explanation blue bibcodes open ADS page with paths to full text
Author name code: leer
ADS astronomy entries on 2022-09-14
author:"Leer, Egil"
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Title: Solar wind originating in funnels: fast or slow?
Authors: Janse, Å. M.; Lie-Svendsen, Ø.; Leer, E.
2007A&A...474..997J Altcode:
Aims:We model a hydrogen-helium solar wind originating in funnels,
regions of rapid flux tube expansion at the base of the solar
corona. <BR />Methods: The time-dependent model describes the particle
density, flow speed, temperature parallel and perpendicular to the
magnetic field, and the heat flow for each ionization state of hydrogen
and helium, and for electrons. <BR />Results: For a large range of
heating parameters, the funnel has two co-existing solutions: both
a slow and a fast solar wind solution result from the same heating
parameters, depending on the initial state from which the model was
started. Though the fast and the slow solar wind can co-exist it is
difficult to change from a fast solar wind to a slow solar wind or vice
versa. A significant change in the heating parameters is required to
“flip” the solution, and it takes a long time, about one month, to
reach the other steady state solution. When either the funnel or helium
is removed from the model, we no longer have two co-existing states.
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Title: The Impact of Solar Eruptions on the Upper Chromosphere,
Transition Region, and Corona
Authors: Lie-Svendsen, Øystein; Leer, Egil
2006ApJ...643.1286L Altcode:
We study how the solar atmosphere and wind respond to sudden and
large increases in the coronal energy input, with the aim of better
understanding the impact of fast coronal mass ejections on the lower
solar atmosphere. We apply a gyrotropic multifluid model extending from
the chromosphere to 1 AU and that accounts for radiative losses in the
transition region. The energy is deposited as pushing of coronal plasma
by a large-amplitude Alfvén wave (simulating expulsion of flux ropes)
and by thermal heating of electrons and protons. Both mechanisms lead
to rapid acceleration of coronal plasma close to the Sun, with speeds
of order 1000-2000 km s<SUP>-1</SUP>, and the resulting solar wind
structures with large-amplitude shocks do not depend sensitively on
the form of energy deposition in the corona. The response of the low
corona and transition region does depend sensitively on the form of
energy input, however. Alfvén wave pushing leads to very low coronal
temperatures and densities and a strong reduction in Lyα radiation
from the transition region, and only the plasma already present
in the corona is expelled. Thermal heating leads to much higher
coronal temperatures and densities and large downward heat fluxes,
causing a strong heating of the upper chromosphere and a resulting
large upflow of chromospheric material. In this case chromospheric
material constitutes 50% or more of the matter ejected from the Sun
as a result of the heating. Heating also leads to a sudden and large
increase in the Lyα radiation during the event. Although the lower
atmosphere responds rapidly to the increased energy input, it takes
half a day or more for the transition region and corona to be restored
to its preeruption state. Without electron or proton coronal heating,
electrons never reach the temperatures required to produce the high
ion charge states that are observed in some CMEs.
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Title: The Helium Abundance of Quiescent Coronal Loops
Authors: Killie, Mari Anne; Lie-Svendsen, Øystein; Leer, Egil
2005ApJ...632L.155K Altcode:
Coronal loops are modeled using a code that solves a newly developed
set of transport equations, in which a more accurate description of
thermal forces and heat conduction is contained. The plasma consists
of hydrogen and helium, and ionization and recombination, as well as
radiative loss, have been accounted for. When the loop is anchored in a
“well-mixed” chromosphere with a helium abundance of approximately
10%, the helium density of the coronal part of the loop becomes larger
than the hydrogen density within 1-3 days. In steady state, the loop is
completely dominated by helium, with a helium density more than 10 times
the hydrogen density. For a loop based in a stratified chromosphere
with very little helium in the upper part, a moderate coronal helium
abundance can be maintained. In this latter case, helium does not
“drain” from the loop, and we get an extreme increase in the helium
abundance from the upper chromosphere to the corona. These results
suggest that the chromosphere underlying closed field regions of the
Sun is highly stratified and that both helium and minor ion abundances
are far from constant throughout the chromosphere.
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Title: Modeling Helium in the Solar Wind with New Gyrotropic
Transport Equations
Authors: Janse, A. M.; Lie-Svendsen, Ø.; Leer, E.
2005ESASP.592..487J Altcode: 2005ESASP.592E..88J; 2005soho...16E..88J
No abstract at ADS
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Title: Modeling Helium in Closed Coronal Structures
Authors: Killie, M. A.; Lie-Svendsen, Ø.; Leer, E.
2005ESASP.592..147K Altcode: 2005ESASP.592E..22K; 2005soho...16E..22K
No abstract at ADS
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Title: Release of Helium from Closed-Field Regions of the Sun
Authors: Endeve, Eirik; Lie-Svendsen, Øystein; Hansteen, Viggo H.;
Leer, Egil
2005ApJ...624..402E Altcode:
Using a numerical model that extends from the chromosphere into the
supersonic solar wind, we study the dynamics of previously closed
coronal flux tubes that open, allowing plasma to be expelled from
the corona. In particular, we study whether the opening of flux tubes
may provide a source of helium-rich material for the solar wind. We
use higher order moment fluid equations to describe the plasma,
which consists of hydrogen (neutral and protons), helium (neutral,
singly ionized, and α-particles), and electrons. The helium abundance
decreases rapidly with altitude in a closed flux tube, caused by the
collisional coupling between α-particles and protons leading to a
small α-particle scale height. When the flux tube is rapidly opened,
protons escape from the Sun immediately. The coronal α-particles
leave the corona only much later, 10-20 hr after the protons, when the
collisional coupling to protons has eased, allowing their temperature
to become sufficiently high for them to escape.
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Title: Mode Conversion in Magneto-Atmospheres
Authors: Bogdan, T. J.; Carlsson, M.; Hansteen, V.; Heggland, L.;
Leer, E.; McMurry, A. D.; Stein, R. F.
2004AGUFMSH13A1162B Altcode:
Numerical simulations of wave propagation in a simple magneto-atmosphere
are employed to illustrate the complex nature of wave transformation
and conversion taking place in solar and stellar atmospheres. An
isothermal atmosphere threaded by a potential poloidal magnetic
field, and a superposed uniform toroidal field, is treated in a local
cartesian approximation. Spatial variations are restricted to the
two poloidal dimensions, but the toroidal field ensures that all
three MHD waves are present in the simulation. As in our previous
purely two-dimensional simulations (Bogdan et al. ApJ 599, 626-60,
2003), mode mixing and transformation take place at surfaces where
the magnetic and thermal pressures are equal. In the present case,
the upward propagating acoustic-gravity (MAG) wave is converted into
roughly equal parts transmitted fast, intermediate (Alfven), and
slow magneto-acoustic-gravity waves in passing through this mixing
layer. Unlike the fast and slow waves, the Alfven wave is weakly
damped, and is able to deposit its energy and momentum in the upper
chromosphere and corona. The fast and slow MAG waves are decoupled
on either side of mixing layer owing to their disparate propagation
speeds. Under certain fortuitous circumstances, the Alfven wave also
decouples from the fast and slow MAG waves.
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Title: Improved Transport Equations for Fully Ionized Gases
Authors: Killie, Mari Anne; Janse, Åse Marit; Lie-Svendsen, Øystein;
Leer, Egil
2004ApJ...604..842K Altcode:
We have developed fluid transport equations for fully ionized gases
that improve the description of Coulomb collisions. The aim has been to
develop simple and versatile equations that can easily be implemented
in numerical models and thus be applied to a large variety of space
plasmas, while they still accurately describe thermal forces and energy
flows in collision-dominated plasmas. Based on exact solutions to the
Boltzmann equation in the collision-dominated limit, the correction term
to the velocity distribution function that account for particle flows is
assumed to be proportional to the third power of the velocity, leading
to a near isotropic core distribution. Applying the fluid equations
derived from this new velocity distribution to a collision-dominated
electron-proton plasma with a small temperature gradient, the resulting
electron heat flux, as well as the thermal force between electrons
and protons, deviate less than 25% from the exact results of classical
transport theory. The new equations predict a factor of 4 reduction in
the thermal force acting on heavy, minor ions caused by an imposed heat
flux, compared with fluid equations that are in common use today. The
improved description of thermal forces is expected to be important
for modeling the composition of stellar atmospheres.
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Title: Helmet Streamers Gone Unstable: Two-Fluid Magnetohydrodynamic
Models of the Solar Corona
Authors: Endeve, Eirik; Holzer, Thomas E.; Leer, Egil
2004ApJ...603..307E Altcode:
The equations of magnetohydrodynamics (MHD) are used to study heating
of electrons and protons in an axially symmetric model of the solar
corona, extending from the coronal base to 15 solar radii. To study
heating of electrons and protons separately, as well as the collisional
coupling between the particle species, we use a two-fluid description
of the electron-proton plasma. A steady coronal heat input, uniform base
pressure, and dipole field boundary conditions produce a magnetic field
configuration similar to that seen with white-light coronagraphs during
quiet-Sun conditions: a helmet streamer is formed in the inner corona
around the equator, surrounded by coronal holes at higher latitudes. The
plasma inside the helmet streamer is in hydrostatic equilibrium, while
in the coronal holes a transonic solar wind is accelerated along the
field. The collisional coupling between electrons and protons becomes
weak close to the coronal base. In the case of proton heating, the
thermal structure along open and closed field lines is very different,
and there is a large pressure jump across the streamer-coronal hole
boundary. When the equations are integrated on a long timescale, the
helmet streamer becomes unstable, and massive plasmoids are periodically
released into the solar wind. These plasmoids contribute significantly
to the total mass and energy flux in the solar wind. The mass of the
plasmoids is reduced when electrons are heated.
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Title: Helium Abundance in the Corona and Solar Wind: Gyrotropic
Modeling from the Chromosphere to 1 AU
Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil
2003ApJ...596..621L Altcode:
We have developed a solar wind model including helium that extends
from the chromosphere to 1 AU. The model is based on the gyrotropic
approximation to the 16-moment set of fluid transport equations,
which allows it to accommodate temperature anisotropies, as well as
nonclassical heat transport. We find that, as in a pure electron-proton
solar wind, the flow geometry close to the Sun also has a large
impact on helium. In a radially expanding flow, downward proton heat
conduction from the corona leads to a high transition region pressure
and a large thermal force that pulls helium ions into the corona. In
this case α-particles may easily become the dominant species in the
corona, resulting in a polar wind type of solar wind in which the
light protons are accelerated outward in the electric field set up by
the α-particles and electrons. By contrast, applying the same form
for the coronal heating in a rapidly expanding geometry intended to
simulate a coronal hole, protons become collisionless closer to the
Sun, and therefore the downward proton heat flux is smaller, resulting
in a lower transition region pressure and a lower thermal force on
helium. In this case the helium abundance is low everywhere and helium
is unimportant for the acceleration of the solar wind. For the low
coronal proton and α-particle densities found in the rapidly expanding
flow, where asymptotic flow speeds are typically significantly higher
than the gravitational escape speed at the solar surface, the solar
wind helium mass flux is determined by the amount of helium available
at the top of the chromosphere. In the radially expanding flow,
with asymptotic flow speeds lower than the escape speed, the helium
mass flux depends on the amount of energy available in the corona
to lift helium out of the gravitational potential. In both cases the
frictional coupling between helium and hydrogen in the chromosphere,
using currently accepted elastic cross sections, is too weak to pull
a sufficient number of helium atoms up to the top of the chromosphere
and thus obtain a mass flux in agreement with observations. A better
understanding of the chromosphere is therefore called for.
