A planetary magnetosphere is the region surrounding a planet within which its own magnetic field dominates the behavior of electrically charged particles. The Earth's magnetosphere is carved out of the solar wind, when the solar wind encounters the Earth's magnetic field. The Earth's magnetic field is close to being dipolar, although the magnetic field lines in the magnetotail are stretched out of the dipole shape by electrical currents flowing across the tail. The Earth's magnetosphere is very dynamic, and has several major components, which we denote with the numbers (1), (2), and (3) in Figure 8.
The first physical regime is interplanetary space (noted as (1) in Figure 8), where the dominant environment is the solar wind. Typical values characteristic of this region are (for high speed solar wind streams at 1A.U., ref. 37): ion number density ~ 3 cm-3, ion temperature ~ 0.01 keV, flow speed velocity ~ 500 km/s, magnetic field ~ 4 nT [27].
The second physical regime, (noted as (2), in Figure 8), is the bow shock/magnetosheath region (colored brown, noted as (2) in the figure), where the plasma environment of interplanetary space and the geophysical magnetic field become separated. The magnetopause is the boundary where the solar wind exerts a force on the magnetosphere and the solar wind particles (electrons/protons) are repelled. The magnetosheath is the region between the magnetopause and the bow shock, where a shockwave forms from the encounter of the supersonic solar wind and the magnetosphere.
The third physical regime is the magnetosphere region (colored black, noted as (3) in Figure 8), including the inner magnetosphere or plasmasphere, dipole field, radiation belts, auroral regions, plasma/current sheet, and the magnetotail. The plasmasphere is a doughnut-shaped region located near the Earth with radial distance less than a few RE (RE = 6378 km) in the equatorial plane, and it contains relatively dense (ne >102 cm-3) and cold (Te~Ti~1eV) plasma of ionospheric origin [28]. The magnetic field in the low latitude plasmasphere region is accurately described by a dipole field, tilted at 10.8° , with a dipole moment of 7.9 1025 gauss-cm3 [ 29]. The plasma in the plasmasphere region corotates with the Earth. The magnetic field accompanying the solar wind merges with that of a planet and stretches it out to produce a long, turbulent magnetotail, or wake, on the downwind side of the planet. In the magnetotail, the solar-wind-driven flow brings the plasma to the equatorial plane, where it is concentrated in the plasma sheet. Typical values for the plasma current sheet are electron number density ~1 cm-3, ion temperature ~5 keV, ion thermal velocity ~600 km/sec, magnetic field ~2 nT [30]. At ~10 RE, the momentum flux of the solar wind balances the Earth's magnetic field [28]. The Earth's magnetotail is several million kilometers long (~1000 RE).
Geostationary orbit (GEO), the orbital location where a body holds a fixed position relative to the rotating Earth, is located at 6.6 RE. This region is a region of high variability. Geostationary orbit tends to skim the inner boundary of the plasma sheet, and the radiation belts and ring current are located near GEO, as well. During solar quiet times, the bodies orbiting at this location are typically at dipolar-like field lines. During large magnetic storms, the bodies orbiting at GEO are within stretched field lines.
For this study, we exclude the region of low Earth orbit (LEO) below (2 RE), and we focus on the following regions: the solar wind, the plasma sheet/magnetotail, the geosynchronous region, and the plasmasphere.
Figure 8: Numbered (1,2,3) regions in the Earth's magnetosphere as described in the text. Figure from Van Allen, J., "Magnetospheres, Cosmic Rays, and the Interplanetary Medium", in The New Solar System, (1991], pg. 29.
In this section we discuss the Earth's plasma.
Plasma Parameters
Electron and ion density.
In space plasmas, the number densities of electrons ne and ions ni are equal, on the average, and the plasma is "quasi-neutral." [28] However, quasi-neutrality doesn't always hold in the dynamic Earth environment, and therefore, we consider both electron and ion density, and "hot" (high temperature) and "cold" (cold temperature) electron and ion populations. Those populations are approximated with a bi-Maxwellian distribution.
