Essay Title - Ionosphere Atmosphere Atmospheric Electrons
Electric fields and vertical drifts at low latitudes and middle latitudes
- The Ionosphere
The ionosphere is the region of the upper atmosphere that contains charged particles (ions and electrons). These particles are originated by the ionization of the neutral atmospheric elements due to corpuscular and electromagnetic radiation. The lower limit of the ionosphere starts from about 60 km and there is no distinct upper limit but a height of about 2000 km is arbitrarily set for practical applications as the upper limit.
The ionosphere is composed of a series of layers due to ionization and the ion number density changes with altitude. These layers are named D, E and F. The latest is subdivided in F1 and F2 region. The vertical structure of the ionosphere changes from day to night, with season, latitude and is also affected by the solar activity, but the differences between daytime and nighttime are the most important features to notice.
The distribution of the regions with respect to the altitude is shown in Figure 1.1, and it indicates the density profile of the ionosphere. During the day, we can detect the presence of two peaks in ion concentration: the E- and F- regions. The solar ionization balanced by chemical losses and diffusion produces these regions of high ion concentration. On the other hand, at night the chemical losses reduce the E- region peak and the F- region peak is maintained by the downward diffusion.
Figure 1.1. The layers of the ionosphere. Regions D, E and F during the day and
Figure 1.2. Typical profiles of neutral atmospheric temperature and ionospheric plasma density for mid-latitude daytime and nighttime conditions (from Kelley, 1989).
The ionosphere is originated by the ionization of atmospheric gases such as N2, O2 and O. At low and middle latitudes the energy required for this process comes from the solar radiation in the extreme ultra-violet (EUV) and X-ray parts of the spectrum. At high latitudes the energetic particle precipitation becomes a more dominant factor for the ionization.
The concentration of ions is determined by the continuity equation
Here, n is the electron density, P is the production rate of free electrons, L the loss rate by recombination, and the last term indicates the loss of electrons by transport, where V is the mean drift velocity. Since we are considering in general the ionosphere as neutral plasma, the electron density is equivalent to the ion density.
Neutral winds, gravity, and external applied potentials to the ionosphere drive a current system that creates electric fields at the low and middle latitudes of the region. The current divergence free condition generates the internal electric polarization fields
The neutral atmosphere is located below the ionosphere and the coupling between them is produced by ion-neutral collisions. Figure 1.2 shows how the atmosphere is divided in regions according mainly to a temperature profile. The lowest region is called troposphere. Here the temperature decreases with altitude with a rate of about 7K/km. At about 10 km, the temperature stops decreasing and the region becomes nearly isothermal.
This level is called the tropopause. Above this layer lies the stratosphere, in this region the temperature increases mainly by the absorption of part of the ultraviolet portion of the solar spectrum by the ozone. The top of the stratosphere is the stratopause and it is located around 50 km., where the temperature has a maximum and starts to decrease.
Above the stratosphere is the mesosphere, which extends up to about 80 km. In this layer, the radiative cooling produces a temperature decrease to a minimum value between 130-190 K at the mesopause, that is located at about 80 km. Above this altitude the temperature increases to values grater than 1000 K. This region is called the thermosphere.
Experimental data of neutral and ion composition with respect to the altitude is illustrated in figure 1.3. Some important features can be noticed such as the greater neutral concentrations in comparison with the electron and ion density. Moreover, the number density of the neutral gases decreases exponentially while the altitude increases.
Below and near 100 km N2 and O2 dominate. Near 110 km the amount of atomic oxygen equals the amount of O2. Above 250 km the atomic oxygen density becomes greater than the N2 density. The curve labeled with e- represents the electron density and has a similar shape as the right side of the Figure 1.2. Near the peak of the plasma density profile, the O+ is the dominant ion, which corresponds to the high concentration of atomic oxygen in the neutral gas [Kelley, 1989].
Figure 1.3. Neutral and ion composition of the ionosphere (from Kelley, 1989).
For this study, we consider a region of the ionosphere, where the lower boundary is chosen at an altitude where the ion density is so low that we assume it is negligible, while the outer boundary consists of the region inside magnetic flux tubes that extends to about 3000 km altitude at the equator with a range of latitude that is around +/- 34° as shown in Figure 1.4.
