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NASA NTRS1976

Theoretical investigations of plasma processes

System analyses are presented for electrically sustained, collision dominated plasma centrifuges, in which the plasma rotates under the influence of the Lorentz forces resulting from the interaction of the current density fields with an external magnetic field. It is shown that gas discharge centrifuges are technically feasible in which the plasma rotates at speeds up to 1 million cm/sec. The associated centrifugal forces produce a significant spatial isotope separation, which is somewhat perturbed in the viscous boundary layers at the centrifuge walls. The isotope separation effect is the more pronounced. The induced magnetic fields have negligible influence on the plasma rotation if the Hall coefficient is small. In the technical realization of collision dominated plasma centrifuges, a trade-off has to be made between power density and speeds of rotation. The diffusion of sputtered atoms to system surfaces of ion propulsion systems and the deposition of the atoms are treated theoretically by means of a simple model which permits an analytical solution. The problem leads to an inhomogeneous integral equation.

Wilhelm, H. E.↗

NASA NTRS1977

Geometrization of the Dirac theory of the electron

Using the concept of parallel displacement of a half vector, the Dirac equations are generally written in invariant form. The energy tensor is formed and both the macroscopic and quantum mechanic equations of motion are set up. The former have the usual form: divergence of the energy tensor equals the Lorentz force and the latter are essentially identical with those of the geodesic line.

Fock, V.↗

NASA NTRS1977

Plasma rotation by electric and magnetic fields in a discharge cylinder

A theoretical model for an electric discharge consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field is developed to study the rotation of the discharge plasma in the crossed electric and magnetic fields. The associated boundary-value problem for the coupled partial differential equations which describe the electric potential and the plasma velocity fields is solved in closed form. The electric field, current density, and velocity distributions are discussed in terms of the Hartmann number and the Hall coefficient. As a result of Lorentz forces, the plasma rotates with speeds as high as 1 million cm/sec around its axis of symmetry at typical conditions. As an application, it is noted that rotating discharges of this type could be used to develop a high-density plasma-ultracentrifuge driven by j x B forces, in which the lighter (heavier) ion and atom components would be enriched in (off) the center of the discharge cylinder.

Wilhelm, H. E.↗

NASA NTRS1977

Boundary-value problem for plasma centrifuge at arbitrary magnetic Reynolds numbers

We solve in closed form the boundary-value problem for the partial differential equations which describe the (azimuthal) rotation velocity and induced magnetic fields in a cylindrical plasma centrifuge with ring electrodes of different radii and an external, axial magnetic field. The electric field, current density, and velocity distributions are discussed in terms of the Hartmann number H and the magnetic Reynolds number R. For small Hall coefficients, the induced magnetic field does not affect the plasma rotation. As a result of the Lorentz forces, the plasma rotates with speeds as high as 100,000 cm/sec around its axis of symmetry at typical conditions, so that the lighter (heavier) ion and atom components are enriched at (off) the center of the discharge cylinder.

Wilhelm, H. E.↗

NASA NTRS1979

A free-electron laser in a uniform magnetic field

The study shows that a free-electron laser can operate in a uniform, longitudinal magnetic field. The fully relativistic Lorentz force equations are examined and solved order by order in a radiation field strength to obtain analytic expressions for the electron trajectory and energy as functions of initial electron position within a wavelength of light. Analytic expressions for the longitudinal and transverse bunching and for laser gain are found. The bunching of this laser process is compared to the bunching processes involved in (1) a Stanford free-electron laser and (2) a cyclotron maser. The results received can be useful in exploring light amplification in astrophysical magnetic fields, the magnetosphere, and in laboratory devices.

Ride, S. K.↗

NASA NTRS1980

Dust in Jupiter's magnetosphere - An Io source

The possibility of removing particles from Io by interactions with the Jovian magnetosphere has been investigated. It is found that dust grains of about 0.1 micron radius will rapidly become charged if exposed to the ambient Jovian plasma. For particles this size in Io's volcanic plumes, the Lorentz force can overcome Io's gravity and these particles can escape. Escaping dust will be controlled by the topology of the magnetosphere and it is suggested that Io-derived dust may be an important source of erosive impacts on large Jovian ring particles and destructive collisions with small particles. The ring particles themselves will interact with the Jovian plasma and it is suggested that Coulomb scattering of plasma particles by charged dust grains may produce a plasma gap or void in the vicinity of the rings.

