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The status of the initial testing of the modeling procedure developed to compute the magnetic fields at satellite orbit due to current distributions in the ionosphere and magnetosphere is reported. The modeling technique utilizes a linear current element representation of the large scale space-current system.
Abstract In this paper, a numerical dart leader model has been implemented to understand the leader's development and the corresponding electric field changes observed by the 3D broadband mapping and polarization (BIMAP‐3D) system. The model assumes the extending leader channel is equipotential and has a linear charge distribution induced by an ambient electric field. The charge distribution induced by the ambient field can be used to model the electric field change at the ground. We then find the ambient electric field which best fits the field change measurements at the two BIMAP stations. The estimated ambient electric field decreases in the direction of dart leader propagation. Our observations and modeling results are consistent with our earlier hypothesis that dart leader speed is proportional to the electric field at the leader tip. The model also supports our earlier analysis that leader speed variations near branch junctions were due to previous charge deposits near the junctions. The modeled tip electric field is generally lower than the breakdown field unless the pre‐dart‐leader channel has a significant temperature of 3,000 K. This is consistent with the fact that dart leaders typically do not form new branches into the virgin air. Furthermore, the tip field is generally close to the negative streamer stability field at ambient temperatures, explaining the nature of the narrow and well‐defined channel structure. In addition to the charge distribution and the ambient and tip electric field, the development of the channel potential and current distribution are also presented.
Progress made in reducing MAGSAT data and displaying magnetic field perturbations caused primarily by external currents is reported. A periodic and repeatable perturbation pattern is described that arises from external current effects but appears as unique signatures associated with upper middle latitudes on the Earth's surface. Initial testing of the modeling procedure that was developed to compute the magnetic fields at satellite orbit due to current distributions in the ionosphere and magnetosphere is also discussed. The modeling technique utilizes a linear current element representation of the large scale space current system.
The SAMPLE computer code models electrophoresis separation in a wide range of conditions. Results are included for steady three dimensional continuous flow electrophoresis (CFE), time dependent gel and acetate film experiments in one or two dimensions and isoelectric focusing in one dimension. The code evolves N two dimensional radical concentration distributions in time, or distance down a CFE chamber. For each time or distance increment, there are six stages, successively obtaining the pH distribution, the corresponding degrees of ionization for each radical, the conductivity, the electric field and current distribution, and the flux components in each direction for each separate radical. The final stage is to update the radical concentrations. The model formulation for ion motion in an electric field ignores activity effects, and is valid only for low concentrations; for larger concentrations the conductivity is, therefore, also invalid.
Electrodynamic propulsion based on the interaction of a conducting tether with the background magnetic field can be implemented across a range of system designs. Bare tethers, bare and insulated tethers with a balloon termination, and insulated tethers with a grid-sphere termination have been proposed for different applications. Electrodynamic tether as a thruster is currently proposed for the Momentum exchange Electrodynamic Reboost (MXER) Tether System that currently under development at NASA Marshal Space Flight Center. The choice of a tether design for a specific mission is based on the analysis of tether system performance. Different parameters describing tether performance such as system acceleration and efficiency can be calculated if the current distribution along the tether at the satellite trajectory is known. The code calculating the tether current collection for the bare and partly insulated tethers with the circular (wire) and rectangular (tape) cross-sections operating in the thrust mode has been developed and applied for MXER that is expected to operate in an equatorial elliptical orbit with perigee in the altitude range of 300-500km and apogee between 5000-8000km. The collected current is calculated as a function of the satellite velocity and the Earth s magnetic field, plasma parameters (plasma density and temperature), and tether parameters (tether length, the length of the bare segment, the type and the dimensions of the cross-section). The deviation of the collected current from the OML model due to the tether thickness and self-induced magnetic field (for tether with a circular cross-section) is taken into account.
Disturbances in the MAGSAT magnetometer data set due to high latitude phenomena were evaluated. Much of the categorization of disturbances due to Birkeland currents, ionospheric Hall currents, fine structure and wave phenomena was done with the MAGSAT data catalog. A color graphics technique was developed for the display of disturbances from multiple orbits, from which one can infer a 'global-image' of the current systems of the auroral zone. The MAGSAT 4/81 magnetic field model appears to represent the Earth's main field at high latitudes very well for the epoch 1980. MAGSAT's low altitude allows analysis of disturbances in the magnetometer data due to ionospheric electrojet currents. These current distributions were modeled properly for single events as a precursor to the inference of the Birkeland current system. MAGSAT's orbit was approximately shared with that of the Navy/APL TRIAD satellite. This allowed space-time studies of the magnetic disturbance signatures to be performed, the result being an approximately 75% agreement in, as well as high frequency of, signatures due to Birkeland currents. Thus the field-aligned currents are a steady-state participant in the Earth's magnetospheric current system.