Figure 1.4. Low and middle latitude ionosphere region to be considered for the electrodynamics study. Includes a representation of the magnetic field lines (from Heelis, 2004).
- Ionospheric Dynamics
In this region, where the neutral and charged particles compose magnetized plasma, we assume that and . Any force that produces a relative motion between the ions and electrons will drive a current j=Ne(Vi - Ve), where N is the particle number density, e is the charge of the particle, Vi is the velocity of the ions and Ve is the velocity of the electrons. In general, any current divergence will create a charge density, that could be demonstrated using the divergence current equation:where r is the charge density that will build up an electric field, which will eliminate the current divergence.
Therefore any variation or gradient in the current density means a variation of the charge respect to the time. This charge produces an electric field as revealed by the Poisson’s equation:
Among the forces that move charged particles we consider:
- Collisions with neutral particles: the collisions with frequency between charged particles of mass m and neutral particles produce a momentum exchange force . In this equation V represents the ion velocity and U is the neutral particle velocity. The mass difference between the ions and electrons makes it possible to neglect the collisions between them. However, the contribution of these collisions can be important for high latitudes, but their effect on the calculations of current driven by neutral winds is minimum.
- Electric fields: a force F = qE is applied to charged particles of charge q due to the electric field E. To insure the condition that the total current in the region is divergence free, , internal electric fields must be generated internally. The time scale for build up the electric gradient is on the order of 10-6 s. Thus the electric field created neutralize very fast any current divergence created by variations in the forces related to the gravity, magnetic fields and plasma pressure gradients that affect the plasma or by changes in the conductivity at the ionosphere. External electric fields will be considered when electric potential distributions are applied at the boundaries.
- The Lorentz force: F = q(V x B), where V is the velocity of the charged particle q moving inside the magnetic field B.
- Partial pressure gradients: The plasma pressure gradient force F = (1/N)Ñ(NkT) produces relative motions of the ions and electrons in directions parallel and perpendicular to the magnetic field. In this equation, N is the particle number density, k is the Boltzmann’s constant, and T is the particle temperature.
2.2 Conservation of Momentum
In the region we are considering there are closed magnetic field lines. The feet of this field lines pass through the base of the region where no current can flow because the ion concentration is negligible. The requirement that the current generated by the forces described before must be divergence free produces electric fields throughout the region.
Since we are considering large-scale systems that evolve over time scales of several hours or more it is acceptable to ignore acceleration of the ions and electrons and all the forces described above are in equilibrium. Thus, the equation of motion for the ions and electrons can be considered as the following:
Here N is the species number density, m is the mass, T the temperature,and V the velocity, k is the Boltzmann’s constant, g the acceleration due to gravity, e the electron charge, E the electric field, nin the collision frequency with neutral particles, and U the neutral wind. The suffix “i” or “e” represents the variables that refers to ions or electrons respectively.
Considering a reference of frame moving with the neutral wind velocity the ion drift and the electric field are given by the primed variables:
All the forces that are independent of the ion velocity can be represented by Fi’.
Replacing equation 1.4 in equation 1.2 we obtain:
By using equation 1.6, equation 1.2 it becomes:
We can express equaton 1.7 in the parallel “||” and perpendicular “^” directions respect to B:
Then applying the cross product with B to equation 1.7a and 1.7b we solve for and .
In equation 1.7a the cross product is zero, giving us:
Using the expression 1.4 we can get:
, this finally gives us the result for :
Now considering the perpendicular direction in equation 1.7b, and taking the cross product with B, we have:
Using the expression 1.4, the equation transforms to:
Making an arrangement of the second term we get:
Transforming the second term using the product rule:
But the dot product is zero, so this gives:
By using 1.7b in the third term we get a new expression:
Rearranging terms and multiplying each term by e/(miuin) allow us to obtain:
In this equation it is possible to include the gyrofrequency, Wi =(eB)/mi:
Here is the unit vector along the direction of the magnetic field.
Figure 1.5. Values of the ratio of the gyrofrequency to the collision frequency with respect to altitude, for ions (Ki) and electrons (Ke) (from Kelley, 1989).