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Title: Thermal forces and the coronal helium abundance
Authors: Hansteen, V. H.; Lie-Svendsen, Ø.; Leer, E.
2003AIPC..679..620H Altcode:
The interaction between protons and minor ions in the
chromosphere-corona transition region produces an upward force on the
minor ions and an enhanced coronal abundance. In this presentation we
compare a “classical” hydrodynamical model of a hydrogen - helium
solar wind and a model based on a 16-moment fluid description where
the heat flux is treated in a self-consistent manner.
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Title: The effect of time-dependent coronal heating on the solar
wind from coronal holes
Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil
2003AIPC..679..299L Altcode:
We have modelled the solar wind response to a time-dependent
energy input in the corona. The model, which extends from the upper
chromosphere to 1 AU, solves the time-dependent transport equations
based on the gyrotropic approximation to the 16-moment set of transport
equations, which allow for temperature anisotropies. Protons are heated
perpendicularly to the magnetic field, assuming a coronal heating
function that varies sinusoidally in time. We find that heating with
periods less than about 3 hours does not leave visible manifestations
in the solar wind (the oscillations are efficiently damped near the
Sun) heating with periods of order 10 hours leads to perturbations
comparable to Ulysses observations; while heating with periods of
order 100 hours results in a series of steady-state solutions. Mass
flux perturbations tend to be larger than perturbations in wind
speed. Heating in coronal holes with periods of order 30 hours leads
to large mass flux perturbations near Earth, even when the amplitude
of the change in heating rate in the corona is small.
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Title: 2D MHD Models of the Large Scale Solar Corona
Authors: Endeve, Eirik; Holzer, Thomas E.; Leer, Egil
2003AIPC..679..331E Altcode:
By solving the equations of ideal MHD the interaction of an isothermal
coronal plasma with a dipole-like magnetic field is studied. We vary the
coronal temperature and the magnetic field strength to investigate how
the plasma and the magnetic field interact to determine the structure
of the large scale solar corona. When our numerical calculations are
initiated with an isothermal solar wind in a dipole magnetic field,
the equations may be integrated to a steady state. Open and closed
regions are formed. In the open regions the atmosphere expands into a
super-sonic wind, and in the closed regions the plasma is in hydrostatic
equilibrium. We find that the magnetic field configuration in the
outer corona is largely determined by the equatorial current sheet.
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Title: Two-dimensional Magnetohydrodynamic Models of the Solar Corona:
Mass Loss from the Streamer Belt
Authors: Endeve, Eirik; Leer, Egil; Holzer, Thomas E.
2003ApJ...589.1040E Altcode:
The equations of magnetohydrodynamics (MHD) are used to study an axially
symmetric model of the large-scale solar corona, extending from the
coronal base to 15 solar radii. We use a uniform heating of the inner
corona to investigate the energy output when the magnetic field is given
as a dipole at the coronal base. The heat input produces a large-scale
magnetic field structure similar to that found by Pneuman and Kopp,
with coronal holes in the polar regions and a helmet streamer around the
equator. We pay special attention to the energy balance in the system,
and find that the role of heat conduction is important in determining
the thermal structure in magnetically closed regions. Insufficient
energy loss to the transition region leads to a high temperature inside
the closed region. In the coronal holes a solar wind is accelerated into
interplanetary space, and the temperature is lower. As the difference
in pressure scale height along open and closed flux tubes is large, the
helmet streamer does not relax to a steady state; it opens periodically
to eject mass into interplanetary space. These mass ejections may
contribute significantly to the mass and energy flux in the solar wind.
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Title: Book Review: Energy conversion and particle acceleration in
the solar corona / Springer, 2003
Authors: Leer, Egil
2003SoPh..218..361L Altcode: 2003SoPh..218..361K
No abstract at ADS
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Title: Effect of time-dependent coronal heating on the solar wind
Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil
2002JGRA..107.1325L Altcode:
We have used a higher-order fluid model to study the effect of
time-dependent coronal heating of protons on the solar wind, both for
the fast wind from rapidly expanding coronal holes and for slower
winds from a radially expanding geometry. The model extends from
the chromosphere to 1 AU in order to capture the coupling between the
chromosphere and corona and therefore the supply of plasma to the solar
wind. The protons are heated in the perpendicular direction (relative
to the magnetic field), assuming a simple sinusoidal variation with
time. With a short time period for the heating, less than about 3 hours,
the oscillations are efficiently damped in the inner part of the solar
wind, even when the amplitude of the change in heating rate is large,
leading to essentially steady state solutions near Earth. Heating
with a period of 10 hours or so leads to perturbations in the wind
near Earth that are comparable to Ulysses observations. Heating with a
period of order 100 hours leads to essentially a series of steady state
solutions. The mass flux perturbations are in general larger than the
perturbations in wind speed, and for heating of coronal holes with
periods of order 30 hours the mass flux perturbations are amplified
in the wind by the interaction between the fast and slow components
of the wind. In this case even moderate changes in the heating rate
in the corona can produce solar wind interaction regions with forward
and reversed shocks and large mass flux perturbations near Earth.
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Title: The Effect of Transition Region Heating on the Solar Wind
from Coronal Holes
Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil;
Holzer, Thomas E.
2002ApJ...566..562L Altcode:
Using a 16 moment solar wind model extending from the chromosphere to
1 AU, we study how the solar wind is affected by direct deposition
of energy in the transition region, in both radially expanding
geometries and rapidly expanding coronal holes. Energy is required
in the transition region to lift the plasma up to the corona, where
additional coronal heating takes place. The amount of energy deposited
determines the transition region pressure and the number of particles
reaching the corona and, hence, how the solar wind energy flux is
divided between gravitational potential and kinetic energy. We find that
when only protons are heated perpendicularly to the magnetic field in a
rapidly expanding coronal hole, the protons quickly become collisionless
and therefore conduct very little energy into the transition region,
leading to a wind much faster than what is observed. Only by additional
deposition of energy in the transition region can a reasonable mass flux
and flow speed at 1 AU be obtained. Radiative loss in the transition
region is negligible in these low-mass flux solutions. In a radially
expanding geometry the same form of coronal heating results in a
downward heat flux to the transition region substantially larger
than what is needed to heat the upwelling plasma, resulting in a
higher transition region pressure, a slow, massive solar wind, and
radiative loss playing a dominant role in the transition region energy
budget. No additional energy input is needed in the transition region
in this case. In the coronal hole geometry the solar wind response to
transition region heating is highly nonlinear, and even a tiny input of
energy can have a very large influence on the asymptotic properties of
the wind. By contrast, the radially expanding wind is quite insensitive
to additional deposition of energy in the transition region.
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Title: Coupling Between Chromosphere and Corona: Why it Matters for
the Solar Wind
Authors: Lie-Svendsen, {; Hansteen, V. H.; Leer, E.
2001AGUSM..SH21B02L Altcode:
The solar wind is driven by energy input which must be deposited mainly
in the corona. In some sense, therefore, the solar wind “starts”
in the corona, and most solar wind models have their lower boundary
here. However, the underlying chromosphere and transition region is
not only a “passive” supplier of solar wind plasma. Energy must
be supplied as well in the upper chromosphere and transition region
to ionize and heat the outflowing gas from chromospheric to coronal
temperatures. While this energy input is usually small compared to the
energy deposited in the corona, it nevertheless can have a crucial
influence on the solar wind because the amount of energy deposited
in the transition region limits the mass flux of the wind. Using a
higher-order (16-moment) fluid solar wind model that extends from the
chromosphere to 1~AU, we find that when protons are heated in the
corona they may quickly become collisionless so that the heat flux
deviates strongly from classical heat conduction, making it difficult
to transport sufficient amounts of energy downwards to the transition
region. The problem is most acute in the rapidly expanding magnetic
field of coronal holes, where we find that adding even a small energy
input in the transition region therefore can increase the solar wind
mass flux by a factor ten or more, and not doing so leads to a wind
much faster than what is observed even in high-speed streams.
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Title: Coronal heating and solar wind acceleration; gyrotropic
electron-proton solar wind
Authors: Endeve, Eirik; Leer, Egil
2001SoPh..200..235E Altcode:
In coronal holes the electron (proton) density is low, and heating of
the proton gas produces a rapidly increasing proton temperature in the
inner corona. In models with a reasonable electron density in the upper
transition region the proton gas becomes collisionless some 0.2 to 0.3
solar radii into the corona. In the collisionless region the proton heat
flux is outwards, along the temperature gradient. The thermal coupling
to electrons is weak in coronal holes, so the heat flux into the
transition region is too small to supply the energy needed to heat the
solar wind plasma to coronal temperatures. Our model studies indicate
that in models with proton heating the inward heat conduction may be
so inefficient that some of the energy flux must be deposited in the
transition region to produce the proton fluxes that are observed in the
solar wind. If we allow for coronal electron heating, the energy that
is needed in the transition region to heat the solar wind to coronal
temperatures, may be supplied by heat conduction from the corona.
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Title: A 16-moment solar wind model: From the chromosphere to 1 AU
Authors: Lie-Svendsen, Øystein; Leer, Egil; Hansteen, Viggo H.
2001JGR...106.8217L Altcode:
We present a solar wind fluid model extending from the chromosphere
to Earth. The model is based on the gyrotropic approximation to
the 16-moment set of transport equations, in which we solve for the
density, drift speed, temperature parallel and perpendicular to the
magnetic field, and transport of parallel and perpendicular thermal
energy along the magnetic field (heat flux). The solar wind plasma is
created dynamically through (photo) ionization in the chromosphere,
and the plasma density in the transition region and corona is computed
dynamically, dependent on the type of coronal heating applied, rather
than being set arbitrarily. The model improves the description of
proton energy transport in the transition region, where classical heat
conduction is only retrieved in the collision-dominated limit. This
model can serve as a “test bed” for any coronal heating mechanism. We
consider heating of protons by a turbulent cascade of Alfvén waves
in rapidly expanding coronal holes. The resulting high coronal proton
temperatures lead to a downward proton energy flux from the corona
which is much smaller than what classical transport theory predicts,
causing a very low coronal density and an extremely fast solar wind
with a small mass flux. Only when some of the wave energy is forcibly
deposited in the lower transition region can a realistic solar wind
be obtained. Because of the poor proton heat transport, in order
to produce a realistic solar wind any viable heating mechanism must
deposit some energy in the transition region, either directly or via
explicit heating of coronal electrons.
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Title: Solar Wind: Theory
Authors: Leer, E.
2000eaa..bookE2308L Altcode:
The supersonic outflow of electrically charged particles, mainly
electrons and protons from the solar CORONA, is called the SOLAR
WIND. The solar wind was described theoretically by E N PARKER,
in 1958. Parker's theory was verified experimentally by in situ
observations by Soviet and American spaceprobes. On its way to Venus, in
1962, the MARINER II spacecraft observed the solar wind for 104 days...
