Theory of a probe in a strong magnetic field

An asymptotic analysis of the Langmuir-probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C-V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented.The theory, which fails beyond certain positive voltage, fields useful results for weak fields, too.

Theory of a Probe in a Strong Magnetic Field. AT(30-1)-1238-MATT 599

A kinetic approach is used to develop a theory of electrostatic probes in a fully ionized plasma in the presence of a magnetic field. A consistent asymptotic expansion is obtained assuming that the electron Larmor radius is small compared to the radius of the probe. The order of magnitude of neglected terms is given. It is found that the electric potential within the tube of force defined by the cross section of the probe decays non-mono tonic ally from the probe; this bump disappears at a certain probe voltage and the theory is valid up to this voltage. The transition region, which extends beyond plasma potential, is not exponential. The possible saturation of the electron current is discussed. Restricted numerical results are given; they seem to be useful for weaker magnetic fields down to the zero-field limit. Extensions of the theory a r e considered.

Evaluation of the Magnetic Field Generated by the Inverter of an Electric Vehicle

In hybrid and electric vehicles, passengers sit very close to an electric system of significant power, which means that they may be subjected to high electromagnetic fields. The hazards of long-term exposure to these fields must be taken into account when designing electric vehicles and their components. Among all the electric devices present in the power train, the electronic converter is the most difficult to analyze, given that it works with different frequencies. In this paper, a methodology to evaluate the magnetic field created by a power electronics converter is proposed. After a brief overview of the recommendations of electromagnetic fields exposure, the magnetic field produced by an inverter is analyzed using finite element techniques. The results obtained are compared to laboratory measurements, taken from a real inverter, in order to validate the model. Finally, results are used to draw some conclusions regarding vehicle design criteria and magnetic shielding efficiency.

Effect of strain and magnetic field on the critical current and electric resistance of the joints between HTS coated conductors

Engineering of devices and systems such as magnets, fault current limiters or cables, based on High Temperature Superconducting wires requires a deep characterization of the possible degradation of their properties by handling at room temperature as well as during the service life thus establishing the limits for building up functional devices and systems. In the present work we report our study regarding the mechanical behavior of spliced joints between commercial HTS coated conductors based on YBCO at room temperature and service temperature, 77 K. Tensile tests under axial stress and the evolution of the critical current and the electric resistance of the joints have been measured. The complete strain contour for the tape and the joint has been obtained by using Digital Image Correlation. Also, tensile tests under external magnetic field have been performed and the effect of the applied field on the critical current and the electric resistance of the joints has been studied. Finally, a preliminary numerical study by means of Finite Element Method (FEM) of the mechanical behavior of the joints between commercial HTS is presented.

Effect of strain and magnetic field on the critical current and electric resistance of the joints between HTS coated conductors

Engineering of devices and systems such as magnets, fault current limiters or cables, based on High Temperature Superconducting wires requires a deep characterization of the possible degradation of their properties by handling at room temperature as well as during the service life thus establishing the limits for building up functional devices and systems. In the present work we report our study regarding the mechanical behavior of spliced joints between commercial HTS coated conductors based on YBCO at room temperature and service temperature, 77 K. Tensile tests under axial stress and the evolution of the critical current and the electric resistance of the joints have been measured. The complete strain contour for the tape and the joints has been obtained by using Digital Image Correlation. Also, tensile tests under external magnetic field have been performed and the effect of the applied field on the critical current and the electric resistance of the joints has been studied. Additionally, fatigue tests under constant cyclic stress and loading-unloading ramps have been carried out in order to evaluate the electromechanical behavior of the joints and the effect of maximum applied stress on the critical current. Finally, a preliminary numerical study by means of the Finite Element Method (FEM) of the electromechanical behavior of the joints between commercial HTS is presented.