When the ratio of the gyrofrequency to the collision frequency is low, which corresponds to low altitudes, the charged particles move parallel to the force that has a perpendicular direction to the magnetic field . On the other hand, at high altitudes, when the ratio of the gyrofrequency to the collision frequency is high, the charged particles move in a direction mutually perpendicular to the forces and the magnetic field,
The current originated by the difference in the velocities of ions and electrons due to the forces is represented by:
If we consider an equivalent electric field for the current equation, we have:
The matrix of equations is called the conductivity tensor, and it is composed by the Direct, Pedersen and Hall conductivities. An altitudinal profile of these conductivities is shown in Figure 1.6.
Figure 1.6. Representation of the altitudinal variation of the conductivities. The lighter curves indicates daytime values while the dark curves indicates nighttime values. The direct conductivity is represented by the curve sigO, the Pedersen current corresponds to the dotted line sigP, and the Hall current is the dashed line sigH (from Heelis, 2004).
2.4 Derivation of Dynamo Equations
- Electric Field Drivers
- E-region winds and currents
Winds resulting from solar heating produce currents in the E-region. This current system is called the Sq “solar quiet” dynamo currents.
Figure 3.1. Peak E-region ion concentration with respect of local time (from Heelis, 2004).
Figure 3.2. The dominant wind system in the E-region is shown in the upper panel. The horizontal current system produced by the winds is represented in the lower panel (from Tarpley, 1970).
- F-region winds and currents
- Magnetospheric potential and currents
- History, some recent studies
The theory of the atmospheric dynamo began with an encyclopedia article by Balfour Stewart (1883), which is an explanation of the daily geomagnetic variations discovered 150 years earlier. Later, the theory of ionospheric conductivity was developed by many scientists such as Cowling, 1945, Maeda, 1952, Baker and Martyn, 1953, Chapman, 1956. The dynamo theory was treated by Maeda and Kato (1966), Matsushita (1969), Rishbeth and Garriot (1969) and Kelley (1989). [Rishbeth, 1997].
Radar, ionosonde, magnetometer, and satellite measurements have been extensively used for studying the time-dependent characteristics of low-latitude disturbance electric fields and currents, and their coupling to the high latitude convection. Fejer et al. (1997) showed results using Jicamarca data for ExB drifts at the magnetic equator.
- Equatorial electric fields and vertical drifts at quiet time
At middle and low latitudes, the quiet time ionosphere plasma drifts perpendicular to the Earth’s magnetic fields are driven by neutral wind generated E-region dynamo electric fields and by F-region polarized electric fields. Rishbeth (1997), described the large-scale features of the middle and low latitudes ionospheric dynamos at the E- and F-layers.
He included a description of the neutral air wind system; the motion of the ions and electrons caused by the winds; the electrical conductivity; currents and drifts driven by winds; electric polarization fields; aspects of the ‘voltage’ and ‘current’ generators’; the field-aligned currents and the effect of conjugate ionospheres.
The observed dayside and nightside fields are the result of charge buildup at the terminators, with negative charge at the dusk and positive charge at the dawn terminator. The thermospheric winds in the equatorial region provide the source of energy that maintains the electric field. The vertical drifts are up, and the zonal drifts are directed to the west during the day, and down and to the east at night.
The behavior of the ExB drift is explained by the existence of a zonal component of the E- and F-region dynamo electric fields, which points toward east during the day, and toward west during the night. The zonal drifts are much larger than the vertical velocities. The vertical drift is often enhanced just after sunset but shows no comparable feature near sunrise.
[Kelley , 1989].
- E-region dynamo
The E-region dynamo is driven by tidal oscillations of the E-region neutral atmosphere.
- F-region dynamo
Thermospheric winds generate electric fields in the F-region, however, during daytime, because of high conductivity along the geomagnetic field lines , off-magnetic equator E-region dynamo electric fields are mapped into the F-region short circuiting the dynamo electric fields of that region. Therefore, during daytime, the F-region vertical and zonal E x B drifts are basically controlled by the E-region electric fields.
Around sunset when the conductivity of the E-region starts decreasing quickly, the electric fields from the e- and F-regions add and the vertical drift velocity is substantially increased over the magnetic equator-that produces the so-called pre-reversal enhancement of the vertical electromagnetic drift. During night-time, the F-region dynamo electric fields become responsible for the behavior of the E x B drifts of the ionosphere plasma. [Rishbeth, 1997; Bertoni et al, 2006].