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Title: The electron velocity distribution in the high-speed solar
wind: Modeling the effects of protons
Authors: Lie-Svendsen, Øystein; Leer, Egil
2000JGR...105...35L Altcode:
The evolution of the electron velocity distribution function
(VDF) in high-speed solar wind streams is modeled taking the
expanding geometry, the polarization electric field, and Coulomb
collisions into account. The VDF we find at the orbit of Mercury
is composed of an isotropic, collision-dominated core, a trapped,
anisotropic population called “halo” in this study, and a narrow,
high-energy “strahl” that escapes along the magnetic field. The
distribution function is very similar to the electron VDF observed
in the low-density, high-speed solar wind by Pilipp et al. [1987] and
Phillips et al. [1989]. The main features of the VDF can be obtained
by considering only electron self-collisions; the effect of proton
collisions is to make the distribution function more isotropic. At
low energies, collisions with protons dominate the angular scattering,
but electron self-collisions alone are frequent enough to keep the core
of the distribution function quite isotropic. The expanding geometry
produces an anisotropic halo and a narrow strahl. The angular scattering
by protons reduces the anisotropy of the trapped halo particles and
broadens the lower-energy part of the strahl. Along the magnetic
field the resulting electron velocity distribution is composed of a
relatively cold core and a halo-strahl spectrum that is “flatter”
than the coronal spectrum. The two-temperature electron distribution
function often observed in the solar wind may therefore be produced
by Coulomb collisions and should not be taken as a “proof” of a
non-Maxwellian (two-temperature) distribution function in the corona.
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Title: Advances in Modelling the Fast Solar Wind
Authors: Hansteen, V. H.; Leer, E.; Lie-Svendsen, Ø.
1999ESASP.448.1091H Altcode: 1999mfsp.conf.1091H; 1999ESPM....9.1091H
No abstract at ADS
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Title: Electron Heat Conduction in the Solar Transition Region:
Validity of the Classical Description
Authors: Lie-Svendsen, Øystein; Holzer, Thomas E.; Leer, Egil
1999ApJ...525.1056L Altcode:
We have studied the transport of energy in the solar transition region,
with the aim of finding out whether classical transport theory is
applicable in this region. We use a test particle approximation,
where test electrons move in a prescribed, background Maxwellian
electron-proton plasma. This approximation is validated by comparing
with the Spitzer-Härm result in the collision-dominated limit,
where the Spitzer-Härm result should be valid. We find that the test
particle approximation yields velocity distribution functions in good
agreement with Spitzer and Härm, and the test particle energy flux
is only 25% lower than the correct result. Then, applying the model
to conditions believed to be found in the solar transition region, we
obtain essentially the same good agreement with the classical result,
showing that classical transport theory is sufficient to describe heat
transport in the solar transition region. When the transition region
pressure (density) is reduced to unrealistically low values, while the
temperature profile is kept unchanged, a significant fraction of the
energy flux is carried by nonthermal electrons from the corona. But
the total energy flux is never larger than the classical Spitzer-Härm
value. The heat flux is independent of density at high densities (the
classical result), and decreases monotonically as the transition region
pressure is reduced.
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Title: The origin of the high speed solar wind
Authors: Hansteen, Viggo H.; Leer, Egil; Holzer, Thomas E.
1999AIPC..471...17H Altcode: 1999sowi.conf...17H
The outflow of coronal plasma into interplanetary space is a
consequence of the coronal heating process. Therefore the formation
of the corona and the acceleration of the solar wind should be
treated as a single problem. The deposition of energy into the corona
through some mechanical or electromagnetic energy flux is balanced
by the various sinks available to the corona, and the sum of these
processes determines the coronal structure, i.e. its temperature and
density. Heating of the extended solar corona leads to high proton and
ion temperatures and relatively low electron temperatures. This is due
to the low heat conductivity in the proton (ion) gas as compared to
the electrons. To a fairly good approximation we can say that most of
the energy flux deposited in the protons and ions is lost as kinetic
and gravitational energy flux in the solar wind flow, whereas a large
fraction of the energy flux added to the electrons is conducted back
into the transition region and lost as radiation. In order to drive
high speed wind most of the energy must be deposited in the ions.
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Title: A study of solar wind acceleration based on gyrotropic
transport equations
Authors: Olsen, Espen Lyngdal; Leer, Egil
1999JGR...104.9963O Altcode:
The gyrotropic transport equations are used to describe an
electron-proton solar wind from the 500,000 K level in the upper
transition region and out to 30 solar radii. These equations allow
for different temperatures parallel and perpendicular to the magnetic
field, as well as transport of parallel and perpendicular thermal
energy along the field. We find that in models with significant coronal
proton heating, the electron temperature is much lower than the proton
temperature. The electron gas is collision dominated, the thermal
anisotropy is small, and the heat flux is close to a “classical” heat
flux. The proton gas is collision dominated in the upper transition
region, but the temperature increases rapidly in the inner corona,
and the protons become collisionless close to the Sun. The proton heat
flux is proportional to the temperature gradient very close to the Sun,
but in the extended corona it deviates substantially from a classical
heat flux. In models where the proton heating is in the direction
perpendicular to the magnetic field, a large perpendicular temperature
is produced locally, but the perpendicular thermal motion couples
into parallel thermal motion, and the parallel temperature increases
outward from the Sun. We obtain a maximum parallel temperature that
is comparable to the maximum perpendicular temperature. This result
seems to hold for all models where the energy flux necessary to drive
high-speed wind is deposited in the corona as heat. The result is not
in agreement with UVCS/SOHO observations of the 1216 Å Ly-α line
in large coronal holes. These observations are consistent with a much
larger random proton motion perpendicular to the magnetic field than
parallel to the field. Such anisotropies can be obtained in models
of high-speed solar wind if we allow for a significant fraction
of the energy flux from the Sun to be in the form of low-frequency,
transverse waves. These waves accelerate the solar wind without heating
the corona, and they contribute to the line broadening in the direction
perpendicular to the magnetic field.
---------------------------------------------------------
Title: Erratum: “An eight-moment approximation two-fluid model of
the solar wind”
Authors: Olsen, Espen Lyngdal; Leer, Egil
1999JGR...104..597O Altcode: 1999JGR...104..596O
<A href="/journals/ja/ja9901/98JA02725/index.html">Abstract
Available</A> from <A href="http://www.agu.org">AGU</A>
---------------------------------------------------------
Title: Working Group 1 Report: Solar Wind Models from the Sun to 1
AU: Constraints by "in situ" and Remote Sensing Measurements
Authors: Leer, E.; Marsch, E.
1999SSRv...87...67L Altcode:
The goal of Working Group 1 was to discuss constraints on solar wind
models. The topics for discussion, outlined by Eckart Marsch in his
introduction, were: (1) what heats the corona, (2) what is the role of
waves, (3) what determines the solar wind mass flux, (4) can stationary,
multi-fluid models describe the fast and slow solar wind, or (5) do we
need time dependent fluid models, kinetic models, and/or MHD models to
describe solar wind acceleration. The discussion in the working group
focused on observations of "temperatures" in the corona, mainly in
coronal holes, and whether the observations of line broadening should
be interpreted as thermal broadening or wave broadening. Observations
of the coronal electron density and the flow speed in coronal holes
were also discussed. There was only one contribution on observations of
the distant solar wind, but we can place firm constraints on the solar
wind particle fluxes and asymptotic flow speeds from observations with
Ulysses and other spacecraft. Theoretical work on multi-fluid models,
higher-order moment fluid models, and MHD models of the solar wind
were also presented.
---------------------------------------------------------
Title: Erratum: "An eight-moment approximation two-fluid model of
the solar wind&quot
Authors: Lyngdal Olsen, Espen; Leer, Egil
1999JGR...104..596L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: An eight-moment model parameter study of the solar wind:
dependence on variations in coronal heating
Authors: Olsen, Espen Lyngdal; Leer, Egil; Lie-Svendsen, Oystein
1998A&A...338..747O Altcode:
The eight-moment two-fluid model describes, self-consistently,
the proton (and electron) heat flux in the solar wind. This is a
crucial parameter in solar wind models with a high coronal proton
temperature. In the present study the eight-moment description is used
to study how the solar wind outflow from an electron-proton corona
responds to variations in coronal heating. Most of the energy flux is
deposited in the proton gas. We find that the asymptotic flow speed
of the solar wind is only weakly dependent on the amplitude of the
energy flux, but it increases with increasing dissipation length. When
most of the energy flux is dissipated in the extended corona, where
the protons are collisionless, we obtain flow speeds characteristic of
high-speed solar wind streams: For a dissipation length of 1 to 2 solar
radii the asymptotic flow speed is 700-1000 km s(-1) . A relatively
modest electron heating in the inner corona may lead to an increased
transition region pressure and hence a large increase in the solar
wind proton flux. This increase in proton flux may be so large that
there is not enough energy available to drive a high-speed wind.
---------------------------------------------------------
Title: Acceleration of the Solar Wind: A New View
Authors: Hansteen, V. H.; Leer, E.
1998HiA....11..838H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Solar Wind
Authors: Leer, E.
1998ESASP.417...11L Altcode: 1998cesh.conf...11L
No abstract at ADS
---------------------------------------------------------
Title: Heating of the corona and acceleration of high speed solar wind
Authors: Evje, H. O.; Leer, E.
1998A&A...329..735E Altcode:
We present a parameter study of the corona--solar wind system. The
corona is heated by an energy flux from the sun. This energy flux is
lost as heat conductive flux into the transition region and as solar
wind energy flux. We consider two-fluid models where most of the energy
flux is deposited in the proton gas. Heating of the inner corona leads
to a significant (electron) heat conductive flux into the transition
region and a relatively high coronal electron density. This gives a
relatively low coronal proton temperature, a large solar wind proton
flux, and a relatively low asymptotic flow speed. In rapidly expanding
flow geometries, where the thermal coupling between electrons and
protons is weaker, heating of the protons in the inner corona may lead
to a somewhat higher proton temperature, and higher asymptotic flow
speed, but in order to drive high speed solar wind, a significant
fraction of the energy flux from the sun must be deposited in the
outer corona, where the protons are collisionless. In such a model
only a small fraction of the energy flux is lost as inward heat flux,
the transition region pressure is low, and the solar wind proton flux
is quite small. The proton temperature in the outer corona is high,
and a larger fraction of the energy flux deposited in the proton gas
may be lost as solar wind kinetic energy flux.
---------------------------------------------------------
Title: Understanding the Solar Wind
Authors: Leer, E.; Hansteen, V. H.; Holzer, T. E.
1998cvsw.conf..263L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Role of Helium in the Outer Solar Atmosphere
Authors: Hansteen, V. H.; Leer, E.; Holzer, T. E.