Johnson, T. V.↗

NASA NTRS1980

Cylindrical prominences and the magnetic influence of the photospheric boundary

The paper constructs exact, nonlinear solutions for a horizontal, cylindrical, current-carrying prominence supported against solar gravity by the Lorentz force. The solutions incorporate the photosphere boundary condition, proposed by van Tend and Kuperus (1978), who analyzed it for line filaments. The solutions have a finite radius for the prominence material and satisfy the equations of magnetostatic equilibrium, and allow for the continuity of gas pressure and of the normal and tangential components of magnetic field across the circular prominence boundary. It is shown that an infinity of solutions is possible; a method is presented for constructing equilibrium fields for any horizontal prominence with arbitrary cross-section and with an arbitrary external magnetic field.

Lerche, I.↗

NASA NTRS1980

The striated dust tail of Comet West 1976 VI as a particle fragmentation phenomenon

The motions of 16 striae in the dust tail of Comet West are studied. It is found that all 16 striae have originated from particle ejections, and that the particles responsible for the formation of a discrete striae must be emitted simultaneously, be subjected to the same repulsive acceleration in the tail, and break up simultaneously. A strong correlation is found between the ejection times and the times of known explosive events. The repulsive accelerations of particle fragments in the striae vary from 0.6 to 2.7 times the solar attraction, indicating submicron grains of strongly absorbing materials. The repulsive acceleration of parent particles range from 0.55 to 1.10, which is only slightly smaller than those of their fragments and suggests highly nonspherical shapes of parents. The mass of dust in an average striae is estimated to be one-billion grams. Rotational bursting is discussed as a possible fragmentation mechanism. The absence of measurable effects of the Lorentz force indicate an upper limit of a few volts for the electric charge of the fragments.

Sekanina, Z.↗

NASA NTRS1980

Evidence for fragmentation of strongly nonspherical dust particles in the tail of Comet West 1976 VI

Motion of 16 striae through the dust tail of Comet West 1976 VI are observed over a time interval of more than three days. Initiation times for most of the 16 striae are found to coincide with the times of discrete violent bursts of dust, determined from the motions of streamers. It is also found that fragments are subjected to repulsive accelerations between 0.6 and 2.7 the solar attraction, indicating submicron-size absorbing particles, while repulsive accelerations imparted to parent articles are slightly lower than the average acceleration of fragments. The sizes of the fragments are estimated to be between one tenth and a few tenths of a micron. No effect of the Lorentz force on striae motion is detected. It is concluded that the theoretical assumption that striae are products of fragmentation of friable dust particles ejected from the nucleus agrees with observations.

Sekanina, Z.↗

NASA NTRS1981

Neutral winds and electric fields in the dusk auroral oval. I - Measurements

Two rockets carrying an upleg and downleg trimethyl aluminum chemical trail release and three barium cannisters were launched from Poker Flat, Alaska on Feb. 28, 1978 and Mar. 2, 1978 in order to study neutral winds and electric fields in the dusk auroral oval. Electric field measurements were also made with a radar system to supplement the barium cloud data. The barium cloud drifts on both days showed intense poleward electric fields in the subauroral region. The drifts were nearly latitude-independent and were equivalent to electric fields of 60 mV/m of February 2 and 40 mV/m on March 2. The data indicate that the Lorentz force and Joule heating had a strong influence on the observed neutral winds.

Mikkelsen, I. S.↗

NASA NTRS1981

Neutral winds and electric fields in the dust auroral oval. II - Theory and model

A two-dimensional numerical model of the thermosphere is applied to the auroral zone neutral wind, electric field, and plasma density data set, presented in an earlier paper. The model shows that the action of the Lorentz force can be responsible to a great extent for the large zonal velocities near the 150-km altitude. Model equations are described, an explanation of the use of the geophysical conditions is given, and model integrations are compared to the wind measurements. However, for the two-dimensional model to be effective, the atmosphere must not cross too many meridians of local time during the integration period, so that the background state should remain fairly uniform. It is concluded that the two-dimensional model cannot accurately explain the details of the wind profiles because of the three-dimensional character of the physical situation. Thus it is noted that the observed winds were part of a large-scale three-dimensional flow which is only weakly coupled to short-term variations in magnetospheric conditions.

Mikkelsen, I. S.↗

NASA NTRS1982

Effects of rotation and magnetic field on the onset of convective instability in a liquid layer due to buoyancy and surface tension

Thermocapillary stability characteristics of a horizontal liquid layer heated from below rotating about a vertical axis and subjected to a uniform vertical magnetic field are analyzed under a variety of thermal and electromagnetic boundary conditions. Results based on analytical solutions to the pertinent eigenvalue problems are discussed in the light of earlier work on special cases of the more general problem considered here to show in particular the effects of the heat transfer, nonzero curvature and gravity waves at the two-fluid interface. Although the expected stabilizing action of the Coriolis and Lorentz force fields in this configuration are in evidence the optimal choice of an appropriate range for the relevant parameters is shown to be critically dependent on the interfacial effects mentioned above.