Effect of magnetic field on current colection on bare tether in LEO

An eiectrodynamic Tether is a long thin conductive string deployed from a spacecraft. A part of the ED tether near one end, which is rendered positive by the Electromotive force (EMF)along the tether, collects electrons from the ambient plasma. In the frame of reference moving with theter, ions flow toward the tether, get deflected near the tether by its high positive potential and create a wake. Due to the asymmetry of plasma distribution and the weak but significant Geomagnetic field, the conventional probe theory becomes almost inapplicable. Computational work for the prediction of current collection is thus necessiated.. In this paper, we analyze effects of magnetic field on velocity distribution funtion at a point that is far from the tether, and discuss a new way to treat electrons at computational boundary. Three cases with different magnetic field are simulated and compiled so as to provide a part of the pre-flight prediction of the space experiment by NASA ProSEDS, which is planned September 2002.

Analysis and Design Considerations of an Electric Vehicle Powertrain regarding Energy Efficiency and Magnetic Field Exposure

En esta tesis se analiza el sistema de tracción de un vehículo eléctrico de batería desde el punto de vista de la eficiencia energética y de la exposición a campos magnéticos por parte de los pasajeros (radiación electromagnética). Este estudio incluye tanto el sistema de almacenamiento de energía como la máquina eléctrica, junto con la electrónica de potencia y los sistemas de control asociados a ambos. Los análisis y los resultados presentados en este texto están basados en modelos matemáticos, simulaciones por ordenador y ensayos experimentales a escala de laboratorio. La investigación llevada a cabo durante esta tesis tuvo siempre un marcado enfoque industrial, a pesar de estar desarrollada en un entorno de considerable carácter universitario. Las líneas de investigación acometidas tuvieron como destinatario final al diseñador y al fabricante del vehículo, a pesar de lo cual algunos de los resultados obtenidos son preliminares y/o excesivamente académicos para resultar de interés industrial. En el ámbito de la eficiencia energética, esta tesis estudia sistemas híbridos de almacenamiento de energía basados en una combinación de baterías de litio y supercondensadores. Este tipo de sistemas son analizados desde el punto de vista de la eficiencia mediante modelos matemáticos y simulaciones, cuantificando el impacto de ésta en otros parámetros tales como el envejecimiento de las baterías. Respecto a la máquina eléctrica, el estudio se ha centrado en máquinas síncronas de imanes permanentes. El análisis de la eficiencia considera tanto el diseño de la máquina como la estrategia de control, dejando parcialmente de lado el inversor y la técnica de modulación (que son incluidos en el estudio como fuentes adicionales de pérdidas, pero no como potenciales fuentes de optimización de la eficiencia). En este sentido, tanto la topología del inversor (trifásico, basado en IGBTs) como la técnica de modulación (control de corriente en banda de histéresis) se establecen desde el principio. El segundo aspecto estudiado en esta tesis es la exposición a campos magnéticos por parte de los pasajeros. Este tema se enfoca desde un punto de vista predictivo, y no desde un punto de vista de diagnóstico, puesto que se ha desarrollado una metodología para estimar el campo magnético generado por los dispositivos de potencia de un vehículo eléctrico. Esta metodología ha sido validada mediante ensayos de laboratorio. Otros aspectos importantes de esta contribución, además de la metodología en sí misma, son las consecuencias que se derivan de ella (por ejemplo, recomendaciones de diseño) y la comprensión del problema proporcionada por esta. Las principales contribuciones de esta tesis se listan a continuación: una recopilación de modelos de pérdidas correspondientes a la mayoría de dispositivos de potencia presentes en un vehículo eléctrico de batería, una metodología para analizar el funcionamiento de un sistema híbrido de