1997ApJ...482..498H Altcode:
We construct models of the outer solar atmosphere comprising the region
from the mid-chromosphere and into the solar wind in order to study
the force and energy balance in models with a significant helium
abundance. The corona is created by dissipation of an energy flux
from the Sun. The energy flux is lost as radiation from the top of the
chromosphere and as gravitational and kinetic solar wind energy flux. We
find that in models with significant ion heating of the extended corona
most of the energy flux is lost in the solar wind. The ion temperatures
are higher than the electron temperature in these models, and the
α-particle temperature is much higher than the proton temperature,
so there is energy transfer from the α-particle fluid to the protons
and electrons, but this energy exchange between the different species
is relatively small. To a fairly good approximation we can say that the
energy flux deposited in the protons and α-particles is lost as kinetic
and gravitational energy flux in the proton and α-particle flow. How
this energy flux is divided between gravitational and kinetic energy
flux (i.e., how large the particle fluxes and flow speeds are) depends
upon details of the heating process. We also find that mixing processes
in the chromosphere play an important role in determining the coronal
helium abundance and the relative solar wind proton and α-particle
fluxes. Roughly speaking, we find that the relative α-particle and
proton fluxes are set by the degree of chromospheric mixing, while
the speeds are set by the details of the coronal heating process.
---------------------------------------------------------
Title: The Coronal Helium Abundance and the Solar Wind
Authors: Hansteen, Viggo H.; Hassler, Donald M.; Leer, Egil; Holzer,
Thomas E.; Woods, Thomas N.
1997SPD....28.0154H Altcode: 1997BAAS...29Q.889H
The coronal Helium abundance depends on the rate Helium is brought into
the corona via the transition region from the chromosphere and on the
rate that Helium is removed from the corona in the Solar wind. Recent
multi-fluid models of the combined chromosphere, corona, solar wind
system show that the corona may have a significant Helium abundance;
perhaps even exceeding 50% of the Hydrogen number density. These models
also indicate that in order to reproduce the Solar wind at 1AU ions
(alpha -particles as well as protons) may be required to be the most
important recipient of the coronal heating process. In these models the
role of electrons in the energetics of the Solar wind is much reduced
compared to the standard thermally driven winds. A measurement of the
coronal Helium abundance will serve to fix these theoretical ideas and
may give important clues as to mixing processes in the chromosphere as
well as to coronal heating processes. Consequently, we will discuss the
current state of observations (i.e. SOHO), and their limitations, as
well as plans for future observations (i.e. sounding rocket, Spartan).
---------------------------------------------------------
Title: Kinetic electrons in high-speed solar wind streams: Formation
of high-energy tails
Authors: Lie-Svendsen, Øystein; Hansteen, Viggo H.; Leer, Egil
1997JGR...102.4701L Altcode:
We study the evolution of the electron velocity distribution function
in high-speed solar wind streams from the collision-dominated corona
and into the collisionless interplanetary space. The model we employ
solves the kinetic transport equation with the Fokker-Planck collision
operator to describe Coulomb collisions between electrons. We use
a test particle approach, where test electrons are injected into
a prescribed solar wind background. The density, temperature, and
electric field associated with the background are computed from
fluid models. The test electrons are in thermal equilibrium with
the background at the base of the corona, and we study the evolution
of the velocity distribution of the test electrons as a function of
altitude. We find that velocity filtration, due to the energy dependence
of the Coulomb cross section, is a small effect and is not capable
of producing significant beams in the distribution or a temperature
moment that increases with altitude. The distribution function is
mainly determined by the electric field and the expanding geometry and
consists of a population with an almost isotropic core which is bound
in the electrostatic potential and a beam-like high-energy tail which
escapes. The trapped electrons contribute significantly to the even
moments of the distribution function but almost nothing to the odd
moments; the drift speed and energy flux moments are carried solely by
the tail. In order to describe the high-speed solar wind observed near
0.3 AU by the Helios spacecraft, we use a multifluid model where ions
are heated preferentially. The resulting test electron distribution
at 0.3 AU, in this background, is in very good agreement with the
velocity distributions observed by the Helios spacecraft.
---------------------------------------------------------
Title: Coronal Hole Structure and the High Speed Solar Wind
Authors: Holzer, T. E.; Leer, E.
1997ESASP.404...65H Altcode: 1997cswn.conf...65H; 1997soho....5...65H
No abstract at ADS
---------------------------------------------------------
Title: Helium in the outer solar atmosphere
Authors: Hansteen, V. H.; Leer, E.; Holzer, T. E.
1997AIPC..385..197H Altcode: 1997recs.conf..197H
We construct models of the outer solar atmosphere comprising the
region from the mid chromosphere and into the solar wind in order
to study the force and energy balance in models with a significant
helium abundance. The corona is created by dissipation of an energy
flux from the Sun. The energy flux is lost as radiation from the
top of the chromosphere and as gravitational and kinetic solar wind
energy flux. We find that in models with significant ion heating of the
extended corona most of the energy flux is lost in the solar wind. The
ion temperatures are higher than the electron temperature in these
models, and the α-particle temperature is much higher than the proton
temperature. Roughly speaking we find that the relative α-particle
and proton fluxes are set by the degree of chromospheric mixing while
the speeds are set by the details of the coronal heating process.
---------------------------------------------------------
Title: Acceleration of the Solar Wind
Authors: Holzer, T. E.; Hansteen, V. H.; Leer, E.
1997cwh..conf..239H Altcode: 2006mslp.conf..239H
No abstract at ADS
---------------------------------------------------------
Title: Outflow of He<SUP>+</SUP> from the polar ionosphere: Comparison
of hydrodynamic and kinetic descriptions
Authors: Leer, Egil; Lie-Svendsen, Øystein; Olsen, Espen Lyngdal;
Hansteen, Viggo H.
1996JGR...10117207L Altcode:
Singly ionized helium, a minor species in the polar ionosphere, is
being propelled out along open magnetic field lines by an outward
polarization electric field. In the present study we compare the
kinetic and hydrodynamic descriptions of this transonic outflow
treating the singly ionized helium as a test particle population in a
static background of singly ionized oxygen and electrons. We find that
the resultant He<SUP>+</SUP> particle fluxes are equal in both the
eight-moment hydrodynamic description and in the kinetic description
based on the Fokker-Planck equation. A five-moment hydrodynamic
description gives a flux that is some 40% lower. The increase of
the He<SUP>+</SUP> energy flux with altitude is also equal in the
eight-moment hydrodynamic and in the kinetic descriptions.
---------------------------------------------------------
Title: An eight moment solar wind model
Authors: Olsen, Espen Lyngdal; Leer, Egil
1996AIPC..382..157O Altcode:
No abstract at ADS
---------------------------------------------------------
Title: An eight-moment approximation two-fluid model of the solar wind
Authors: Olsen, Espen Lyngdal; Leer, Egil
1996JGR...10115591O Altcode:
In fluid descriptions of the solar wind the heat conductive flux
is usually determined by the use of the classical Spitzer-Härm
expression. This expression for the heat flux is derived assuming the
gas to be static and collision-dominated and is therefore strictly
not valid in the solar wind. In an effort to improve the treatment
of the heat conductive flux and thereby fluid models of the solar
wind, we study an eight-moment approximation two-fluid model of the
corona-solar wind system. We assume that an energy flux from the Sun
heats the coronal plasma, and we solve the conservation equations for
mass and momentum, the equations for electron and proton temperature,
as well as the equations for heat flux density in the electron
and proton fluid. The results are compared with the results of a
“classical” model featuring the Spitzer-Härm expression for the
heat conductive flux in the electron and proton gas. In the present
study we discuss models with heating of the coronal protons; the
electrons are only heated by collisional coupling to the protons. The
electron temperature and heat flux are small in these cases. The proton
temperature is large. In the classical model the transfer of thermal
energy into flow energy is gradual, and the proton heat flux in the
solar wind acceleration region is often too large to be carried by a
reasonable proton velocity distribution function. In the eight-moment
model we find a higher proton temperature and a more rapid transfer
of thermal energy flux into flow energy. The heat fluxes from the
corona are small, and the velocity distribution functions, for both
the electrons and protons, remain close to shifted Maxwellians in the
acceleration region of the solar wind.
---------------------------------------------------------
Title: A kinetic study of solar wind electrons
Authors: Lie-Svendsen, Øystein; Leer, Egil
1996AIPC..382...58L Altcode:
The evolution of the distribution function for a test population of
electrons in an isothermal electron-proton corona has been studied
using a Fokker-Planck description. The aim is to investigate whether
a suprathermal tail forms due to the energy dependence of the Coulomb
cross section. We find that a Maxwellian test population, injected into
this background close to the coronal base with a temperature equal
to that of the background electrons, maintains its shape throughout
the transition from collision-dominated to collisionless flow. No
significant suprathermal tail in the electron distribution function
is seen in the outer corona.
---------------------------------------------------------
Title: An eight-moment approximation two-fluid model of the solar wind
Authors: Lyngdal Olsen, Espen; Leer, Egil
1996JGR...10115591L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Thermally Driven One-Fluid Electron-Proton Solar Wind:
Eight-Moment Approximation
Authors: Olsen, Espen Lyngdal; Leer, Egil
1996ApJ...462..982O Altcode:
In an effort to improve the "classical" solar wind model, we study
an eight-moment approximation hydrodynamic solar wind model, in
which the full conservation equation for the heat conductive flux is
solved together with the conservation equations for mass, momentum,
and energy. We consider two different cases: In one model the energy
flux needed to drive the solar wind is supplied as heat flux from a hot
coronal base, where both the density and temperature are specified. In
the other model, the corona is heated. In that model, the coronal
base density and temperature are also specified, but the temperature
increases outward from the coronal base due to a specified energy
flux that is dissipated in the corona. The eight-moment approximation
solutions are compared with the results from a "classical" solar wind
model in which the collision-dominated gas expression for the heat
conductive flux is used. It is shown that the "classical" expression for
the heat conductive flux is generally not valid in the solar wind. In
collisionless regions of the flow, the eight-moment approximation gives
a larger thermalization of the heat conductive flux than the models
using the collision-dominated gas approximation for the heat flux, but
the heat flux is still larger than the "saturation heat flux." This
leads to a breakdown of the electron distribution function, which
turns negative in the collisionless region of the flow. By increasing
the interaction between the electrons, the heat flux is reduced, and a
reasonable shape is obtained on the distribution function. By solving
the full set of equations consistent with the eight-moment distribution
function for the electrons, we are thus able to draw inferences about
the validity of the eight-moment description of the solar wind as
well as the validity of the very commonly used collision-dominated
gas approximation for the heat conductive flux in the solar wind.
---------------------------------------------------------
Title: Coronal heating, densities, and temperatures and solar wind
acceleration
Authors: Hansteen, Viggo H.; Leer, Egil
1995JGR...10021577H Altcode:
The outflow of coronal plasma into interplanetary space is a
consequence of the coronal heating process. Therefore the formation
of the corona and the acceleration of the solar wind should be treated
as a single problem. The deposition of energy into the corona through
some “mechanical” energy flux is balanced by the various energy sinks
available to the corona, and the sum of these processes determines the
coronal structure, i.e., its temperature and density. The corona loses
energy through heat conduction into the transition region and through
the gravitational potential energy and kinetic energy put into the solar
wind. We show from a series of models of the chromosphere-transition
region-corona-solar wind system that most of the energy deposited in
a magnetically open region goes into the solar wind. The transition
region pressures and the coronal density and temperature structure may
vary considerably with the mode and location of energy deposition,
but the solar wind mass flux is relatively insensitive to these
variations; it is determined by the amplitude of the energy flux. In
these models the transition region pressure decreases in accordance
with the increasing coronal density scale height such that the solar
wind mass loss is consistent with the energy flux deposited in the
corona. On the basis of the present study we can conclude that the
exponential increase of solar wind mass flux with coronal temperature,
found in most thermally driven solar wind models, is a consequence of
fixing the transition region pressure.