The ionospheric plasma currents associated with the operation of an orbiting, constant current electrodynamic tethered satellite system are calculated using linear cold plasma theory and a tethered system current distribution model that takes into account the peculiar dumbbell shape of the system. The field line current calculations show plasma sheet currents at each end of the tethered system whose structure is roughly that of the Alfven wings. The disturbance caused by the moving tethered system extends behind its dimensions along the line of sight. The form of the wings alters as they travel away from the system. The front boundary becomes sharper while the ripples in J(z) in the wake extend to greater distances with larger amplitude. The wave impedance is calculated for a wide range of system dimension values. The expression is in sharp disagreement with a recently published result by Dobrowolny and Veltri (1986).
Full scale and half scale versions of the Princeton Benchmark and Flared Anode self-field MPD thrusters have been investigated to determine the influence of scale and design upon MPD behavior. Thruster performance determined by impulsive thrust and terminal voltage measurements is found to depend primarily on propellant flow rate and the ratio of electrode radii, but not on thruster size. Current distributions obtained from magnetic field probes are independent of scale for both thruster designs. Voltage depends upon current, electrode geometry, and propellant flow rate. This behavior agrees qualitatively with calculations based on a fundamental MHD formulation.
A small, portable device has been developed to measure return stroke velocities. With the device, velocities from 135 strokes that consist of 92 natural return strokes and 43 triggered return strokes have been analyzed. The average return stroke velocity for longer channels, greater than 500 meters, is 1.2 + or - 0.3 x 10 to the 8th m/s for both natural and triggered return strokes. For shorter channel lengths, less than 500 m, natural lightning has a statistically higher average return stroke velocity of 1.9 + or - 0.7 x 10 to the 8th m/s than triggered lightning with an average return stroke velocity of 1.4 + or - 0.4 x 10 to the 8th m/s. Using the transmission line model of the return stroke, natural lightning has a peak current distribution that is log-normal with a median value of 19 kA. Return stroke velocities and currents were determined for two distant single stroke natural positive cloud-to-ground flashes. The velocities were 1.0 and 1.7 x 10 to the 8th ms/s while the estimated peak current for each positive flash was over 125 kA.
Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.
The problem of microstrip antennas covered by a dielectric substrate is formulated in terms of coupled integro-differential equations with the current distribution on the conducting patch as an unknown quantity. The Galerkin method is used to solve for the unknown patch current. Using the present formulation, the radiation pattern, the resonant frequency, and the bandwidth of a rectangular microstrip antenna are computed. Design data for a rectangular microstrip antenna are also presented.
The role of the thundercloud in the global electric circuit has been considered by many researchers. Thus, Holzer and Saxon (1952) have constructed a simple model of a bipolar thunderstorm. The global models considered provide insight into the atmospheric electric circuit but are restricted, both by various analytical mathematical representations and by computer size, to a grid of about five degrees in latitude and longitude. A need exists, therefore, for the development of a numerical regional model capable of resolving small-scale phenomena so that their coupling into the global-scale circuit can be examined. The construction of a two-dimensional quasi-static numerical model of atmospheric electricity is discussed. The model provides a basis for the calculation of the global electric field and current distribution produced by a single thunderstorm generator. In connection with the calculations, the thunderstorm was defined by a quasi-static current source function which generates a dipole charge configuration.
The distribution of ion current density as a function of angle from the thruster axis was measured at nominal operating conditions of 300 Volts discharge voltage and 4.5 Amperes discharge current for two SPT-100 stationary plasma thrusters from Fakel Enterprises, a D-55 anode layer thruster from the Central Scientific Research Institute for Machine Building (TsNIIMASH), and a first, second, and third generation T-100 stationary plasma thruster from the Scientific Research Institute of Thermal Process (NIITP). The data showed that the current density distributions of these thrusters were similar. Some differences in peak ion current density were observed. Multiply charged ions were found to be a small fraction of the plasma plume for all of the thrusters. The effect of facility pressure on ion current density distribution was found to be nonnegligible at pressures above 2 x 10(exp -6) Torr. The ion current density distributions of a new SPT-100 and a 6000 hour wear tested SPT-100 exhibited no discernible difference. Ion current density measurements were also taken at off-nominal thruster operating conditions.
