitudes are displayed in plasmagrams as function of virtual range in units of Earth radii R E and frequency hi khz. Measurements are typically made about every 2 minutes during which tune the satellite travels about 500 km along its trajectory. Figure 1 shows an example of RPI plasmagrams when IMAGE was inside the plasmasphere. 05»f.« Frequency (khz) 2001 June 08,20:40:56 UT Magnetic Latitude Ο Fig. 1. (a) Plasmagram recorded inside the plasmasphere displaying the echo amplitude as function of frequency and virtual range. The thin red lines on top of the two strongest traces are echo traces predicted according to the density profile shown in (b). The insert shows the orbit (red line) and location (red square) of IMAGE at the time of the sounding. The field lines of L=4 are shown in black lines, (b) The density profile, as function of magnetic latitude, inverted from the plasmagram shown in (a). The two strongest traces have been identified as X mode echoes (Reinisch et al., 2001). The virtual range, P, for a point on a trace must satisfy the integral where c is the speed of light in free space, and V g (f) is the group velocity of the wave with frequency/, traveling from the spacecraft along the path F f to the reflection point, assuming the

3 107 wave travels back to the spacecraft on the same path at the same speed as to the reflection point. With the cold plasma and geometric optics approximations we can write P(/)= jvcosacfc (2) r/ where n'=3(n/)/9/is the so-called group refractive index with η the refractive index for the extraordinary mode, and ctis the angle between the group velocity and the wave normal. In an earlier paper, Muldrew (1963) suggested that the echoes are traveling along the magnetic field line intersecting the spacecraft. The multiple echo traces on the plasmagram in Figure la are the result of waves propagating to the local and conjugate hemispheres. The echoes from the local (northern) hemisphere produce the trace with smaller virtual ranges, while the longer virtual ranges result from reflections in the conjugate hemisphere. The trace at ~8 R E (not used for the inversion) propagates first to one hemisphere, then to the conjugate one, and then back to the spacecraft. For propagation along the field line, the deviation angle a becomes zero, and the wave normal is parallel to the group velocity, simplifying (2) to P(f}=\n\fJ P,f B )ds (3) r/ The group refractive index n' is a function of the wave frequency/, the electron plasma frequency/p, and the electron gyro-frequency^. A new algorithm, based on the method used to invert the topside ionograms (Huang and Reinisch, 1982), was developed to solve the integral equation (3) numerically for the true reflection distance. The integration is carried out along the field line using a global magnetic field model (Tsyganenko and Stern, 1996). The X mode traces in Figure la extend from/= 350 khz to higher frequencies with virtual ranges increasing from 0 to ~2.5 RE for the local trace, and 4-6 RE for the conjugate trace. The local trace determines the electron density distribution along the field line (L=3.0) from the satellite position (MLAT=12.9o) to higher latitudes. The conjugate trace with echoes reflected in the southern hemisphere does not start at 0 range. The waves must propagate across the equator region where the densities are lower than at the satellite location. The first conjugate echo at the lowest frequency is reflected at the point approximately conjugate to the spacecraft location. For f close to and slightly above 350 khz, the group velocities are very small in the whole region near the equator, producing very large virtual ranges of ~6 RE. Higher frequencies, on the other hand, have higher group velocities across the equator, and low group velocities occur only for a relatively short distance near the reflection point at higher latitudes. Combining these two effects, the virtual ranges are shorter for higher frequencies although the echoes actually travel longer distances. No echoes return from the equatorial region of the path from the spacecraft to its conjugate point. However, the total electron content in this region is known from the time delay of the first conjugate echo. The equatorial densities are interpolated assuming that the density gradients are continuous in this region. When the satellite flies through the equator, sometimes echo traces can be received near the equator. The quality of the interpolation of the equatorial densities can be assessed by comparing the profiles

4 108 from the interpolated densities with the directly measured ones. As will be seen later in this paper, the uncertainty due to the interpolation is much smaller than the inherent variations of the plasma structures. After subtraction of the virtual range to the satellite's conjugate point from the left side of (3), the inversion procedure is applied to the adjusted conjugate trace. The inversion results for the plasmagram in Figure la are shown in Figure Ib. Using the derived density profile, the time delays for each frequency can be calculated. The thin red lines marked on each of the two strongest traces show the calculated traces using the electron density profile in Figure Ib. EMPIRICAL MODEL Since the launch of IMAGE in March 2000, RPI has continuously recorded plasmagrams in the plasmasphere. The inversion technique described above has been applied to process plasmagrams with echo traces of good quality. The profile inverted from a single plasmagram gives the density distribution along the field line, and it can be regarded as an instantaneous measurement over a large region. Combining the profiles obtained from different L-values, it is possible to construct an empirical model showing the global density distribution in the plasmasphere. In this paper, we demonstrate, as the first step, the possibility to derive a 2-D plasma density model. On June 8, 2001, IMAGE passed through L = 2.22 to L = 3.23 in the morning sector as shown in Figure 2. During this pass within 22 minutes, 7 plasmagrams were obtained with good discrete traces, a rare opportunity. I 1 I I I I Fig. 2. Trajectory of IMAGE on June 8, The meridian cut is near 0800 MLT. The red dots on the trajectory indicate where plasmagrams were made. The black lines show the field lines from the empirical field model.