---------------------------------------------------------
Title: Coronal Heating and Solar Wind Energy Balance
Authors: Sandbaek, Ornulf; Leer, Egil
1995ApJ...454..486S Altcode:
In this paper we present a parameter study of a two-fluid and a
one-fluid model of the solar wind where coronal heating and solar wind
acceleration is treated as one problem. To study the energy balance in
the corona/solar wind system, we consider a "mechanical" energy flux
emanating from the Sun which is transferred to the coronal plasma
as heat with a characteristic dissipation length of a few tenths
of a solar radius. The mechanical energy flux adding energy to the
coronal plasma as heat is varied, and the dissipation length of the
mechanical energy flux and the fraction of the energy added to protons
(electrons) are varied. The low heat conductivity in the proton gas
and the relatively weak thermal coupling between electrons and protons
cause large temperature differences in the corona. In two-fluid models
with electron heating and in one-fluid models, a larger fraction of
the mechanical energy flux is lost as heat conduction and radiation
than in two-fluid models with pure proton heating. In all models
where an energy flux is added to the quasi-static corona as heat,
the asymptotic flow speed is low. We demonstrate how a flux of Alfvén
waves emanating from the Sun can accelerate the thermally driven solar
wind to asymptotic flow speeds higher than the Sun's escape speed.
---------------------------------------------------------
Title: Eight-moment approximation solar wind models
Authors: Olsen, Espen Lyngdal; Leer, Egil
1995sowi.confR..66O Altcode:
Heat conduction from the corona is important in the solar wind
energy budget. Until now all hydrodynamic solar wind models have
been using the collisionally dominated gas approximation for the
heat conductive flux. Observations of the solar wind show particle
distribution functions which deviate significantly from a Maxwellian,
and it is clear that the solar wind plasma is far from collisionally
dominated. We have developed a numerical model for the solar wind
which solves the full equation for the heat conductive flux together
with the conservation equations for mass, momentum, and energy. The
equations are obtained by taking moments of the Boltzmann equation,
using an 8-moment approximation for the distribution function. For
low-density solar winds the 8-moment approximation models give results
which differ significantly from the results obtained in models assuming
the gas to be collisionally dominated. The two models give more or
less the same results in high density solar winds.
---------------------------------------------------------
Title: A kinetic study of solar wind electrons in the transition
region from collision dominated to collisionless flow
Authors: Lie-Svendsen, O.; Leer, E.
1995sowi.conf...30L Altcode:
We have studied the evolution of the velocity distribution function
of a test population of electrons in the solar corona and inner solar
wind region, using a recently developed kinetic model. The model solves
the time dependent, linear transport equation, with a Fokker-Planck
collision operator to describe Coulomb collisions between the 'test
population' and a thermal background of charged particles, using a
finite differencing scheme. The model provides information on how
non-Maxwellian features develop in the distribution function in the
transition region from collision dominated to collisionless flow. By
taking moments of the distribution the evolution of higher order
moments, such as the heat flow, can be studied.
---------------------------------------------------------
Title: Stellar Winds
Authors: Leer, E.
1995fras.conf..125L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the Relation between Coronal Heating, Flux Tube Divergence,
and the Solar Wind Proton Flux and Flow Speed
Authors: Sandbaek, Onulf; Leer, Egil; Hansteen, Viggo H.
1994ApJ...436..390S Altcode:
A one-fluid solar wind model is used to investigate some relations
between coronal heating, the flux tube divergence near the Sun, and the
solar wind proton flux and flow speed. The effects of energy addition
to the supersonic region of the flow are also studied. We allow for
a mechanical energy flux that heats the corona, and an Alfven wave
energy flux that adds energy, mainly to the supersonic flow, both
as momentum and as heat. We find that the mechanical energy flux
determines the solar wind mass flux, and in order to keep an almost
constant proton flux at the orbit of Earth with changing flow geometry,
that the mechanical energy flux must vary linearly with the magnetic
field in the inner corona. This thermally driven wind generally has a
low asymptotic flow speed. When Alfven waves are added to the thermally
driven flow, the asymptotic flow speed is increased and is determined
by the ratio of the Alfven wave and the mechanical energy fluxes at
the coronal base. Flow speeds characteristic of recurrent high-speed
solar wind streams can be obtained only when the Alfven wave energy
flux, deposited in the supersonic flow, is larger than the mechanical
energy flux heating the corona.
---------------------------------------------------------
Title: Coupling of the coronal He abundance to the solar wind
Authors: Hansteen, V. H.; Leer, E.; Holzer, T. E.
1994SSRv...70..347H Altcode:
Models of the transition region — corona — solar wind system are
investigated in order to find the coronal helium abundance and to
study the role played by coronal helium in controlling the the solar
wind proton flux. The thermal force on α-particles in the transition
region sets the flow of helium into the corona. The frictional coupling
between α-particles and protons and/or the electric polarization field
determines the proton flux in the solar wind as well as the fate of
the coronal helium content.
---------------------------------------------------------
Title: Coupling of the Coronal Helium Abundance to the Solar Wind
Authors: Hansteen, Viggo H.; Leer, Egil; Holzer, Thomas E.
1994ApJ...428..843H Altcode:
Models of the transition region-corona-solar wind system are
investigated in order to find the coronal helium abundance and to
study the role played by coronal helium in controlling the solar wind
proton flux. The thermal force on alpha-particles in the transition
region sets the flow of helium into the corona. The frictional coupling
between alpha-particles and protons and/or the electric polarization
field determines the proton flux in the solar wind as well as the fate
of the coronal helium content. The models are constructed by solving
the time-dependent population and momentum equations for all species
of hydrogen and helium in an atmosphere with a given temperature
profile. Several temperature profiles are considered in order to very
the roles of frictional coupling and electric polarization field in the
solar wind, and the thermal force in the transition region. Steady-state
solutions are found for coronae with a hydrogen flux at 1 AU of 1.0
x 10<SUP>9</SUP>/cm<SUP>2</SUP>/sec or larger. For coronae with
lower hydrogen fluxes, the helium flux into the corona is larger
than the flux 'pulled out' by the solar wind protons, and solutions
with increasing coronal helium content are found. The timescale for
forming a helium-filled corona, that may allow for a steady outflow,
is long compared to the mixing time for the corona.
---------------------------------------------------------
Title: Acceleration and Heating of Two-Fluid Solar Wind by Alfven
Waves
Authors: Sandbaek, Ornulf; Leer, Egil
1994ApJ...423..500S Altcode:
Earlier model studies of solar wind driven by thermal pressure
and Alfven waves have shown that wave amplitudes of 20-30 km/s at
the coronal base are sufficient to accelerate the flow to the high
speeds observed in quasi-steady streams emanating from large coronal
holes. We focus on the energy balance in the proton gas and show that
heat conduction from the region where the waves are dissipated may
play an important role in determining the proton temperature at the
orbit of Earth. In models with 'classical' heat conduction we find
a correlation between high flow speed, high proton temperature, and
low electron temperature at 1 AU. The effect of wave heating on the
development of anisotropies in the solar wind proton gas pressure is
also investigated in this study.
---------------------------------------------------------
Title: Neutral Hydrogen in the Solar Wind Acceleration Region
Authors: Olsen, Espen Lyngdal; Leer, Egil; Holzer, Thomas E.
1994ApJ...420..913O Altcode:
Observation of solar Ly alpha radiation scattered by coronal neutral
hydrogen atoms can be used to investigate the acceleration region of the
solar wind. In this paper we focus on the use of these observations to
study Alfven waves, which can accelerate the solar wind plasma to flow
speeds observed in high-speed streams if their amplitude at the coronal
base is 20 km/s or larger. The wave amplitude is then larger than the
proton thermal speed in the outer corona, so that the mean proton speed
(averaged over a wave period) is significantly larger than the proton
thermal speed. For low-frequency wave the hydrogen atoms follow the
proton motion in the waves, while for higher frequencies the protons
move relative to the neutrals. Nevertheless, in the higher frequency
case, the rates for charge exchange and recombination are high enough
to broaden the velocity distribution function of neutral hydrogen. Both
the wave motion of the hydrogen atoms in low-frequency Alfven waves
and the 'heating' by higher frequency waves lead to a broadening of
the scattered solar Ly alpha line. For coronal base amplitudes of 20
km/s, the line broadening increases with heliocentric distance beyond
4-5 solar radii.
---------------------------------------------------------
Title: Diffusion Effects on the Helium Abundance of the Solar
Transition Region and Corona
Authors: Hansteen, Viggo H.; Holzer, Thomas E.; Leer, Egil
1993ApJ...402..334H Altcode:
The diffusion of helium in the solar transition region is
studied by solving the mass and momentum conservation equations
for a hydrogen-helium plasma given a representative temperature
profile. Steady state solutions show that two distinct atmospheres
may result. In cases where the thermal force on alpha-particles is
balanced by the partial pressure gradient force, helium is the dominant
coronal species. On the other hand, if it is the frictional force
between protons and alpha-particles which balances the thermal force on
alpha-particles then hydrogen is the major coronal component. In order
to explore which of these solutions are attainable within reasonable
time scales, the time-dependent equations are solved, starting from
an initial state with a uniform helium abundance of 10 percent. The
atmosphere as a whole is close to hydrostatic equilibrium, but due the
thermal forces the individual elements are not. This force inbalance
leads to a differential flow between species. It is found that this
differential flow leads to a significant enhancement of the coronal
helium abundance. Even for the relatively shallow temperature gradient
used the helium abundance in the lower corona increases to 30 percent
over a 24 hr period.
---------------------------------------------------------
Title: Alfvén wave broadening of the scattered solar Ly-α line.
Authors: Olsen, E. L.; Leer, E.
1993wpst.conf...83O Altcode:
The authors study the effects of Alfvén waves from the sun on an
electron-proton solar wind and the density, motion, and temperature
of the neutral hydrogen gas in this background. The flow parameters
are used to compute the width and intensity of the scattered solar
Ly-α line. The authors find that the density of neutral hydrogen in
the corona and inner solar wind is determined by the local balance
between ionization and recombination. Both, high and low frequency
Alfvén waves, may cause broadening of the scattered solar Ly-α line.
---------------------------------------------------------
Title: A Parameter Study of the Two-Fluid Solar Wind
Authors: Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.