almacenamiento de energía para aplicaciones de tracción, una explicación de cómo ponderar energéticamente los puntos de operación par-velocidad de un vehículo eléctrico (de utilidad para evaluar el rendimiento de una máquina eléctrica, por ejemplo), una propuesta de incluir un convertidor DC-DC en el sistema de tracción para minimizar las pérdidas globales del accionamiento (a pesar de las nuevas pérdidas introducidas por el propio DC-DC), una breve comparación entre dos tipos distintos de algoritmos de minimización de pérdidas para máquinas síncronas de imanes permanentes, una metodología predictiva para estimar la exposición a campos magnéticos por parte de los pasajeros de un vehículo eléctrico (debida a los equipos de potencia), y finalmente algunas conclusiones y recomendaciones de diseño respecto a dicha exposición a campos magnéticos. ABSTRACT This dissertation analyzes the powertrain of a battery electric vehicle, focusing on energy efficiency and passenger exposure to electromagnetic fields (electromagnetic radiation). This study comprises the energy storage system as well as the electric machine, along with their associated power electronics and control systems. The analysis and conclusions presented in this dissertation are based on mathematical models, computer simulations and laboratory scale tests. The research performed during this thesis was intended to be of industrial nature, despite being developed in a university. In this sense, the work described in this document was carried out thinking of both the designer and the manufacturer of the vehicle. However, some of the results obtained lack industrial readiness, and therefore they remain utterly academic. Regarding energy efficiency, hybrid energy storage systems consisting in lithium batteries, supercapacitors and up to two DC-DC power converters are considered. These kind of systems are analyzed by means of mathematical models and simulations from the energy efficiency point of view, quantifying its impact on other relevant aspects such as battery aging. Concerning the electric machine, permanent magnet synchronous machines are studied in this work. The energy efficiency analysis comprises the machine design and the control strategy, while the inverter and its modulation technique are taken into account but only as sources of further power losses, and not as potential sources for further efficiency optimization. In this sense, both the inverter topology (3-phase IGBT-based inverter) and the switching technique (hysteresis current control) are fixed from the beginning. The second aspect studied in this work is passenger exposure to magnetic fields. This topic is approached from the prediction point of view, rather than from the diagnosis point of view. In other words, a methodology to estimate the magnetic field generated by the power devices of an electric vehicle is proposed and analyzed in this dissertation. This methodology has been validated by laboratory tests. The most important aspects of this contribution, apart from the methodology itself, are the consequences (for instance, design guidelines) and the understanding of the magnetic radiation issue provided by it. The main contributions of this dissertation are listed next: a compilation of loss models for most of the power devices found in a battery electric vehicle powertrain, a simulation-based methodology to analyze hybrid energy storage performance in traction applications, an explanation of how to assign energy-based weights to different operating points in traction drives (useful when assessing electrical machine performance, for instance), a proposal to include one DC-DC converter in electric powertrains to minimize overall power losses in the system (despite the new losses added by the DC-DC), a brief comparison between two kinds of loss-minimization algorithms for permanent magnet synchronous machines in terms of adaptability and energy efficiency, a predictive methodology to estimate passenger magnetic field exposure due to power devices in an electric vehicle, and finally some useful conclusions and design guidelines concerning magnetic field exposure.

