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NASA NTRS1971

The solar envelope

Processes which occur within the region between approximately 2 solar radii and 25 solar radii, which is called the solar envelope and the effect on the solar wind as seen at 1 AU are discussed. In the envelope the wind speed becomes supersonic and super-Alfvenic, the magnetic energy density is larger than the flow energy density, and the magnetic energy density is much larger than the thermal energy density. Large azimuthal gradients in the bulk speed are expected in the envelope, but the stream interactions near the outer edge of the envelope are probably relatively small. Cosmic ray observations suggest the presence of hydromagnetic waves in the envelope. The collisionless damping of such waves could heat protons out to approximately 25 solar radii and thereby cause an increase in V and T sub p consistent with the observed T sub p -V relation. A mechanism which couples protons and electrons would also heat and accelerate the wind. Alfven waves can accelerate the wind in the envelope without necessarily causing heating of protons; the Lorentz force might have a similar effect.

Burlaga, L. F.↗

NASA NTRS1972

Model development of supersonic trough wind with shocks

The time dependent one dimensional hydrodynamic equations describe the evolution of the thermal plasma flow along closed magnetic field lines outside of the plasmasphere. The convection of the supersonic polar wind onto a closed fieldline results in the assumed formation of collisionless plasma shocks. These shocks move earthward as the field line with its frozen-in plasma remains fixed or contracts with time to smaller L coordinates. The high equatorial plasma temperature (of the order of electron volts) produced by the shock process decreases with time if the flow is isothermal but it will increase if the contraction is under adiabatic conditions. Assuming adiabaticity a peak in the temperature forms at the equator in conjunction with a depression in the ion density. After an initial contraction, if the flux tube drifts to higher L coordinates the direction of the shock motion can be reversed so that the supersonic region will expand along the field line towards the state characterizing the supersonic polar wind. A rapid expansion will lower the equatorial density while the temperature decreases with time under adiabatic but not isothermal conditions.

Grebowsky, J. M.↗

NASA NTRS1972

Computer experiments on the structure and dynamics of spiral galaxies

The evolution of an initially balanced rotating disk of stars with an initial velocity dispersion given by Toomre's local criterion was investigated by means of a computer model for isolated disks of stars. It was found that the disk is unstable against very large scale modes. A stable axisymmetric disk with a velocity dispersion much larger than that given by Toomre's criterion was generated. The final mass distribution for the disk gives a high density central core and a disk population of stars that is closely approximated by an exponential variation. Various methods and rates of cooling the hot axisymmetric disks were investigated. It was found that the cooling resulted in the development of two-arm spiral structures which persisted as long as cooling continued. An experiment was performed to induce spiral structure in a galaxy by means of the close passage of a companion galaxy. Parameters similar to those expected for M51 and its companion were used. It was found that because of the high velocity dispersion of the disturbed disk galaxy, only a weak two-arm spiral structure appeared. The evolution of a uniformly rotating disk galaxy which is a stationary solution of the collisionless Boltzmann equation was investigated for various values of the initial rms velocity dispersion. It was found that the disk becomes stable at a value of the velocity dispersion predicted by theory.

Hohl, F.↗

NASA NTRS1972

Resonance, particle trapping, and Landau damping in finite amplitude obliquely propagating waves

The equations of motion for a particle in resonance with a small finite amplitude wave are solved approximately, using secularity free perturbation theory. The wave propagates at an arbitrary angle to a uniform background magnetic field in an infinite collisionless plasma. The wave fields include a longitudinal electrostatic component and elliptically polarized transverse electric and magnetic components. The trajectories of trapped and resonant untrapped particles are described, for each of the possible wave-particle resonances. These trajectories are used to construct an estimate of the nonlinear time dependent Landau damping rate of the wave.

Palmadesso, P. J.↗

NASA NTRS1970

Turbulence structure of finite-beta perpendicular fast shocks

In a finite-beta plasma ion cyclotron, radius dispersion which forms a trailing wave train for a perpendicular fast shock is examined. Collisionless dissipation is provided by the three wave decay of the wave train into very oblique fast and parallel Alfven waves. Particle thermalization results from Landau damping of oblique fast wave turbulence. The shock damping length to three wave decay is many ion cyclotron radii. Undamped Alfven turbulence should persist far downstream from the shock.

Coroniti, F. V.↗

NASA NTRS1971

Theoretical constraints on the microscale fluctuations in the interplanetary medium.

Theoretical constraints on the character of microscale fluctuations in the solar wind are examined. The microfluctuations could be either ?discontinuities' or more smoothly varying structures. If the fluctuations are waves, they are probably mostly Alfv]en waves (or rotational discontinuities), and if they are stationary structures, they are tangential pressure balances (or tangential discontinuities). It is formally proved that a true analog of the small-amplitude MHD ?entropy wave' (or contact discontinuity) does not exist for collisionless plasmas.

Barnes, A.↗

NASA NTRS1971

Model for rotating and nonuniform planetary exospheres.