1992ApJ...400..362S Altcode:
A two-fluid model of the solar wind was introduced by Sturrock and
Hartle (1966) and Hartle and Sturrock (1968). In these studies the
proton energy equation was integrated neglecting the heat conductive
term. Later several authors solved the equations for the two-fluid
solar wind model keeping the proton heat conductive term. Methods
where the equations are integrated simultaneously outward and inward
from the critical point were used. The equations were also integrated
inward from a large heliocentric distance. These methods have been
applied to cases with low coronal base electron densities and high
base temperatures. In this paper we present a method of integrating
the two-fluid solar wind equations using an iteration procedure where
the equations are integrated separately and the proton flux is kept
constant during the integrations. The technique is applicable for a
wide range of coronal base densities and temperatures. The method is
used to carry out a parameter study of the two-fluid solar wind.
---------------------------------------------------------
Title: Solar wind from a corona with a large helium abundance
Authors: Leer, Egil; Holzer, Thomas E.; Shoub, Edward C.
1992JGR....97.8183L Altcode:
Observations of quasi-steady high-speed solar wind streams show
that the proton mass flux density at 1 AU is remarkably constant,
varying by less than 10% over long time periods. The observations are
problematic, for simple theoretical models predict that the proton mass
flux density is a sensitive function of the coronal base temperature,
which is not expected to be unvarying to the degree required by the
observations. In this paper we investigate the possibility that the
presence of alpha particles in the coronal base region can reduce the
sensitivity of the proton mass flux to base temperature. The equations
of mass and momentum conservation are solved for electrons, protons,
and alpha particles using a variety of assumed temperature profiles
for each species. A wide range of base conditions are considered. We
find that for an alpha particle to proton density ratio at the base
as small as 10%, alpha particles can reduce the sensitivity of the
proton mass flux density to variations in the base temperature. We
also study the effects of enhanced collisional coupling and of Alfvén
waves on the flux of protons and alpha particles. As an aid to future
observational determination of the alpha particle density in the corona,
we present calculations of the intensities of the resonantly scattered
lines HeII λ304 and HI λ1216 for selected models.
---------------------------------------------------------
Title: Adiabatic Cooling of Solar Wind Electrons
Authors: Sandbaek, Ornulf; Leer, Egil
1992JGR....97.1571S Altcode:
In thermally driven winds emanating from regions in the solar corona
with base electron densities of n<SUB>0</SUB>>=10<SUP>8</SUP>
cm<SUP>-3</SUP>, a substantial fraction of the heat conductive flux
from the base is transferred into flow energy by the pressure gradient
force. The adiabatic cooling of the electrons causes the electron
temperature profile to fall off more rapidly than in heat conduction
dominated flows. Alfvén waves of solar origin, accelerating the
basically thermally driven solar wind, lead to an increased mass flux
and enhanced adiabatic cooling. The reduction in electron temperature
may be significant also in the subsonic region of the flow and lead to
a moderate increase of solar wind mass flux with increasing Alfvén
wave amplitude. In the solar wind model presented here the Alfvén
wave energy flux per unit mass is larger than in models where the
temperature in the subsonic flow is not reduced by the wave, and
consequently the asymptotic flow speed is higher.
---------------------------------------------------------
Title: A two-fluid model of the solar wind
Authors: Sandbaek, O.; Leer, E.; Holzer, T. E.
1992sws..coll...95S Altcode:
A method is presented for the integration of the two-fluid
solar-wind equations which is applicable to a wide variety of coronal
base densities and temperatures. The method involves proton heat
conduction, and may be applied to coronal base conditions for which
subsonic-supersonic solar wind solutions exist.
---------------------------------------------------------
Title: Coronal holes and the solar wind
Authors: Leer, E.
1992HiA.....9..663L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Magnetic reconnection in physics astrophysics: Summary of
the workshop.
Authors: Leer, E.
1992mrpa.work..207L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The solar wind mass flux problem.
Authors: Leer, E.; Holzer, T. E.
1991AnGeo...9..196L Altcode: 1991AnG.....9..196L
The variation of the proton flux with coronal temperature and density
in thermally driven solar wind models is discussed. It is shown that
the rapid increase of the proton flux with increasing temperature can
be reduced by adiabatic cooling of the expanding plasma. A significant
coronal helium abundance can also act as a "regulator" for the solar
wind proton flux.
---------------------------------------------------------
Title: Solar wind models
Authors: Leer, Egil; Sandbaek, Ornulf
1991AdSpR..11a.197L Altcode: 1991AdSpR..11..197L
Our understanding of the solar wind is based upon Parker's description
of a thermally driven subsonic - supersonic outflow from a fully
ionized electron-proton corona. The basic physical processes of
thermally driven solar wind models are discussed. We also study the
effect of alpha particles in the corona on the solar wind proton flux,
and further discuss the acceleration of the solar wind by Alfvén waves.
---------------------------------------------------------
Title: Models of the solar wind and similar types of flow.
Authors: Leer, E.
1991cwlt.conf..139L Altcode:
Our current understanding of the solar wind and other types of flow is
based upon Parker's theoretical model of an electron-proton solar wind
(Parker, 1958). The electric field plays an important role for the
dynamics of the electron-proton solar wind as well as in winds with
several types of ions. The author discusses the role of the electric
field in the solar wind and the polar wind, and shows how α-particles
in the solar corona moderate variations in the solar wind proton flux
with changing coronal conditions by exerting a collisional drag on
the protons and modifying the electric field in the subsonic solar
wind region.
---------------------------------------------------------
Title: Diagnostics of solar oscillation observations. Proceedings.
Authors: Maltby, P.; Leer, E.
1991dsoo.conf.....M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Coronae and winds in late-type stars. Proceedings.
Authors: Leer, E.; Maltby, P.
1991cwlt.conf.....L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Standing Shocks in the Inner Solar Wind
Authors: Leer, Egil; Holzer, Thomas E.
1990ApJ...358..680L Altcode:
It has been pointed out by several authors that the equations describing
rapidly diverging flow in the solar wind and in related astrophysical
systems allow for solutions with standing shocks in the acceleration
region of the flow. The range of plasma and flow-geometry parameters
that allow for such solutions are investigated. It is shown that, for
reasonable geometries, shocks can occur only for a very narrow range
of flow parameters in the case of the solar wind. Similar results can
be expected for related astrophysical systems.
---------------------------------------------------------
Title: Flow of oxygen ions in the solar wind acceleration region
Authors: Esser, Ruth; Leer, Egil
1990JGR....9510269E Altcode:
A solar wind model with protons, electrons, OVII and OVI ions is
studied. It is found that ionization and recombination processes
lead to an approximately constant density ratio of the oxygen states
(n<SUB>OVI</SUB>/n<SUB>OVII</SUB>~const<<1) in the solar wind
acceleration region. Although ionization and recombination have a
significant effect on the flow speed of the OVI ions, these processes
are not fast enough to bring the speed of OVI up to the flow speed of
the OVII ions.
---------------------------------------------------------
Title: Propagation of magnetohydrodynamic (MHD) waves in the solar
transition region and corona.
Authors: Leer, E.; Hansteen, V.
1990ppst.conf...81L Altcode:
The propagation of MHD waves in the solar transition region and the
corona is discussed. It is shown that the non-compressive Alfvén mode
is the best candidate for energy transport into the corona and in the
solar wind.
---------------------------------------------------------
Title: Physical processes in the solar transition-region and
corona. Proceedings.
Authors: Maltby, P.; Leer, E.
1990ppst.conf.....M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Mini-Workshop on Flux Tubes in the Solar Atmosphere, held
June 19-21, 1989, in Oslo, Norway
Authors: Leer, E.; Maltby, P.
1989ftsa.conf.....L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Mass loss mechanisms for cool stars
Authors: Leer, E.
1988ASSL..143..297L Altcode: 1988acse.conf..297L
The discussion of mass loss mechanisms for cool stars is based upon
the understanding of thermally driven stellar winds. First the author
discusses Parker's thermally driven solar wind model, and considers
the effects of energy addition to the flow in the form of heat and
momentum. On the basis of this general discussion he examines a few
particular mechanisms to see if they can play a role in driving massive
winds from cool giants and supergiants.
---------------------------------------------------------
Title: Drawing inferences about solar wind acceleration from coronal
minor ion observations
Authors: Esser, Ruth; Holzer, Thomas E.; Leer, Egil
1987JGR....9213377E Altcode:
A parameter study is designed and carried out to illustrate the physical
effects that can be studied through analysis and interpretation of
coronal minor ion spectral line observations. It is shown that minor
ion line width, together with the coronal Lyα line width and coronal
white light observations, can yield important information concerning the
transport and dissipation of energy carried outward from the coronal
base by hydromagnetic waves. Although it is difficult to infer minor
ion velocities through the Doppler dimming technique, the application
of this technique using both radiatively and collisionally excited
lines can provide constraints on the acceleration of coronal minor
ions. It is concluded tha the observation of coronal minor ion spectral
lines represents an important component of a concerted observational
approach to the solar wind acceleration problem. It must be emphasized,
however, that the measurement of line widths is the most important
coronal minor ion observation to obtain.
---------------------------------------------------------
Title: Solar corona and solar wind.
Authors: Leer, Egil
1987ESASP.275...11L Altcode: 1987sspp.symp...11L
Parker's thermally driven solar wind model is reviewed. The model can
describe the quiet solar wind quite well, but energy must be added
to the flow to drive high speed streams. It is argued that the Solar
and Heliospheric Observatory (SOHO) should be used to study possible
acceleration mechanisms of the solar wind, in particular acceleration
by magnetohydrodynamic (MHD) waves. In the inner corona a nonnegligible
wave energy flow introduces a substantial nonthermal broadening of
lines from heavy ions. Simultaneous observations of line widths and
of the corona density profile in the source region of the solar wind,
as well as the flow emanating from that region, should lead to a better
understanding of the energy balance in the solar wind.
---------------------------------------------------------
Title: Wave Acceleration Mechanisms for the Solar Wind (R)
Authors: Leer, E.
1987sowi.conf...89L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Viscosity in the solar wind
Authors: Holzer, T. E.; Leer, E.; Zhao, X. -P.
1986JGR....91.4126H Altcode:
The effects of viscosity on a steady, radial, spherically
symmetric solar wind with an embedded, non-radial magnetic field are
reconsidered. The correct expression for the classical viscosity in
the presence of a non-radial magnetic field is shown to be different
from that used in the past, and a means of describing non-classical
viscosity is presented. A physical interpretation of the classical and
nonclassical description of viscosity is provided, and observational
inferences are used in discussing the nature and degree of viscous
effects in the solar wind.
---------------------------------------------------------
Title: A two-fluid solar wind model with Alfven waves: parameter
study and application to observations
Authors: Esser, Ruth; Leer, Egil; Habbal, Shadia R.; Withbroe,
George L.
1986JGR....91.2950E Altcode:
The effects of Alfven waves from the inner corona on the solar wind
density profile, flow velocity and on the random motion of protons
are studied. Different base densities, temperatures, and wave velocity
amplitudes, as well as different flow geometries, are considered. The
model calculations are compared to simultaneous observations of the
electron density profile and the resonantly scattered Lyman alpha
line. Present observations, out to 4 solar radii, can be used to
place limits on the coronal base density and temperature, and put
an upper limit on the wave amplitude. It is pointed out that future
observations of the electron density and the Lyman alpha line, out
to larger heliocentric distances, and of lines from heavier elements,
should be used to place more stringent constraints on the amplitudes
of MHD waves in the corona.
