The Earth has a long tail stretching away from the sun, somewhat like the plasma component of a comet's tail. The Earth's magnetotail is not visible optically because the gas density is too low. The gas is so hot that nearly all atoms are ionized, or in the plasma state.
We are trying to learn more about the thermodynamics of the Earth's plasma sheet. This is a region of relatively dense plasma at the center of the Earth's magnetotail. The equatorial part of the plasma sheet, where the magnetic field strength is a minmum, is called the neutral sheet. The region of the plasma sheet that is farthest from the neutral sheet is called the plasma sheet boundary layer (PSBL).
The first step in our procedure is to use data from the Geotail satellite to generate long-term averaged 3-D models of several hundred measured plasma and field parameters or combinations of these parameters. The availability of fully 3-D models allows us to study the variations of all parameters as one moves along an average magnetic field line or as one moves in any direction within the neutral sheet. It also is possible to integrate along the magnetic field lines generated in each model in order to determine the volume, plasma content, and other properties of a unit magnetic flux tube.
We now are extending the study of entropy by exammining its dependence on x, y, and the transport rate. Several additional entropy-related parameters also are being included in this ongoing study.
Three-dimensional long term averaged data based models of the plasma sheet were generated using Geotail satellite data. The 3-D models then were used to:
The Boltzmann H function was used to evaluate entropy in the plasma
sheet and to compare ten-year averages of several entropy parameters.
Gradients of the ion entropy density s_i were very similar to gradients
of the ion paraticle density n_i.
Similarly, gradients of the ion entropy per unit flux tube S_f,i were
very similar to gradients of the number of ions per unit flux tube N_f.
A parameter that is proportional to the average entropy per ion was
evaluated using the H function for the actual nonMaxwellian plasma
(S/Ncv)_H,i.
This entropy per ion parameter showed an earthward increase while the
ion entropy per unit flux tube exhibited an earthward decrease.
The entropy per ion reached a maximum at midnight, while the ion
entropy per unit flux tube reached a minimum at midnight.
These differences were attributed to differences in N_f, the average
number of particles per unit flux tube.
A second entropy per ion parameter, (S/Ncv)_P,i, showed the average entropy
an ion would have in a Maxwellian plasma with the observed temperature
and density.
The difference between (S/Ncv)_P,i and (S/Ncv)_H,i provides a measure
of the deviation of the observed plasma from equilibrium.
Boltzmann H function and entropy in the plasma sheet [2009]
The ion heat flux q_i is the energy flux carried by ions as seen
in a frame moving at the ion bulk flow velocity, V_i.
This heat flux is produced by asymmetries in the ion distribution function
as seen in the ion bulk flow frame.
The largest contribution to the average energy transport rate is the
thermal energy or enthalpy flux density term Q_T.
Since it is independent of V_i, the heat flux dominates energy transport
in regions where V_i is very small.
The q_i and V_i vectors often pointed in different directions.
A comparison of these directions enabled us to detemine where energy
dependent cross-tail drift was most important, where cross-tail ExB
drift became substantial, where low latitude boundary layer (LLBL)
sources and where effects of reconnection made significant contributions.
Sorting data according to the direction of the interplanetary magnetic
field (IMF) showed that the generation of a cold dense plasma sheet
had little effect on the superthermal ions that contribute most to q_i.
Ion heat flux and energy transport near the magnetotail
neutral sheet [2008]
The same sets of twelve 3-D data based models were used to study the
transport of particles and magnetic flux in the plasma sheet.
It was found that the volumes of unit flux tubes and the entropy
parameter, PV^5/3, depend only weakly upon flow speed. However, the flux
tube content was much smaller and the energy parameter, TV^2/3, was
much larger when transport rates were high.
The creation of separate 3D models for different ranges of flow speed
also showed why so much of the net particle, magnetic flux, and energy
transport takes place during BBF events.
Substantial transport takes place during slower flow periods,
but earthward and tailward transports nearly cancel each other
at such times.