Safety study of transcranial static magnetic field stimulation (tSMS) of the human cortex

Transcranial static magnetic field stimulation (tSMS) in humans reduces cortical excitability. Objective: The objective of this study was to determine if prolonged tSMS (2 h) could be delivered safely in humans. Safety limits for this technique have not been described. Methods: tSMS was applied for 2 h with a cylindric magnet on the occiput of 17 healthy subjects. We assessed tSMS-related safety aspects at tissue level by measuring levels of neuron-specific enolase (NSE,a marker of neuronal damage) and S100 (a marker of glial reactivity and damage). We also included an evaluation of cognitive side effects by using a battery of visuomotor and cognitive tests. Results: tSMS did not induce any significant increase in NSE or S100. No cognitive alteration was detected. Conclusions: Our data indicate that the application of tSMS is safe in healthy human subjects, at least within these parameters

Novel system for bite-force sensing and monitoring based on magnetic eear field communication

Intraoral devices for bite-force sensing have several applications in odontology and maxillofacial surgery, as bite-force measurements provide additional information to help understand the characteristics of bruxism disorders and can also be of help for the evaluation of post-surgical evolution and for comparison of alternative treatments. A new system for measuring human bite forces is proposed in this work. This system has future applications for the monitoring of bruxism events and as a complement for its conventional diagnosis. Bruxism is a pathology consisting of grinding or tight clenching of the upper and lower teeth, which leads to several problems such as lesions to the teeth, headaches, orofacial pain and important disorders of the temporomandibular joint. The prototype uses a magnetic field communication scheme similar to low-frequency radio frequency identification (RFID) technology (NFC). The reader generates a low-frequency magnetic field that is used as the information carrier and powers the sensor. The system is notable because it uses an intra-mouth passive sensor and an external interrogator, which remotely records and processes information regarding a patient?s dental activity. This permits a quantitative assessment of bite-force, without requiring intra-mouth batteries, and can provide supplementary information to polysomnographic recordings, current most adequate early diagnostic method, so as to initiate corrective actions before irreversible dental wear appears. In addition to describing the system?s operational principles and the manufacture of personalized prototypes, this report will also demonstrate the feasibility of the system and results from the first in vitro and in vivo trials.

Magnetic self-field effects on current collection by an ionospheric bare tether

It was recently suggested that the magnetic field created by the current of a bare tether strongly reduces its own electron-collection capability when a magnetic separatrix disconnecting ambient magnetized plasma from tether extends beyond its electric sheath. It is here shown that current reduction by the self-field depends on the ratio meterizing bias and current profiles along the tether (Lt tether length, characteristic length gauging ohmic effects) and on a new dimensionless number Ks involving ambient and tether parameters. Current reduction is weaker the lower Ks and L*/ Lt, which depend critically on the type of cross section: Ks varies as R5/3, h2/3R, and h2/3 1/4 width for wires, round tethers conductive only in a thin layer, and thin tapes, respectively; L* varies as R2/3 for wires and as h2/3 for tapes and round tethers conductive in a layer (R radius, h thickness). Self-field effects are fully negligible for the last two types of cross sections whatever the mode of operation. In practical efficient tether systems having L*/Lt low, maximum current reduction in case of wires is again negligible for power generation; for deorbiting, reduction is <1% for a 10 km tether and 15% for a 20 km tether. In the reboost mode there are no effects for Ks below some threshold; moderate effects may occur in practical but heavy reboost-wire systems that need no dedicated solar power.

Magnetic self-field effects on bare-tether current collection

It has been recently suggested that the magnetic field created by the current in a bare tether could sensibly reduce its electron collection capability in the magnetised ionosphere, a region of closed magnetic surfaces disconnecting the cylinder from infinity. In this paper, the ohmic voltage drop along the tether is taken into account in considering self-field effects. Separate analyses are carried out for the thrust and power generation and drag modes of operation, which are affected in different ways. In the power generation and drag modes, bias decreases as current increases along the tether, starting at the anodic, positively-biased end (upper end in the usual, eastward-flying spacecraft); in the thrust mode of operation, bias increases as current increases along the tether, starting at the lower end. When the ohmic voltage drop is considered, self-field effects are shown to be weak, in all cases, for tape tethers, and for circular cross-section tethers just conductive in a thin outer layer. Self-field effects might become important, in the drag case only, for tethers with fully conductive cross sections that are unrealistically heavy.

Magnetic and electric current morphoiogy in the plasma ejected by a laser-irradiated foil

A quasisteady model for the plasma ablated from a thick foil by a laser pulse, at low $lln $ and R /A i within a low, narrow range, is given (4, is absorbed intensity, /zL wavelength, R focalspot radius). An approximate analytical solution is given for the two-dimensional plasma dynamics. At large magnetic Reynolds number Rm, the morphology of the magnetic field shows features in agreement with recent results for high intensities. Current lines are open: electric current flows toward the spot near its axis, then turns and flows away. The efficiency of converting light energy into electric energy peaks at Rm- 1, both the validity of the model. and accuracy of the solution are discussed, The neighborhood of the spot boundary is analyzed in detail by extending classical Prandtl-Meyer results.