---------------------------------------------------------
Title: Solar Wind and Coronal Holes
Authors: Leer, E.; Holzer, T. E.
1985ESASP.235....3L Altcode: 1985fmsh.work....3L; 1985shpp.rept....3L
The authors discuss the basic physics of the solar wind emanating from
coronal holes, and show that thermally driven solar wind models cannot
explain the high flow speeds. The effect of MHD waves on both the solar
wind and wind from late-type giants and supergiants is also considered.
---------------------------------------------------------
Title: Fast-mode magnetohydrodynamic waves in coronal holes and the
solar wind
Authors: Fla, T.; Habbal, S. R.; Holzer, T. E.; Leer, E.
1984ApJ...280..382F Altcode:
Fast-mode MHD waves in the solar corona can propagate in any direction
relative to the background magnetic field. In coronal holes, they
refract into regions of low Alfven speed and are relatively difficult
to damp. These characteristics lead to the possibility that fast-mode
waves transport energy from magnetically closed coronal regions into
coronal holes, that they are refracted into the central regions of
coronal holes, and that they deposit most of their energy in the
region of supersonic flow of high-speed solar wind streams emanating
from coronal holes. To investigate whether this possibility might be
realized and fast-mode waves might play a significant role in driving
high-speed streams, a parameter study is carried out to examine the
propagation and damping of fast-mode waves in various coronal hole
models. This study indicates a broad range of coronal hole parameters
for which fast-mode waves can play such a role and emphasizes the need
for an improved knowledge of large-scale coronal magnetic structure,
which is required before any firm conclusions can be drawn.
---------------------------------------------------------
Title: Alfven waves in stellar winds
Authors: Holzer, T. E.; Fla, T.; Leer, E.
1983ApJ...275..808H Altcode:
An analytic description of a stellar wind with waves which are undamped
in the region of subsonic flow is developed for a range of stellar
conditions, and numerical models with wave damping are applied to the
massive winds from cool, low gravity stars, in an examination of the
propagation and damping of Alfven waves in stellar winds. Attention is
also given to the effects of these waves on the wind mass loss rate,
asymptotic flow speed, and radial temperature profile. No evidence is
found for the belief that winds driven by Alfven waves from cool, low
gravity stars can exhibit both a very large mass loss rate and a very
small asymptotic flow speed. It is noted that the radial temperature
profile produced by invoking a constant damping length for the waves
is different from that produced by self-consistent description of
frictional wave damping for a wave frequency which is presumably
consistent with the chosen constant damping length.
---------------------------------------------------------
Title: Theory of solar wind acceleration.
Authors: Leer, E.
1983NASCP2280..147L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The structure of cosmic ray shocks
Authors: Axford, W. I.; Leer, E.; McKenzie, J. F.
1982A&A...111..317A Altcode:
The acceleration of cosmic rays by steady shock waves has been discussed
in brief reports by Leer et al. (1976) and Axford et al. (1977). This
paper presents a more extended version of this work. The energy
transfer and the structure of the shock wave is discussed in detail,
and it is shown that even for moderately strong shock waves most of
the upstream energy flux in the background gas is transferred to the
cosmic rays. This holds also when the upstream cosmic ray pressure is
very small. For an intermediate Mach-number regime the overall shock
structure is shown to consist of a smooth transition followed by a
gas shock (cf. Drury and Voelk, 1980).
---------------------------------------------------------
Title: Acceleration of the solar wind.
Authors: Leer, E.; Holzer, T. E.; Fla, T.
1982SSRv...33..161L Altcode:
In this review, we discuss critically recent research on the
acceleration of the solar wind, giving emphasis to high-speed solar
wind streams emanating from solar coronal holes. We first explain why
thermally driven wind models constrained by solar and interplanetary
observations encounter substantial difficulties in explaining high speed
streams. Then, through a general discussion of energy addition to the
solar wind above the coronal base, we indicate a possible resolution of
these difficulties. Finally, we consider the question of what role MHD
waves might play in transporting energy through the solar atmosphere
and depositing it in the solar wind, and we conclude by examining,
in a simple way, the specific mechanism of solar wind acceleration by
Alfvén waves and the related problem of accelerating massive stellar
winds with Alfvén waves.
---------------------------------------------------------
Title: Electron heating by fast mode magnetohydrodynamic waves in
the solar wind emanating from coronal holes
Authors: Habbal, S. R.; Leer, E.
1982ApJ...253..318H Altcode:
It is shown that fast mode magnetohydrodynamic waves, propagating
outwards from the sun in coronal hole regions, will dissipate primarily
through collisionless interaction with electrons rather than with
protons. This dissipation can lead to higher electron than proton
temperatures in the accelerating region of the solar wind, provided
the waves carry a sufficiently large energy flux.
---------------------------------------------------------
Title: Theory of Mass and Energy Flow in the Solar Wind
Authors: Holzer, T. E.; Leer, E.
1981sowi.conf...28H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Conductive solar wind models in rapidly diverging flow
geometries
Authors: Holzer, T. E.; Leer, E.
1980JGR....85.4665H Altcode:
A detailed parameter study of conductive models of the solar wind has
been carried out, extending the previous similar studies of Durney
(1972) and Durney and Hundhausen (1974) by considering collisionless
inhibition of thermal conduction, rapidly diverging flow geometries, and
the structure of solutions for the entire n<SUB>0</SUB>-T<SUB>0</SUB>
plane (n<SUB>0</SUB> and T<SUB>0</SUB> are the coronal base density
and temperature). Primary emphasis is placed on understanding the
complex effects of the physical processes operative in conductive
solar wind models. There are five points of particular interest that
have arisen from the study: (1) neither collisionless inhibition
of thermal conduction nor rapidly diverging flow geometries can
significantly increase the solar wind speed at 1 AU; (2) there exists
a firm upper limit on the coronal base temperature consistent with
observed values of the coronal base pressure and solar wind mass
flux density; (3) the principal effect of rapidly diverging flow
geometries is a decrease in the solar wind mass flux density at 1 AU
and an increase in the mass flux density at the coronal base; (4)
collisionless inhibition of thermal conduction can lead to a solar
wind flow speed that either increases or decreases with increasing
coronal base density (n<SUB>0</SUB>) and temperature (T<SUB>0</SUB>,
depending on the region of the n<SUB>0</SUB>-T<SUB>0</SUB> plane
considered; (5) there is a region of the n<SUB>0</SUB>-T<SUB>o</SUB>
plane at high coronal base densities where low-speed, high-mass-flux,
transonic solar wind flows exist-a region not previously considered.
---------------------------------------------------------
Title: Energy addition in the solar wind.
Authors: Leer, E.; Holzer, T. E.
1980JGR....85.4681L Altcode:
A general study of energy addition, energy loss, and energy
redistribution in the solar wind, for both spherically symmetric and
rapidly diverging flow geometries, is presented. It is found that
energy addition in the region of subsonic flow increases the solar
wind mass flux but either has little effect on (for heat addition) or
significantly reduces (for momentum addition) the solar wind flow speed
at 1 AU. In contrast, energy addition in the region of supersonic flow
has no effect on the solar wind mass flux but significantly increases
the flow speed at 1 AU. It is also found that both momentum loss in the
subsonic region and energy exchange (involving loss in the subsonic
region and gain in the supersonic region) can lead to an increase in
the asymptotic flow speed. This general study thus places certain
constraints on viable mechanisms for driving high-speed solar wind
streams and points to a number of specific, self-consistent studies
of such mechanisms that need to be carried out in the future.
---------------------------------------------------------
Title: Alfvén-wave acceleration of the solar wind.
Authors: Leer, E.; Fla, T.; Holzer, T. E.
1980NCimC...3..114L Altcode:
The increase in mass flux and energy flux from the sun is calculated
for an increasing Alfven-wave amplitude, in the lower corona and
fixed values for the coronal pressure, the coronal temperature and the
interplanetary magnetic field. The energy per mass and the flow speed
at the orbit of the earth increase with the wave amplitude and reach a
maximum for a wave amplitude of approximately 50 km/sec. For reasonable
values of the coronal pressure and temperature and of the magnetic
field, high-speed solar-wind streams can be driven by Alfven waves with
an amplitude approximately equal to 20-25 km/sec in the lower corona.
---------------------------------------------------------
Title: Plasma drift in the polar ionosphere.
Authors: Bratteng, O.; Leer, E.
1980FFV....42...37B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Heating of Coronal Loops by Fast-Mode Magnetohydrodynamic Waves
Authors: Habbal, Shadia Rifai; Leer, Egil; Holzer, Thomas E.
1979SoPh...64..287H Altcode:
A possible mechanism for the formation and heating of coronal loops
through the propagation and damping of fast mode waves is proposed
and studied in detail. Loop-like field structures are represented by
a dipole field with the point dipole at a given distance below the
solar surface. The density of the medium is determined by hydrostatic
equilibrium along the field lines in an isothermal atmosphere. The
fast mode waves propagating outward from the coronal base are refracted
into regions with a low Alfvén speed and suffer collisionless damping
when the gas pressure becomes comparable to the magnetic pressure. The
propagation and damping of these waves are studied for three different
cases: a uniform density at the coronal base, a density depletion
within a given flux tube, and a density enhancement within a given flux
tube. The fast mode waves are found to be important in the formation
and heating of the loops if the wave energy flux density is of the order
10<SUP>5</SUP> ergs cm<SUP>-2</SUP> s<SUP>-1</SUP> at the coronal base.
---------------------------------------------------------
Title: Constraints on the solar coronal temperature in regions of
open magnetic field.
Authors: Leer, E.; Holzer, T. E.
1979SoPh...63..143L Altcode:
It is shown that the simultaneous consideration of observed values
of the solar wind proton flux density at 1 AU and of the electron
pressure at the base of the solar corona leads to relatively strong
constraints on the coronal temperature in the region of subsonic solar
wind flow. The extreme upper limit on the mean coronal temperature
in the subsonic region is found to be about 2.6 × 10<SUP>6</SUP> K,
but this upper limit is reduced to about 2.0 × 10<SUP>6</SUP> K if
reasonable, rather than extreme, assumptions are made; the limit on
the maximum temperature is about 0.5 × 10<SUP>6</SUP> K greater than
the limit on the mean. It is also found that the same two observations
limit the rate of momentum addition possible in the region of subsonic
solar wind flow.
---------------------------------------------------------
Title: Discussion
Authors: Wentzel, D.; Leer, E.
1979phsp.coll..231W Altcode: 1979IAUCo..44..231W
No abstract at ADS
---------------------------------------------------------
Title: Heating of Coronal Loops by Fast Mode Mhd-Waves
Authors: Habbal, S. R.; Holzer, T. E.; Leer, E.