It is only during the fastest flow events that earthward transport
is clearly dominant.
Reasons for the decrease in PV^5/3 as one moves earthward,
a feature that is referred to as
the pressure balance inconsistency, also were examined.
A specific series of stages that involve reconnection and the generation
of fast flows was described that could account for the observed spatial
variations of the observed thermodynamic parameters.
Magnetic flux and particle transport in the
plasma sheet [2006]
Twelve separate models were created, each based only on measurements
when ions were flowing in a specified velocity range.
It was found that field lines are dipolar whenever the ions are flowing
rapidly, either earthward or tailward.
A localized Birkeland current system in the region 1 sense was found
to surround a typical fast or bursty bulk flow (BBF) region.
The plasma temperatures were high and the densities were low
during fast flows, resulting in little
association of pressure with the flow speed.
An entropy per particle parameter, P/n^5/3
was high during the fast flow events, showing that plasma was
irreversibly heated when a BBF was generated.
The dependence of electron and ion anisotropies on flow speed showed that
average particles are scattered by 90 degrees as often as every 10 seconds
during the fastest flow periods.
Systematic variations of the ion to electron temperature ratio
also were found, showing that acceleration was more complicated than
resulting from gradient and curvature drifts in the presence of an average
cross tail electric field.
Relationships between the ion flow speed, magnetic
flux transport rate, and other plasma sheet parameters [2005]
Calculate the volumes, V, and plasma content, N, of unit magnetic
flux tubes.
It was found that both the entropy parameter, PV^5/3, and N
of an average flux tube decreased by 70% to 80% as an average flux
tube moved earthward from x = -30 Re to x = -10 Re.
The rate of loss of the most energetic particles was found to be a
little faster than the rate of loss of other particles.
Pressure, volume, density relationships in the
plasma sheet [2004]
Study the spatial variations of the magnetic moment, the
magnetization vector, and the CGL double adiabatic invariants.
The magnetization vector measurements were used to separate bound or
magnetization currents from free or guiding center drift currents.
These two current components pointed in nearly opposite directions
near the neutral sheet, so the total neutral sheet current was
much smaller than either the bound or the free current
components.
The spatial studies also showed that ions and electrons both undergo
strong scattering in what is often referred to as the collisionless
plasma sheet.
It was found that the average ion and electron undergoes one 90 degree
scattering episode every minute.
Magnetization of the plasma sheet [2004]
Carry out the first study of the generation of field aligned
(Birkeland) currents within the plasma sheet.
It was found that cross tail currents are being diverted to generate
Birkeland currents throughout the plasma sheet rather than just near
the neutral sheet or near the plasma sheet boundary layer (PSBL).
Effects of the interplanetary magnetic field (IMF) direction also
were studied.
Current diversion was found to be nearly symmetric in the
northern and southern hemispheres
when the IMF was predominantly northward or southward.
Strong asymmetries in the Birkeland currents were found when the
IMF was predominantly eastward or westward, implying the presence of
an interhemispheric current system.
Birkeland currents in the plasma sheet [2003]
Show that the variations observed along field lines of the ion and
electron pressure anisotropies imply the presence of parallel electric fields
near the neutral sheet.
These electric fields are required to maintain charge neutrality in the
region where electrons follow guiding center orbits and the ions
follow complex chaotic orbits.
As a result, the frozen in field concept
is not valid near the neutral sheet.
Three-dimensional analyses of electric currents and
pressure anisotropies in the plasma sheet [2002]
Determine the cross tail currents using particle observations and
Ampere's law plus magnetic field data.
This study included a crude separation of the common electron and ion drifts
from the differential drifts that create electric currents.
Plasma sheet thickness and electric currents [2001]
Evaluate the spatial variations of the long term averaged
firehose instability parameter throughout the plasma sheet.
Pressure anisotropy and By in the magnetotail current sheet
[2000]
Summary and Abstracts of older papers
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