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At least 1,765 records · Page 98
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Convection in an Infinite Vertical Cylinder in the Presence of a Horizontal Magnetic Field

The use of a magnetic field to suppress convection in low gravity materials processing is an area of active research. This study aims to investigate some of the basic features of an verse magnetic field on convective motion in electrically conducting melts. The geometry considered is in infinite vertical column of liquid metal with an axial temperature gradient and an imposed transverse magnetic field. The incipience and azimuthal orientation of convective roM is investigated. The governing transport equations are nondimensionalized, linearized and the eigen value problem is solved to determine the most physically significant states. The analysis shows that the initial degeneracy (with no magnetic field) is removed by the presence of a magnetic field and the primary convection roll aligns itself so that its plane is perpendicular to the applied magnetic field. A cross over to another mode is also found when the strength of the magnetic field is increased. Velocity distributions are presented corresponding to the lowest modes and the system behavior within limit s of non-linearity is discussed.

Mazuruk, Konstantin↗
NASA NTRS1999

Mars Crustal Remanent Magnetism: An Extinct Dynamo Leaves a Record of Field Reversals in the Heavily Cratered Highlands

The Mars Global Surveyor spacecraft, in a highly elliptical polar orbit about Mars, obtained vector magnetic field measurements just above the surface of Mars (altitudes > 100 kilometers). Crustal magnetization, largely confined to the most ancient, heavily cratered Mars highlands, is frequently organized in east-west trending linear features, the largest of which extends over 2000 km. A representative set of survey passes are modeled using uniformly magnetized thin plates and a generalized inverse methodology. Crustal remanent magnetization exceeds that deduced for the largest terrestrial magnetic anomalies by more than an order of magnitude. Groups of quasi-parallel linear features of alternating magnetic polarity are found. They are reminiscent of similar magnetic features associated with sea floor spreading and crustal genesis on Earth but with a much larger spatial scale.

Connerney, John E.↗
NASA NTRS2000

Magnetically Actuated Propellant Orientation, Controlling Fluids in a Low-Gravity Environment

Cryogenic fluid management (CFM) is a technology area common to virtually every space transportation propulsion concept envisioned. Storage, supply, transfer and handling of sub-critical cryogenic fluids are basic capabilities that have long been needed by multiple programs and the need is expected to continue in the future. The use of magnetic fields provides another method, which could replace or augment current/traditional approaches, potentially simplifying vehicle operational constraints. The magnetically actuated propellant orientation (MAPO) program effort focused on the use of magnetic fields to control fluid motion as it relates to positioning (i.e. orientation and acquisition) of a paramagnetic substance such as LO2. Current CFM state- of-the-art systems used to control and acquire propellant in low gravity environments rely on liquid surface tension devices which employ vanes, fine screen mesh channels and baskets. These devices trap and direct propellant to areas where it's needed and have been used routinely with storable (non-cryogenic) propellants. However, almost no data exists r,egarding their operation in cryogenics and the use of such devices confronts designers with a multitude of significant technology issues. Typical problems include a sensitivity to screen dry out (due to thermal loads and pressurant gas) and momentary adverse accelerations (generated from either internal or external sources). Any of these problems can potentially cause the acquisition systems to ingest or develop vapor and fail. The use of lightweight high field strength magnets may offer a valuable means of augmenting traditional systems potentially mitigating or at least easing operational requirements. Two potential uses of magnetic fields include: 1) strategically positioning magnets to keep vent ports clear of liquid (enabling low G vented fill operations), and 2) placing magnets in the center or around the walls of the tank to create an insulating vapor pocket (between the liquid and the tank wall) which could effectively lower heat transfer to the liquid (enabling increased storage time).