1979phsp.coll..228H Altcode: 1979phsp.conf..228H; 1979IAUCo..44..228H
This paper discusses the formation and heating of solar coronal loops
by fast mode MHD waves which, unlike Alfven waves, have an acoustic
component. These fast mode waves can carry a substantial energy flux
along the wave normal only in coronal regions with a strong magnetic
field. The propagation and damping of these waves in a two dimensional
solar atmosphere is considered. It is noted that the damping occurs
mainly in the region where beta = 2nkT/(B-squared/8pi) is larger than
0.05, and that most of the energy is transferred to the plasma in the
region where beta approximately equals 0.2. In this case the plasma
in the flux tube with a height approximately equal to 0.2R is heated
most, and the wave energy flux from the base deposits more energy
in this tube than is lost by radiation and heat conduction at the
footpoints. Therefore, density and temperature perturbations across the
field lines will develop and 'loops' may be formed. Heating mechanisms
of the surrounding plasma in both large density and low density loops
are then described.
---------------------------------------------------------
Title: Group velocity of whistlers in a two-ion plasma
Authors: Leer, E.; Johansen, K. M.; Albrigtsen, R.
1978JGR....83.3125L Altcode:
Computations of goup velocity of whistlers in a two-ion plasma show that
a quasi-longitudinal (QL) right-handed polarized wave (electron wave)
has a minimum group velocity at the so-called crossover frequency;
a QL left-handed polarized wave has a maximum group velocity at the
ion hybrid frequency. In an oxygen/hydrogen plasma this minimum occurs
only for almost perpendicular waves, whereas in a helium/hydrogen
plasma it occurs also for waves propagating off perpendicular to the
magnetic field. We also find that a small concentration of helium in
a hydrogen plasma introduces a 'stop band' for quasi-transverse waves
with frequencies just above the helium gyrofrequency. The theoretical
results are used to interpret satellite observations of quasi-tranverse
low-frequency whistlers.
---------------------------------------------------------
Title: Oscillating echoes from the polar E layer
Authors: Bratteng, O.; Leer, E.
1978JGR....83.1162B Altcode:
Radio waves with a freuency of 4 MHz transmitted vertically into
the polar ionosphere and reflected in the E layer occasionally show
very stable oscillations in intensity. This phenomenon, which occurs
mainly in the evening sector under quiet conditions, has been studied
at Ny-Ălesund, Spitzbergen, by using a 4-MHz transmitter and four
spaced receiving antennas. The observed oscillations can be explained
as interference of waves reflected from a pair of enhanced ionization
regions some 30 km apart and moving with a horizontal velocity of
the order of 100 m/s. The low drift velocity is consistent with low
magnetic activity.
---------------------------------------------------------
Title: Acceleration of cosmic rays by shock waves.
Authors: Axford, W. I.; Leer, E.; Skadron, G.
1978cosm.conf..125A Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Stimulated Brillouin scattering in the ionosphere
Authors: Dysthe, K. B.; Leer, E.; Trulsen, J.; Stenflo, L.
1977JGR....82..717D Altcode:
We discuss the possibility of obtaining stimulated backscattering from
the ionosphere. It is found that stimulated Brillouin scattering off
ion modes and quasi modes may be possible with the signal power that
is planned for the Eiscat radar.
---------------------------------------------------------
Title: The Acceleration of Cosmic Rays by Shock Waves
Authors: Axford, W. I.; Leer, E.; Skadron, G.
1977ICRC...11..132A Altcode: 1977ICRC...15k.132A; 1978ICRC...11..132A
The possibility of cosmic ray acceleration by shock waves has been
considered by many workers during the last twenty years on the
basis of various assumptions on the exact nature of the acceleration
mechanism. The paper examines the question further on the assumption
that the cosmic rays are constrained to move diffusively with
respect to the background medium, and finds that acceleration is very
efficient. The acceleration of cosmic rays in flows involving shocks
and other compressional waves is considered in terms of one-dimensional
steady flows and the diffusion approximation. The results suggest that
very substantial energy conversion can occur.
---------------------------------------------------------
Title: Acceleration of Cosmic Rays at Shock Fronts (Abstract)
Authors: Axford, W. I.; Leer, E.; Skadron, G.
1977ICRC....2..273A Altcode: 1977ICRC...15b.273A
No abstract at ADS
---------------------------------------------------------
Title: Electrostatic waves in the ionosphere.
Authors: Leer, E.
1977rpap.conf...55L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Group velocity of whistlers
Authors: Johansen, K. M.; Leer, E.
1976JGR....81.4503J Altcode:
The dispersion relation of waves in a cold magnetoplasma
can be given in the form ∑<SUB>ı=0</SUB><SUP>p</SUP>
A<SUB>i</SUB>(k)ω<SUP>ı</SUP> ≡ 0, where ω is the frequency
and the coefficients A<SUB>ı</SUB> are functions of the wave vector
k. The group velocity V<SUB>g</SUB> can be expressed as V<SUB>g</SUB> =
-∑<SUB>i=0</SUB><SUP>p</SUP>(∂A<SUB>i</SUB>/∂k)ω<SUP>ı</SUP>/∑<SUB>i=0</SUB><SUP>p</SUP>iA<SUB>i</SUB>ω<SUP>ı-1</SUP>.
This equation is used for numerical studies of the slow and fast mode
propagation in a one-ion plasma. The slow mode is always guided by the
magnetostatic field B<SUB>0</SUB>, whereas the fast mode is guided only
for frequencies in the ‘whistler band.’ The ‘nose frequency’
for the whistlers decreases as the angle θ = ∠(k, B<SUB>0</SUB>)
increases.
---------------------------------------------------------
Title: Parametric excitation of standing electromagnetic waves.
Authors: Leer, E.
1976PhyS...13...47L Altcode:
The threshold for parametric excitation of standing electromagnetic
waves by a standing electromagnetic pump wave with the same frequency
is derived. A homogeneous plasma is considered, and a method based
on energy balance is used. The threshold is found to depend on the
amplitude of the electron motion in the pump wave and on the angle
between the direction of this motion and the electric component of the
excited wave. Waves in the same mode as the pump wave can be excited
more easily than waves in the opposite mode. This instability may be
important in ionospheric-modification experiments.
---------------------------------------------------------
Title: Plasma drift in the polar ionosphere, Ny Alesund, 6 - 10
September 1974.
Authors: Leer, E.; Bratteng, O.
1976PhyNr...8..129L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Heated Solar Atmosphere: A One-Fluid Model
Authors: Leer, Egil
1974SoPh...35..467L Altcode:
A one-fluid model of the solar atmosphere is considered. The corona
is heated by waves propagating out from the Sun, and profiles for
temperature, flow speed and number density are obtained. For a
relatively quiet Sun the inwards heat flux in the inner corona is
constant in T ≲ 5-6 × 10<SUP>5</SUP> K and the temperature maximum
is reached for r — R<SUB>⊙</SUB> = 0.4 — 0.5 R<SUB>⊙</SUB>
where R<SUB>⊙</SUB> is the solar radius. The number density in the
inner corona decreases with an increasing particle flux.
---------------------------------------------------------
Title: Solar Wind Heating Beyond 1 AU
Authors: Holzer, Thomas E.; Leer, Egil
1973Ap&SS..24..335H Altcode:
The effect of an interplanetary atomic hydrogen gas on solar
wind proton, electron and α-particle temperatures beyond 1 AU is
considered. It is shown that the proton temperature (and probably
also the α-particle temperature) reaches a minimum between 2 AU and
4 AU, depending on values chosen for solar wind and interstellar gas
parameters. Heating of the electron gas depends primarily on the thermal
coupling of the protons and electrons. For strong coupling (when T
<SUB> p </SUB> ≳T <SUB> e </SUB>), the electron temperature reaches a
minimum between 4 AU and 8 AU, but for weak coupling (Coulomb collisions
only), the electron temperature continues to decrease throughout the
inner solar system. A spacecraft travelling to Jupiter should be able
to observe the heating effect of the solar wind-interplanetary hydrogen
interaction, and from such observations it may be possible of infer
some properties of the interstellar neutral gas.
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Title: A Two-Fluid Solar Wind Model with Anisotropic Proton
Temperature
Authors: Leer, E.; Axford, W. I.
1972SoPh...23..238L Altcode:
A two-fluid model of the solar wind with anisotropic proton temperature
and allowing for extended coronal proton-heating is considered for the
case of a purely radial and of a spiral magnetic field. Proton-proton
Coulomb-collisions together with a spiral interplanetary magnetic
field are found to be sufficient to reduce the thermal anisotropy in
the proton gas to a value in agreement with observations. Reasonable
values are obtained for the flow-velocity, number density and the
protontemperature near the orbit of the Earth.
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Title: Collisionless solar wind protons: A comparison of kinetic
and hydrodynamic descriptions
Authors: Leer, Egil; Holzer, Thomas E.
1972JGR....77.4035L Altcode:
Kinetic and hydrodynamic descriptions of a collisionless solar wind
proton gas are compared. Heat conduction and viscosity are neglected
in the hydrodynamic formulation but are automatically included in the
kinetic formulation. The fact that the results of the two models are
very nearly the same indicates that heat conduction and viscosity are
not important in the solar wind proton gas beyond approximately 0.1
AU. It is concluded that the hydrodynamic equations provide a valid
description of the collisionless solar wind protons and, hence, that
future models of the quiet solar wind should be based on a hydrodynamic
formulation.
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Title: Galactic cosmic rays in interplanetary space.
Authors: Leer, E.
1972PhyNr...6..193L Altcode:
No abstract at ADS
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Title: Ion-reflection of downward-propagating whistlers at low
latitudes
Authors: Egeland, A.; Leer, E.; Holtet, J. A.
1970JATP...32.1983E Altcode:
The real time a.c. (10-1500 Hz) electric field measurements, received
on 2 May 1967 when the Satellite OV1-10 (altitude about 700 km)
moved from 0° to 20° N geomagnetic latitude, are presented. Several
long fractional hop whistlers, strongly influenced by ions, were
observed. The main findings are: For downward propagating whistlers a
frequency band is reflected. The width and the location of this band
are latitude dependent. Whistler-pairs separated in time by 0.15 sec
and with a 15 per cent difference in dispersion were observed. These
pairs are probably generated by the same lightning stroke and propagate
along different ray paths. Whistlers propagating on higher L-shells
seem to be less connected to the magnetic fieldlines than those on
lower L-shells. Resonance damping may be important for a limited
frequency band.
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Title: Low latitude subprotonospheric and ion cyclotron whistlers
generated by the same lightning discharge
Authors: Egeland, A.; Leer, E.
1970P&SS...18D....E Altcode:
No abstract at ADS
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Title: Low latitude subprotonospheric and ion cyclotron whistlers
generated by the same lightning discharge
Authors: Egeland, A.; Leer, E.
1970P&SS...18.1848E Altcode:
No abstract at ADS
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Title: Exact motion of a charged particle in an arbitrary plane wave
propagating along a constant homogeneous magnetic field.
Authors: Leer, E.
1969PhFl...12.2206L Altcode:
The classical relativistic equations of motion are solved for a
charged particle moving in an arbitrary plane electromagnetic wave
propagating along a constant homogenous magnetic field. The solutions
are expressed by (proper time) evolution tensor factors, operating upon
the initial value quantities. The calculations are performed in terms
of tensor-component matrices. Elliptically polarized waves are then
considered. At resonance frequency an expression for the increase in
the kinetic energy is obtained. This expression shows that the kinetic
energy increases indefinitely, and that the energy exchange is caused
by the field component rotating in the same direction as the particle.