The model neutral exosphere with a uniformly rotating exobase is generalized by allowing variations in exobase density and temperature which characterize the thermosphere just below the base. The corresponding velocity distribution function, satisfying the collisionless Boltzmann equation, is constructed and used to form a general expression for the velocity moments. Resulting density profiles of rotating exospheres with nonuniform densities and temperatures on the exobase are compared with corresponding nonrotating exospheres. Density enhancements due to rotation are found to be greatest above regions of exobase density or temperature minima. Equatorial density enhancements of terrestrial hydrogen, resulting from rotation, are estimated to be 15%-17% at altitudes of 10-20 earth radii. Corresponding increases in terrestrial helium are 30%-50% on the equator at altitudes of 0.7 to 1 earth radii even when there is a polar density bulge in the barosphere.

Hartle, R. E.↗

NASA NTRS1971

Ion-wave current instabilities and anomalous resistivity.

A theory of ion-wave current instabilities which takes into account, in a self-consistent manner, the inhomogeneities generated by field-aligned currents in a collisionless plasma is presented. Diamagnetic current associated with the current-produced density gradient is included in the distribution. The theory predicts that for a given frequency, the current threshold for ion-wave current instabilities is, in general, much below the threshold of ion acoustic instability in a uniform plasma as given by Fried and Gould. The current threshold is essentially zero in the limit when the ion Landau damping effect is negligible, or equivalently, the ion-wave current instabilities are absolute if there are no limitations on the wavelength. This is true even in the absence of externally applied density gradients in contrast to Kadomtsev's drift-wave results. For dimensions of interest in laboratory plasmas, the predicted linear growth rate increases with increasing longitudinal wavelength and with decreasing wavelength parallel to the diamagnetic current. Under the conditions of an experiment on anomalous resistivity (the dimensions but not the geometry of the machine have been considered), there is good agreement between the predicted onset of ion-wave current instabilities and the experimental data on the onset of anomalous resistivity.

Kan, J. R.↗

NASA NTRS1971

Ion-acoustic instability of a two-temperature, collisional, fully-ionized plasma.

From a perturbation analysis of the fluid equations for a homogeneous unmagnetized plasma, it is shown that long wavelength ion waves are unstable when the electron temperature exceeds the ion temperature. Thus, the temperature difference can drive a resistive-type ion wave instability in a plasma which on a collisionless basis is stable. The additional destabilizing effect of a current is also investigated.

Rognlien, T. D.↗

NASA NTRS1971

Integration methods where force is obtained from the smoothed gravitational field.

Discussion of the possibilities to study the dynamics of collisionless stellar systems by condensing the large number of stars that such systems may contain into a smaller number of superparticles and using numerical or computer models to perform computer experiments simulating Vlasov phenomena by following the simultaneous motion of a large number of superparticles. A computer model for disks of stars and a two-dimensional rod model are considered.

Hohl, F.↗

NASA NTRS1972

Measurement of the wave-normal vector of proton whistlers on Ogo 6.

Description of the first experimental determination of the wave-normal vector of proton whistlers in the ionosphere. Between the crossover frequency and the proton gyrofrequency, both right-hand and left-hand modes of propagation can occur for upgoing waves. Theoretically, the amount of energy in the respective modes depends on theta, the angle between the wave normal and the magnetic field. For proton whistlers with only left-hand mode energy between the crossover and proton gyrofrequency, theta ranged from 36 to 51 deg. For proton whistlers with strong right-hand and left-hand mode signals, theta ranged from 24 to 29 deg. The result is in good agreement with Wang's (1971) collisionless mode-coupling model. The angle between the wave normal and the vertical is found to increase with increasing altitude.

Chan, K. W.↗

NASA NTRS1971

Hydromagnetic waves and discontinuities in the solar wind.

Development of a theory of hydromagnetic waves and discontinuities which is appropriate for the solar wind. The experimental evidence for the various waves, discontinuities, and some of the instabilities which are predicted by this theory is reviewed. Nearly all of the discontinuities given by the theory are shown to exist in the solar wind. These include tangential discontinuities, forward and reverse fast and slow shocks, perpendicular shocks, and Alfven shocks. Parallel shocks and contact discontinuities have not been found. A number of special cases are considered which show the basic physical properties of hydromagnetic waves in an anisotropic, multifluid, collisionless plasma. A treatment of discontinuities is presented which most resembles those of Chao (1970) and Hudson (1970). On the basis of the experimental results reviewed it is concluded that hydromagnetic theory is applicable to the solar wind.

Burlaga, L. F.↗

NASA NTRS1972

Interaction of the solar wind with the moon.

During its orbit about the earth, the moon is located in the interplanetary medium or in the geomagnetosheath-geomagnetotail formed by the solar wind interaction with earth. In the tail, no evidence is found for a lunar magnetic field. In the interplanetary medium, no evidence exists for a bow shock or a trailing shock, although a well defined plasma wake region is observed in the anti-solar wind direction. The moon absorbs the solar wind plasma that strikes its surface and creates a void region or cavity in the flow. The observed lunar Mach cone gives evidence for the anisotropic propagation of waves in the magnetized collisionless warm plasma of the solar wind. The transmission of microstructural discontinuities in the interplanetary medium past the moon shows little distortion, indicating a low effective electrical conductivity of the lunar body. Fluctuations of the interplanetary magnetic field upstream from the plasma wake are stimulated by the disturbed conditions in that region. The moon behaves like a cold, nonmagnetic, fully absorbing dielectric sphere in the solar wind flow.