5 June 08, MLT = 8.0 έ* η w fi Magnetic Latitude Π Fig 3. Density profiles on June 8,2001. The solid black lines are inverted from measurements, and the red dashed lines are the empirical model. The 7 inverted density profiles are shown in Figure 3. The densities vary as functions of latitude λ and L-value. After experimenting with many different possible functional forms, noting that a single functional form has to describe the intrinsic properties of all 7 profiles, we choose the following form: D-L ''INV β(ι-) η αλ where Xjn V is the invariant latitude of the L shell. Parameter No(L) is the equatorial density. Parameter γ describes the asymmetry of the north-south distribution around the equator, γ < 0 meaning that the density in the southern hemisphere is higher than at the conjugate points in the northern hemisphere, and visa versa. Careful inspection of Figure 3 shows the asymmetry. The power index β(ί,) defines the steepness of the profile at high latitudes. Parameter α specifies the flatness of the profile at low latitudes. Parameter Β roughly gives the location of the plasmapause. From a multi-variant best fit, we obtain A=4833 cm" 3, 5=3.64, C=0.2, D=0.03, γ=-0.14, and a=1.25 for the morning sector on June 8 The two-dimensional distribution of density in magnetic local time 0800 on June 8, 2001 can then be determined as shown in Figure 4. A similar model was used to describe the refilling process after the March 31, 2001 storm (Reinisch et al., 2003). For the equinox period, the asymmetry factor γ was found to be zero. To illustrate the seasonal asymmetry, Figure 5 shows the vertical plasmaspheric total electron content (TEC) at equinox (left) and solstice 'INV _ (4)

6 110 (right). In June, the plasmaspheric TEC in the southern hemisphere is -10% higher than in the northern hemisphere *? Εu CO ο D Ο «t * u <ΰ Hi Geocentric Distance (RE) Fig. 4. Empirical model for the June 8, 2001 event. 30 Before the storm on 2001 March 31, MLT= MAGNETIC LATITUDE Π MAGNETIC LATITUDE ( ) Fig. 5. Vertical plasmaspheric electron content above 1 RE altitude at equinox (left) and solstice (right). At 30 latitude, the relative TEC difference ATEC is -10%.

7 Nsumei et al. (2003) have analyzed RPI plasmagrams in the northern polar cap and have derived an empirical polar cap density model for high sunspot activity: Ill N e (R,Kp)[cm- 3 ] = 3433(R/R E )~ 5 09 e ' 229Kp. (5) The density decreases with height as a power law with exponent of approximately -5. The analysis of one year of data in showed a strong dependence of the density on the magnetic activity. The exponential Kp dependence indicates that magnetospheric energetic precipitated particles and electromagnetic energy deposited during disturbed geomagnetic conditions are important sources for additional ionization. SUMMARY The basic techniques have been described for the development of an empirical model of the inner magnetospheric electron density distribution based on IMAGE/RPI measurements. The electron density distribution is determined from ~0.5 R E to ~5 R E. ACKNOWLEDGMENTS This work was supported by NASA under subcontract from Southwest Research Institute. REFERENCES Burch, J. L., S. B. Mende., D. G. Mitchell, T. E., Moore., C. J. Pollock, B. W. Reinisch, B. R. Sandel, S. A. Fuselier, D. L. Gallagher, J. L. Green, J. D. Perez, and P. H. Reiff, Views of the Earth's magnetosphere with the IMAGE satellite, Science, 291, 5504,2001. Huang, X. and B.W. Reinisch, Automatic Calculation of Electron Density Profiles from Digital lonograms. 2. True Height Inversion of Topside lonograms with the Profile-fitting Method. Radio ScL, 17,4, Muldrew, D.B., Radio Propagation along Magnetic Field-aligned Sheets of lonization Observed by the Alouette Topside Sounder, J. Geophys. Res., 68,19, Nsumei, P., X. Huang, B.W. Reinisch, P. Song, V.M. Vsyliunas, J.L. Green, S.F, Fung, R.F. Benson, and D.L. Gallagher, Electron density distribution over the northern polar region deducted from IMAGE/radio plasma imager sounding, J. Geophys. Res., 108(A2), 1078, doi: /2002ja009616,2003 Reinisch, B.W., X. Huang, P. Song, G.S. Sales, S.F. Fung, J.L. Green, D.L. Gallagher, and V.M. Vasyliunas, Plasma Density Distribution Along the Magnetospheric Field: RPI Observations From IMAGE. Geophys. Res. Lttrs., 28, 24, Reinisch, B.W., X. Huang, P. Song, S. F. Fung, J. L. Green, V. M. Vasyliunas, D. Gallagher, and B. R. Sandel, Plasmaspheric Mass Loss and Refilling as a Result of a Magnetic Storm, J. Geophys. Res., submitted, Tsyganenko, N.A. and D.P. Stern, Modeling the global magnetic field and the large-scale Birkeland current systems, J. Geophys. Res., 101, ,1996.