Electron and ion energy. The electron energy: Ee = k Te is generally different from ion energy Ei = k Ti,
Electron and ion thermal speed. The electron speed is:
;
Equation 13
k = 8.616x10-5 eV/K, and me = 9.11 10-31 kg. A corresponding equation holds for ions.
Electron and ion flux. The electron flux is the particle number density times the electron speed.
;
Equation
14
A corresponding equation holds for ions.
Debye length. The Debye screening length is the distance that the Coulomb field of an arbitrary charge of
the plasma is shielded:
(m);
Equation
15
The value of the Debye length indicates whether collective processes are important.
If the mean separation between the dust particles in the plasma 
(where L is the spatial density of the particles) is smaller than the Debye length,
then neighboring dust particles are not shielded and isolated from each other, and they begin to act like a solid
dielectric. We assume that the interparticle distances to be larger than the Debye shielding length, so that interparticle
Coulomb interactions are negligible.
Figure 9 Some rough plasma parameters: electron flux
e and Debye length
D, as a function of electron density and electron thermal energy. For comparison, we show
the photoelectron flux pe = 2.5x1010
cm-2 s-1 from metals and a 10 times lower flux from insulators..
In order to evaluate the different currents, we need to know the details of the parameters of the plasma in which the particles are immersed. In January/February 2000, we received from A. Juhász (KFKI, Budapest, Hungary) detailed plasma data for "Quiet" Earth plasma conditions, defined by Kp=1, Ap=120, and plasma data for "Active" or "disturbed" Earth plasma conditions, defined by Kp=5, Ap=1200.
Plasma Data Modeling Strategy
Juhász's plasma data was derived from an "engineering" strategy to piece together plasma models, and calculate plasma parameter values for different portions of Earth's magnetosphere (Juhász and Horányi [25]). These regions collectively are: the plasmasphere, geosynchronous, magnetotail (plasma sheet, tail-lobes), and the magnetosheath.
Our initial assumptions for Earth plasma parameters, before we received data from A. Juhász, are listed below. These numbers are still valid for back-of-the-envelope estimates of Earth plasma.
-
1 Solar wind
Outside Earth's magnetosphere.
ne =[3 ... 9] cm-3, kTe =[100 ... 10] eV;Reference: [28, 32]
2. Plasma sheet/magnetotail
Outside about 10 RE to about 15 RE (Sunward) or several 100 RE tailward.
The configuration depends strongly on solar wind conditions (pressure).
ne = [0.8 ... 0.5] cm-3, kTe =[1.7e3 ... 2.5e4] eV;Reference: [25]
3. Geosynchronous plasma environment
Outside plasmasphere out to approx. 10 RE.
ne = [10 ... 0.5] cm-3, kTe =[1.e3 ... 3.e3] eV;Reference: [31]
4. Plasmasphere
Inside 4 to 5 RE. Outer boundary has local time variations.
ne = [1.e4 ... 1.e3] cm-3, kTe = [0.2 ... 1.2] eV; Reference: [25]
Table 5: Rough Earth plasma numbers for back-of-the-envelope calculations.
These figures show in graphical format, some of the plasma data, which we received from A. Juhász, in January and February 2000, and with which we used for most of this study.
Figure 10 "Cold" component of the electron flux in Quiet plasma conditions.
Figure 11 "Cold" component of the electron flux in Active (disturbed) plasma conditions.
Figure 12 "Hot" component of the electron flux in Quiet plasma conditions.
Figure 13 "Hot" component of the electron flux in Active (disturbed) plasma conditions.
Figure 14 "Cold" component of the electron density in Quiet plasma conditions.
Figure 15 "Cold" component of the electron density in Active (disturbed) plasma conditions.
Figure 16 "Hot" component of the electron density in Quiet plasma conditions.
Figure 17 "Hot" component of the electron density in Active (disturbed) plasma conditions.
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The Earth's Magnetosphere
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