Analysis of Magnetic Nozzles For Space Plasma Thrusters = Análisis de Toberas Magnéticas para Motores Espaciales de Plasma

Esta tesis presenta un análisis teórico del funcionamiento de toberas magnéticas para la propulsión espacial por plasmas. El estudio está basado en un modelo tridimensional y bi-fluido de la expansión supersónica de un plasma caliente en un campo magnético divergente. El modelo básico es ampliado progresivamente con la inclusión de términos convectivos dominantes de electrones, el campo magnético inducido por el plasma, poblaciones electrónicas múltiples a distintas temperaturas, y la capacidad de integrar el flujo en la región de expansión lejana. La respuesta hiperbólica del plasma es integrada con alta precisión y eficiencia haciendo uso del método de las líneas características. Se realiza una caracterización paramétrica de la expansión 2D del plasma en términos del grado de magnetización de iones, la geometría del campo magnético, y el perfil inicial del plasma. Se investigan los mecanismos de aceleración, mostrando que el campo ambipolar convierte la energía interna de electrones en energía dirigida de iones. Las corrientes diamagnéticas de Hall, que pueden hallarse distribuidas en el volumen del plasma o localizadas en una delgada capa de corriente en el borde del chorro, son esenciales para la operación de la tobera, ya que la fuerza magnética repulsiva sobre ellas es la encargada de confinar radialmente y acelerar axialmente el plasma. El empuje magnético es la reacción a esta fuerza sobre el motor. La respuesta del plasma muestra la separación gradual hacia adentro de los tubos de iones respecto de los magnéticos, lo cual produce la formación de corrientes eléctricas longitudinales y pone el plasma en rotación. La ganancia de empuje obtenida y las pérdidas radiales de la pluma de plasma se evalúan en función de los parámetros de diseño. Se analiza en detalle la separación magnética del plasma aguas abajo respecto a las líneas magnéticas (cerradas sobre sí mismas), necesaria para la aplicación de la tobera magnética a fines propulsivos. Se demuestra que tres teorías existentes sobre separación, que se fundamentan en la resistividad del plasma, la inercia de electrones, y el campo magnético que induce el plasma, son inadecuadas para la tobera magnética propulsiva, ya que producen separación hacia afuera en lugar de hacia adentro, aumentando la divergencia de la pluma. En su lugar, se muestra que la separación del plasma tiene lugar gracias a la inercia de iones y la desmagnetización gradual del plasma que tiene lugar aguas abajo, que permiten la separación ilimitada del flujo de iones respecto a las líneas de campo en condiciones muy generales. Se evalúa la cantidad de plasma que permanece unida al campo magnético y retorna hacia el motor a lo largo de las líneas cerradas de campo, mostrando que es marginal. Se muestra cómo el campo magnético inducido por el plasma incrementa la divergencia de la tobera magnética y por ende de la pluma de plasma en el caso propulsivo, contrariamente a las predicciones existentes. Se muestra también cómo el inducido favorece la desmagnetización del núcleo del chorro, acelerando la separación magnética. La hipótesis de ambipolaridad de corriente local, común a varios modelos de tobera magnética existentes, es discutida críticamente, mostrando que es inadecuada para el estudio de la separación de plasma. Una inconsistencia grave en la derivación matemática de uno de los modelos más aceptados es señalada y comentada. Incluyendo una especie adicional de electrones supratérmicos en el modelo, se estudia la formación y geometría de dobles capas eléctricas en el interior del plasma. Cuando dicha capa se forma, su curvatura aumenta cuanto más periféricamente se inyecten los electrones supratérmicos, cuanto menor sea el campo magnético, y cuanto más divergente sea la tobera magnética. El plasma con dos temperaturas electrónicas posee un mayor ratio de empuje magnético frente a total. A pesar de ello, no se encuentra ninguna ventaja propulsiva de las dobles capas, reforzando las críticas existentes frente a las propuestas de estas formaciones como un mecanismo de empuje. Por último, se presenta una formulación general de modelos autosemejantes de la expansión 2D de una pluma no magnetizada en el vacío. El error asociado a la hipótesis de autosemejanza es calculado, mostrando que es pequeño para plumas hipersónicas. Tres modelos de la literatura son particularizados a partir de la formulación general y comparados. Abstract This Thesis presents a theoretical analysis of the operation of magnetic nozzles for plasma space propulsion. The study is based on a two-dimensional, two-fluid model of the supersonic expansion of a hot plasma in a divergent magnetic field. The basic model is extended progressively to include the dominant electron convective terms, the plasma-induced magnetic field, multi-temperature electron populations, and the capability to integrate the