The paper presents a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinate. The current J is taken to be proportional to the cube of the magnetostatic potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of similarity solution examples are displayed depending on the values of the similarity parameters. Each similarity parameter corresponds to a symmetry of the underlying nonlinear elliptic equation for A. The similarity parameters also determine the source currents for the potential field solution of the family. The solutions show the interplay between the gravitational force, the J & B force (B, magnetic field induction) and the gas pressure gradient.
We study the formation of a very thin current sheet (CS) and associated plasma electrodynamics using three-dimensional (3-D) particle-in-cell simulations with ion to electron mass ratio M/m=1836. The CS is driven by imposed anti-parallel magnetic fields. The noteworthy features of the temporal evolution of the CS are the following: (i) Steepening of the magnetic field profile B,(z) in the central part of the CS, (ii) Generation of three-peak current distribution with the largest peak in the CS center as B,(z) steepens, (iii) Generation of converging electric fields forming a potential well in the CS center in which ions are accelerated. (iv) Electron and ion heating in the central part of the CS by current-driven instabilities (CDI). (v) Re-broadening of the CS due to increased kinetic plasma pressure in the CS center. (vi) Generation of electron temperature anisotropy with temperature perpendicular to the magnetic field being larger than the parallel one. (vii) Current disruption by electron trapping in an explosively growing electrostatic instability (EGEI) and electron tearing instability (ETI). (viii)The onset of EGEI coincides with an increase in the electron temperature above the temperature of the initially hot ions as well as the appearance of new shear in the electron drift velocity. (ix) Bifurcation of the central CS by the current disruption. (x) Magnetic reconnection (MR) beginning near the null in B, and spreading outward. (xi) Generation of highly energized electrons reaching relativistic speeds and having isotropic pitch-angle distribution in the region of reconnected magnetic fields. We compare some of these features of the current sheet with results from laboratory and space experiments.
The paper determines the electric potential in a plane which is fed current from a pair of field-aligned current sheets. The ionospheric conductivity is modelled as a constant with an enhanced conductivity annular ring. It is shown that field-aligned current distributions are arbitrary functions of azimuth angle (MLT) and thus allow for asymmetric potential configurations over the pole cap. In addition, ionospheric surface currents are computed by means of stream functions. Finally, the discussion relates these methods to the electrical characteristics of the magnetosphere.
Two-dimensional photoelectric return stroke velocities from 130 strokes are presented, including 86 negative natural, 41 negative triggered, one positive triggered, and two positive natural return strokes. For strokes starting near the ground and exceeding 500 m in length, the average velocity is 1.3 + or - 0.3 X 10 to the 8th m/s for natural return strokes and 1.2 + or - 0.3 X 10 to the 8th m/s for triggered return strokes. For strokes with lengths less than 500 m, the average velocities are slightly higher. Using the transmission line model (TLM), the shortest segment one-dimensional return stroke velocity, and either the maximum or plateau electric field, it is shown that natural strokes have a peak current distribution that is lognormal with a median value of 16 kA (maximum E) or 12 kA (plateau E). Triggered lightning has a medium peak current value of 21 kA (maximum E) or 15 kA (plateau E). Correlations are found between TLM peak currents and velocities for triggered and natural subsequent return strokes, but not between TLM peak currents and natural first return stroke velocities.
Numerous observations have revealed that power-law distributions are ubiquitous in energetic solar processes. Hard X-rays, soft X-rays, extreme ultraviolet radiation, and radio waves all display power-law frequency distributions. Since magnetic reconnection is the driving mechanism for many energetic solar phenomena, it is likely that reconnection events themselves display such power-law distributions. In this work, we perform numerical simulations of the solar corona driven by simple convective motions at the photospheric level. Using temperature changes, current distributions, and Poynting fluxes as proxies for heating, we demonstrate that energetic events occurring in our simulation display power-law frequency distributions, with slopes in good agreement with observations. We suggest that the braiding-associated reconnection in the corona can be understood in terms of a self-organized criticality model driven by convective rotational motions similar to those observed at the photosphere.