- Typical vertical drift at low latitude at quiet time
There is a large day-to-day, seasonal and solar cycle variation of the equatorial vertical plasma drifts; however they show a general pattern in average. Fejer (1991; 1997) described the main characteristics of the vertical drifts using Jicamarca measurements at the F-region.
Fig. 2.3.1. Vertical drifts during magnetically quiet conditions and moderate to high solar flux conditions. AE drifts are averaged longitudinally and the Jicamarca data belongs to the F-region [Fejer, 1997].
Fig. 2.3.2. Vertical and zonal drifts during equinox solar maximum conditions from Jicamarca and a numerical simulation obtained from Crain et al. 1993.
- Equatorial vertical drifts during the day
The vertical plasma drifts are upward during the day. At the postsunset time an enhancement of the vertical plasma drift occurs before it turns downward. The zonal drifts are westward during the day.
Fig. 1.3. Zonal drifts from Jicamarca (from Fejer, 1991)
Fig. 1.4. Vertical drifts from Jicamarca for different solar flux conditions (from Fejer, 1991)
- Equatorial Vertical drifts during the night
During the nighttime period the vertical drifts are downward and the zonal drifts are eastward.
- Equatorial electric fields and vertical drifts at disturbed conditions
Although the vertical E x B drift has a day-to-day variation, the main features remain the same for magnetically periods. Two generalized source mechanism exist for the disturbance fields and currents. The first one is called the 'solar wind/magnetosphere dynamo' or 'magnetospheric dynamo' and is caused by the interaction of the solar wind and the magnetosphere producing electric fields and currents along the geomagnetic field lines between the magnetosphere and the high latitude ionosphere.
Some of these currents and the associated electric fields can penetrate to the low latitudes through the conducting ionosphere. During magnetically disturbed periods on the other hand, penetration of electric fields originating at high latitudes can reach the equatorial ionosphere, usually within seconds to a few minutes. The second mechanism is called 'ionospheric disturbance dynamo' or 'disturbance dynamo'. The ionospheric wind dynamo action alters the electric fields and currents because of changes in global thermospheric circulation due to the input of energy to the thermosphere during magnetic activity.
[Blanc and Richmond, 1980]
- Disturbance dynamo
The ionospheric electric fields and currents at middle and low latitudes differ from the quiet time measurements. External sources to the ionosphere such as particle heating and Joule heating in the auroral zone drive neutral winds which create a current system that originates the disturbance dynamo [ Heelis, 2004]. The auroral heating produced during magnetic storms generates thermospheric winds.
These winds affect the features of the ionospheric disturbance dynamo. According to the observations the ionospheric disturbance dynamo has a strong influence on storm-time ionospheric electric fields at middle and low latitudes [Blanc and Richmond, 1980].
Momentum and energy deposition into the high-latitude ionosphere by Joule heating and particle precipitation can trigger winds/ gravity waves that propagate toward the equator resulting in a disturbed dynamo system that produces electric field at the magnetic equatorial region within a few hours after the prompt penetration electric field [Bertoni et al., 2006].
- Penetration electric fields
- Mid-latitude electric fields and vertical drifts at quiet time
- Mid-latitude electric fields and vertical drifts at disturbed time
Solar cycle dependence
There are strong solar cycle effects in the vertical drifts and moderate seasonal effects.
(added Set 24, 2007)
There are different possible sources of longitude variations of the ion drift including longitude variations in the driving neutral winds, variations due to the magnetic field orientation and offset with respect to the geographic equator, and variations in the wind driven current due to longitude variations in the ionospheric conductivities.
Kil et al. (2007) studied the longitudinal structure of the vertical ExB drift and ion density using ROCSAT-1 data for quiet conditions (Kp £ 3+). The ROCSAT ExB observations presented in figure 7.1, at 1000-1100 LT, showed a longitudinal pattern of the ExB drift coincident with the longitudinal structure of the horizontal meridional winds on the daytime at 1100 LT.