Martin, James J.↗
NASA NTRS1999

Three-Dimensional Simulations of Electron Beams Focused by Periodic Permanent Magnets

A fully three-dimensional (3D) model of an electron beam focused by a periodic permanent magnet (PPM) stack has been developed. First, the simulation code MAFIA was used to model a PPM stack using the magnetostatic solver. The exact geometry of the magnetic focusing structure was modeled; thus, no approximations were made regarding the off-axis fields. The fields from the static solver were loaded into the 3D particle-in-cell (PIC) solver of MAFIA where fully 3D behavior of the beam was simulated in the magnetic focusing field. The PIC solver computes the time-integration of electromagnetic fields simultaneously with the time integration of the equations of motion of charged particles that move under the influence of those fields. Fields caused by those moving charges are also taken into account; thus, effects like space charge and magnetic forces between particles are fully simulated. The electron beam is simulated by a number of macro-particles. These macro-particles represent a given charge Q amounting to that of several million electrons in order to conserve computational time and memory. Particle motion is unrestricted, so particle trajectories can cross paths and move in three dimensions under the influence of 3D electric and magnetic fields. Correspondingly, there is no limit on the initial current density distribution of the electron beam, nor its density distribution at any time during the simulation. Simulation results including beam current density, percent ripple and percent transmission will be presented, and the effects current, magnetic focusing strength and thermal velocities have on beam behavior will be demonstrated using 3D movies showing the evolution of beam characteristics in time and space. Unlike typical beam optics models, this 3D model allows simulation of asymmetric designs such as non- circularly symmetric electrostatic or magnetic focusing as well as the inclusion of input/output couplers.

Kory, Carol L.↗
NASA NTRS1999

An Assessment of Magnetic Conditions for Strong Coronal Heating in Solar Active Regions by Comparing Observed Loops with Computed Potential Field Lines

We report further results on the magnetic origins of coronal heating found from registering coronal images with photospheric vector magnetograms. For two complementary active regions, we use computed potential field lines to examine the global non-potentiality of bright extended coronal loops and the three-dimensional structure of the magnetic field at their feet, and assess the role of these magnetic conditions in the strong coronal heating in these loops. The two active regions are complementary, in that one is globally potential and the other is globally nonpotential, while each is predominantly bipolar, and each has an island of included polarity in its trailing polarity domain. We find the following: (1) The brightest main-arch loops of the globally potential active region are brighter than the brightest main- arch loops of the globally strongly nonpotential active region. (2) In each active region, only a few of the mainarch magnetic loops are strongly heated, and these are all rooted near the island. (3) The end of each main-arch bright loop apparently bifurcates above the island, so that it embraces the island and the magnetic null above the island. (4) At any one time, there are other main-arch magnetic loops that embrace the island in the same manner as do the bright loops but that are not selected for strong coronal heating. (5) There is continual microflaring in sheared core fields around the island, but the main-arch bright loops show little response to these microflares. From these observational and modeling results we draw the following conclusions: (1) The heating of the main-arch bright loops arises mainly from conditions at the island end of these loops and not from their global non-potentiality. (2) There is, at most, only a loose coupling between the coronal heating in the bright loops of the main arch and the coronal heating in the sheared core fields at their feet, although in both the heating is driven by conditions/events in and around the island. (3) The main-arch bright loops are likely to be heated via reconnection driven at the magnetic null over the island. The details of how and where (along the null line) the reconnection is driven determine which of the split-end loops are selected for strong heating. (4) The null does not appear to be directly involved in the heating of the sheared core fields or in the heating of an extended loop rooted in the island. Rather, these all appear to be heated by microflares in the sheared core field.

Gary, G. A.↗
NASA NTRS2000

A Cryogenic Magnetostrictive Actuator Using a Persistent High Temperature Superconducting Magnet: Concept and Design - Part 1

Cryogenic magnetostrictive materials, such as rare earth zinc crystals, offer high strains and high forces with minimally applied magnetic fields, making the material ideally suited for deformable optics applications. For cryogenic temperature applications the use of superconducting magnets offer the possibility of a persistent mode of operation, i.e., the magnetostrictive material will maintain a strain field without power. High temperature superconductors (HTS) are attractive options if the temperature of operation is higher than 10 degrees Kelvin (K) and below 77 K. However, HTS wires have constraints that limit the minimum radius of winding, and even if good wires can be produced, the technology for joining superconducting wires does not exist. In this paper, the design and capabilities of a rare earth zinc magnetostrictive actuator using bulk HTS is described. Bulk superconductors can be fabricated in the sizes required with excellent superconducting properties. Equivalent permanent magnets, made with this inexpensive material, are persistent, do not require a persistent switch as in HTS wires, and can be made very small. These devices are charged using a technique which is similar to the one used for charging permanent magnets, e.g., by driving them into saturation. A small normal conducting coil can be used for charging or discharging. Because of the magnetic field capability of the superconductor material, a very small amount of superconducting magnet material is needed to actuate the rare earth zinc. In this paper, several designs of actuators using YBCO and BSCCO 2212 superconducting materials are presented. Designs that include magnetic shielding to prevent interaction between adjacent actuators will also be described. Preliminary experimental results and comparison with theory for BSCCO 2212 with a magnetostrictive element will be discussed.