Sarma, G. S. R.↗

NASA NTRS1982

The vertical filamentary structures of quiescent prominences

The thin vertical filaments making up the quiescent prominence plasma, as revealed by fine spatial resolution H-alpha photographs, are characterized by a magnetostatic theory in which a horizontal row of long vertical filaments whose weights are supported by bowed magnetic field lines is described by a class of exact equilibrium solutions. The Kippenhahn-Schlueter (1957) solution for a long sheet without filamentary structures is a member of this class of solutions. In illustrating the role of the magnetic field in supporting and thermally shielding the filament plasma, it is found that the filament can have a sharp transition perpendicular to the local field, while the transition in the direction of the local field is diffuse. A consequence of the filamentary structure is that its support by the Lorentz force requires the electric current to have a component along the magnetic field.

Low, B. C.↗

NASA NTRS1981

The aurora - An electrical discharge phenomenon surrounding the earth

An attempt to model the processes underlying the appearance of auroral phenomena as a chain of events beginning with power production and resulting in auroral light emissions is presented. Power is produced by the interaction of the solar wind with the earth magnetosphere, creating a dynamo effect which is a function of the solar wind speed and the magnitude and orientation of the solar wind magnetic field. The dynamo power generates the convective motion of magnetospheric plasma, and subsequent magnetic-field aligned currents communicate the dynamo power to the polar ionosphere. The currents close as Pederson currents, and the associated Lorentz force accelerates the ionosphere in the direction of the convective motion. An electric potential structure develops at a few thousand km height, forcing current-carrying electrons to flow down the field lines to the ionosphere, where interactions with atmospheric constituents create auroral displays.

Akasofu, S.-I.↗

NASA NTRS1982

Reducing the non-axisymmetry of a planetary dynamo and an application to Saturn

A simple model for the tendency toward axisymmetrization observed in planets is developed. The model is presented in general but linear form, assuming that the differentially rotating fluid is thin, which means that Lorentz forces or Ohmic dissipation are neglected. Two cases are considered: uniform shear throughout the shell and shear concentrated within a very thin boundary layer. In each case, explicit expressions are obtained for the spatial attenuation of the non-spin-axisymmetric field components. The substantial nonlinear effects which prevent these results from being directly applicable to planets are discussed, with particular emphasis on the Taylor constraint. The model is applied to Saturn and found to give a satisfactory semiquantitative explanation for the near-axisymmetry of the field. The parameter choices required to reproduce the observed tilt are entirely reasonable and potentially testable. The model explains why Jupiter and Saturn are so different.

Stevenson, D. J.↗

NASA NTRS1982

Nonlinear dynamo oscillations

The stability of steady equilibrium amplitudes of magnetic fields generated by convection flows is investigated. Two cases are considered in detail, for which steady solutions are available from the previous work of Busse (1973) and Busse (1977). In the first case instability occurs primarily because of magnetic flux expulsion at high magnetic Reynolds numbers. In the second case the change in the velocity field caused by the Lorentz force enhances dynamo action. This subcritical finite amplitude dynamo is potentially unstable. In typical cases the nonlinear dynamo oscillations that replace the steady equilibrium solutions are investigated by numerical integration.

Busse, F. H.↗

NASA NTRS1983

Ions upstream of the earth's bow shock - A theoretical comparison of alternative source populations

The trajectories of ions reflected or leaked upstream from the earth's bow shock and subject solely to the Lorentz force in a steady interplanetary magnetic field B and the V x B electric field are studied theoretically. Expressions are obtained for the guiding center motion and gyromotion in a frame (the Hoffman-Teller frame) moving parallel to the shock surface with sufficient speed to transform the incident solar wind velocity into motion entirely along the interplanetary magnetic field. Equations are derived which transform these motions back to the observer's frame. The predicted upstream motions for four different source models for upstream ions are compared using these expressions: magnetic moment-conserving reflection of solar wind ions, specular reflection of solar wind ions, magnetic moment-conserving leakage of magnetosheath ions, and leakage of magnetosheath ions parallel to the shock normal.

Schwartz, S. J.↗

NASA NTRS1983

Heat transfer and horizontally averaged temperature of convection with large viscosity variations

It is pointed out that the understanding of convection in large-Prandtl-number Boussinesq fluids with uniform properties and contained in simple geometries is virtually complete. Present efforts are typically directed towards relaxing some of the original assumptions by going to lower Prandtl number, more complicated geometries, variable material properties, or introducing new dynamical processes such as the Lorentz forces. A description is given of experiments which are concerned with the effect on convection of relaxing the assumption of a uniform viscosity. The reported experiments were designed to measure both the horizontally averaged temperature as a function of depth and the heat transfer of convection over a range of viscosity variations up to 100,000.

Richter, F. M.↗