These meridional winds were simulated by the Global Scale Wave Model (GSWM) at 111 km for April conditions. Moreover, results from the averaged ion density from ROCSAT-1 (1999-2004) at 1000-1200 LT, as shown in figure 7.2 (top), showed a similar pattern as the one obtained from the ExB drift in which the peaks locations distributed in longitude appear around the same longitude regions. However, the nighttime ion density map presented in figure 7.2 (bottom), at 2100-2300 LT, differ from the daytime ion density representation.
The ExB drift plotted versus longitude presents a wavenumber-4 shape. The four peaks noticed coincides with the peaks of the horizontal structure of the meridional winds. Immel et al. (2006) showed also the wavenumber-4 characteristic of the large-scale longitudinal variation of the equatorial ionospheric anomaly (EIA), and their relation with the non-migrating diurnal atmospheric tides, which are driven mainly by the tropical weather.
Figure 7.3 shows the longitudinal variability of the equatorial ionization anomaly. The coincidence between the TIMED GUVI and the IMAGE FUV data with peaks of the amplitude of the diurnal temperature variation at 115 km driven by meridional lower atmospheric tides is also presented in figure 7.4. England et al. (2006) showed similar results that relates the meridional winds with the temperature obtained at 110 km using the GSWM-02 model for april conditions at 11 LT. These results are shown in Figure 7.5.
The proposed mechanism to explain the longitudinal wavenumber-4 pattern of the density structure during quiet time conditions is the daytime E-region dynamo electric field driven by modulated tropospheric tidal winds [Immel et al. 2006; England et al. 2006, Kil et al. 2007]. During magnetically quiet time periods, daytime eastward electric fields are created mainly by tidal wind motions in the dayside E-region. These tides drive daytime Pedersen currents, that originates a build up of polarization charge along the terminator [England et al. 2006].
Fig. 7.1. The ROCSAT-1 ExB drift pattern in blue shows a wavenumber-4 structure at 1000-1100 LT. Simulations results of the horizontal meridional winds at 1100 LT using the GSWM-02 model for April conditions are shown as contour pattern plots. The positive values in solid lines of the contour patterns correspond to upward drifts and the negative values in dotted lines correspond to southward winds. [Kil et al. 2007]
Figure 7.2. Ion density maps at 1000 -1200 LT (top) and 2100-2300 LT (bottom). The averaged density in each bin of 10° longitude by 2° latitude is calculated from ROCSAT-1 data during March 1999 to June 2004.[Kil et al. 2007]
Fig. 7.3. IMAGE-FUV observations of nighttime ionospheric emissions at 2000 LT. The longitudinal variability of the equatorial ionospheric anomaly can be noticed. The southern anomaly is represented with a mirror image of the northern anomaly due to a poor sampling of the southern observations. The amplitude of the diurnal temperature variation at 115 km. is represented in white dashed contour lines. [Immel et al. 2006]
Fig. 7.4. The black line in the top figure (a) shows the average latitude of the peak brightness of the EIA versus longitude from the IMAGE-FUV observations of 135.6-nm recombination airglow emissions at 2030-2200 LT. The red line represents the same parameter from an ionospheric model using TIMED FUV observations. The amplitude of the temperature variation is illustrated by the blue line. This temperature variation is driven by the diurnal tide at 115 km, as reported by the GSM. The bottom figure (b) shows the brightness of the EIA from IMAGE and TIMED vs. longitude, as well as the temperature variation amplitude [Immel et al. 2006].
Fig. 7.5. The top figure shows the horizontal structure of the meridional winds. The positive values indicate northward winds and negative values correspond to southward winds.The bottom figure represents the temperatures associated with the diurnal tides simulated by the GSWM-02 model for April at 11 LT [England et al., 2006].
Fig. 7.6. Representation of the process that generates the perturbation electric field by tidal winds. The sinusoidal curve is the northward tidal wind (U) in the northern low latitude. The tidal winds induce the Pedersen current UxB represented by the filled arrows. Ep is the polarization electric field induced by the divergence of the Pedersen current. Eb is the background E-region dynamo eastward electric field. The resultant electric field is shown as the sum of Ep + Eb. The length of the arrows represents the amplitude of the fields [Kil et al., 2007].
Local time dependence
Low Middle High Latitude interaction
- Problem statement
A description of the major features of the electrodynamics of the low latitude ionosphere is developed in this review. Electromagnetic drifts have a strong influence on the behavior of plasma in the ionosphere.
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