Ness, N. F.↗

NASA NTRS1972

Stability of a steady, large amplitude whistler wave.

Study of the behavior of weak electrostatic waves in a collisionless magnetoplasma supporting a steady large amplitude whistler wave. All waves are assumed to propagate parallel to a uniform background magnetic field B sub zero. In the presence of the whistler wave fields each particle executes an oscillatory motion parallel to B sub zero, in addition to a translation along B sub zero and transverse motions. This oscillation causes the Landau resonance to be replaced by a series of new resonances between particles and the electrostatic modes. A distribution function for the perturbed plasma is constructed by solving the Vlasov equation, linearized in the electrostatic wave amplitudes. A dispersion relation is obtained and solved approximately for the growth/damping rate of the perturbations. Growing electrostatic modes are found to be approximately uncoupled. Trapped particles have a strong influence on the stability of the system.

Palmadesso, P. J.↗

NASA NTRS1972

Area influences and floating potentials in Langmuir probe measurements.

Analysis of the influence of a relatively small reference electrode on a Langmuir probe measurement of plasma density and temperature. The analysis employs the collisionless theory of Laframboise for spherical and cylindrical probes and in a completely general way includes a broad range of electron densities and temperatures, as well as all possible values of ion mass and multiplicity of ionization. It is shown that a ratio alpha of reference-electrode area to probe area of 10,000 will guarantee no distortion of the measurement as a result of a shifting reference-electrode potential. It is further shown that the constraint on alpha can be relaxed by approximately two orders of magnitude when the charge-normalized ion mass is decreased from 200 to 1 amu and the ratio of reference-electrode radius to Debye length is decreased from 100 to 0. An additional result of the analysis is the dependence of a probe's floating potential on its geometry and radius, as well as on the properties of the plasma. A discussion of the latter result reveals in a striking manner the significant differences between the ion-current responses of spherical and cylindrical probes.

Szuszczewicz, E. P.↗

NASA NTRS1971

Ion acoustic waves in a multi-ion plasma.

An exact treatment of the multispecies ion acoustic dispersion relation is given for an argon/helium plasma. Phase velocity and damping are obtained as a function of ion-electron temperature ratio and relative densities of the two species. There are two important modes in the plasma, with quite different phase velocities, which are referred to as principal heavy ion mode and principal light ion mode. Which of these is dominant depends on the relative densities of the two components, but, in general, the light ion mode becomes important for surprisingly small light ion contamination. Approximate analytic expressions are derived from damping rates and phase velocities and their domains of validity are investigated. Relevance of the results for the investigation of collisionless shocks is discussed.

Fried, B. D.↗

NASA NTRS1972

Observation of nonuniform structure of the earth's bow shock correlated with interplanetary field orientation.

Explorer 33 and 35 magnetometers, on the western and eastern flanks of the earth's bow shock, respectively, observed the boundary concurrently between 0130 and 0430 UT, Oct. 30, 1968. Contrasting shock structures were recorded. Explorer 35 saw a quiet abrupt shock, whereas Explorer 33 saw an irregular noisy boundary with much upstream wave activity. The interplanetary field was roughly in the average archimedean spiral angle and was therefore approximately tangent to the shock at Explorer 35 and normal to the shock at Explorer 33. Gross motions and variable tilting of the aberrated shock probably contributed to the peculiar sequence of shock crossings at the two spacecraft. The observations support a model of the shock in which perpendicular and oblique collisionless structures coexist and form a nonuniform magnetosheath outer boundary.

Greenstadt, E. W.↗

NASA NTRS1972

The impedance characteristic of a spherical probe in an isotropic plasma.

Experimental investigation of the impedance characteristic of a spherical plasma probe for a quantitative assessment of theoretical work, and of hydrodynamic or fluid theory in particular. A stable, low-temperature (about 500K) plasma was produced in nitrogen by a cold-cathode discharge, with a plasma frequency of the order of 15 MHz and with an electron collision frequency in the range from one to ten million per sec. Hydrodynamic probe theory was tested against the experimental results for the specific cases corresponding to the probe at floating potential and at space potential. Good agreement was obtained for both the real and imaginary parts. The real part of the impedance shows a peak near the plasma frequency, a small shift being explicable in terms of realistic sheath profiles. Electron density can thus be deduced rather accurately, and electron temperature approximately, on the basis of hydrodynamic theory. Accurate values of the electron-neutral collision frequency were also obtained for plasmas where the collision frequency was larger than 0.4 times the radian plasma frequency. At lower pressures the presence of collisionless or Landau damping was clearly established, and the more accurate kinetic theory is necessary to explain the experimental results.

Tarstrup, J.↗