plasma flow in the far expansion region. The hyperbolic plasma response is integrated accurately and efficiently with the method of the characteristic lines. The 2D plasma expansion is characterized parametrically in terms of the ion magnetization strength, the magnetic field geometry, and the initial plasma profile. Acceleration mechanisms are investigated, showing that the ambipolar electric field converts the internal electron energy into directed ion energy. The diamagnetic electron Hall current, which can be distributed in the plasma volume or localized in a thin current sheet at the jet edge, is shown to be central for the operation of the magnetic nozzle. The repelling magnetic force on this current is responsible for the radial confinement and axial acceleration of the plasma, and magnetic thrust is the reaction to this force on the magnetic coils of the thruster. The plasma response exhibits a gradual inward separation of the ion streamtubes from the magnetic streamtubes, which focuses the jet about the nozzle axis, gives rise to the formation of longitudinal currents and sets the plasma into rotation. The obtained thrust gain in the magnetic nozzle and radial plasma losses are evaluated as a function of the design parameters. The downstream plasma detachment from the closed magnetic field lines, required for the propulsive application of the magnetic nozzle, is investigated in detail. Three prevailing detachment theories for magnetic nozzles, relying on plasma resistivity, electron inertia, and the plasma-induced magnetic field, are shown to be inadequate for the propulsive magnetic nozzle, as these mechanisms detach the plume outward, increasing its divergence, rather than focusing it as desired. Instead, plasma detachment is shown to occur essentially due to ion inertia and the gradual demagnetization that takes place downstream, which enable the unbounded inward ion separation from the magnetic lines beyond the turning point of the outermost plasma streamline under rather general conditions. The plasma fraction that remains attached to the field and turns around along the magnetic field back to the thruster is evaluated and shown to be marginal. The plasmainduced magnetic field is shown to increase the divergence of the nozzle and the resulting plasma plume in the propulsive case, and to enhance the demagnetization of the central part of the plasma jet, contrary to existing predictions. The increased demagnetization favors the earlier ion inward separation from the magnetic field. The local current ambipolarity assumption, common to many existing magnetic nozzle models, is critically discussed, showing that it is unsuitable for the study of plasma detachment. A grave mathematical inconsistency in a well-accepted model, related to the acceptance of this assumption, is found out and commented on. The formation and 2D shape of electric double layers in the plasma expansion is studied with the inclusion of an additional suprathermal electron population in the model. When a double layer forms, its curvature is shown to increase the more peripherally suprathermal electrons are injected, the lower the magnetic field strength, and the more divergent the magnetic nozzle is. The twoelectron- temperature plasma is seen to have a greater magnetic-to-total thrust ratio. Notwithstanding, no propulsive advantage of the double layer is found, supporting and reinforcing previous critiques to their proposal as a thrust mechanism. Finally, a general framework of self-similar models of a 2D unmagnetized plasma plume expansion into vacuum is presented and discussed. The error associated with the self-similarity assumption is calculated and shown to be small for hypersonic plasma plumes. Three models of the literature are recovered as particularizations from the general framework and compared.

The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

Magnetic pumping of whistler waves by tether current modulation

Magnetic excitation of whistlers by a square array of electrodynamic tethers is discussed. The array is made of perpendicular rows of tethers that carry equal, uniform, and time-modulated currents at equal frequency with a 90° phase shift. The array would fly vertical in the orbital equatorial plane, which is perpendicular to the geomagnetic field B0 when its tilt is ignored. The array radiates a whistler wave along B0. A parametric instability due to pumping by the background magnetic field through the radiated wave gives rise to two unstable coupled whistler perturbations. The growth rate is maximum for perturbations with wave vector at angles 38.36° and 75.93° from B0. For an experiment involving a wavefront that moves with the orbiting array, which might serve to study nonlinear wave interactions and turbulence in space plasmas, characteristic values of growth rate and parameters, such as the number of tethers and their dimensions and distances in the array, are discussed for low Earth orbit ambient conditions.