Horner, Garnett↗
NASA NTRS2001

Experimental and Computational Studies of the Control of Convection of Non-Conducting Liquids During solidification by Means of a Magnetic Field Gradient

The elimination of convection is essential in experimental investigations of diffusive transport (of heat and matter) during solidification. One classical approach to damping convection in a conducting liquid is the application of a magnetic field. The damping phenomenon is the induction, by the motion of a conductor in a magnetic field, of currents which interact with the field to produce Lorentz forces that oppose the flow. However, there are many liquids which are not sufficiently conducting to exploit this phenomenon; examples include the transparent liquids (such as succinonitrile-acetone) that are used as "model alloys" in fundamental solidification studies. There have been several investigations of the solidification of these liquids that have been carried out in orbiting laboratories to eliminate natural convection. The paper describes an investigation of an alternative approach whereby a magnetic field gradient is applied to the liquid. A magnetic body force then arises which is dependent on the susceptibility of the liquid and thereby on the temperature and or concentration. With the field gradient aligned vertically and of correct magnitude, the variation of gravitational body force due to temperature/concentration dependent density can be counterbalanced by a variation in magnetic body force. Experiments have been carried out in a super-conducting magnet at Marshall Space Flight Center to measure velocities in an aqueous manganese chloride solution. The solution was contained in a chamber with temperature controlled end walls and glass side walls. Velocities were measured by particle image velocimetry. Starting from zero current in the magnet (zero field gradient) flow driven by the temperature difference between the end walls was measured. At a critical current the flow was halted. At higher currents the normal convection was reversed. The experiments included ones where the solution was solidified and were accompanied by solution of the flow/transport equations using the software package FLUENT.

Seybert, C. D.↗
NASA NTRS1998

The Parsec-Scale Magnetic Field Properties of Low-Optical Polarization Blazars

Past variability studies of flat-spectrum, compact extra-galactic radio sources have suggested that low- and high-optically polarized quasars (LPQ/HPQ) are the same type of object, differing only in the angle their relativistic jets make to the line of sight. This view has been challenged, however, by recent millimeter-wave polarization observations which indicate intrinsic differences in the inner magnetic field properties of the two classes. The inner jets of LPQs tend to have lower fractional polarizations than HPQs, and inferred magnetic field directions that are mostly parallel to the jet. The magnetic fields of HPQs, on the other hand, lie mainly in a transverse direction. The latter configuration is a prediction of the standard shock-in-jet model, in which a portion of a jet undergoes a strong transverse compression, thereby enhancing the perpendicular components of an originally tangled magnetic field. The main goal of this study is to establish a connection between the optical polarization and magnetic field properties of the inner jets of blazars. The magnetic field orientations of several HPQs have been shown to be stable over many years, which may be due to standing shock(s) located close to the base of the jet. Since these shocks are able to produce large amounts of optically polarized synchrotron radiation, their presence may very well determine whether an object is classified as an HPQ or LPQ. We have imaged the parsec-scale jet regions and magnetic fields of 11 LPQs with the Very Long Baseline Array (VLBA) at 43 and 22 GHz, and have obtained near- simultaneous optical polarization data for the sample. We discuss correlations between the optical and radio polarization data, and compare the LPQ properties to those of a sample of HPQs presently being monitored with the VLBA and JCMT at mm and sub-mm wavelengths, respectively. This research was performed in part at the Jet Propulsion Laboratory, California Institute of Technology, under contract to NASA.

Lister, Matthew L.↗
NASA NTRS2000

Reconnection Remnants in the Magnetic Cloud of October 18-19, 1995: A Shock, Monochromatic Wave, Heat Flux Dropout and Energetic Ion Beam

Evidence is presented that the WIND spacecraft observed particle and field signatures on October 18-19, 1995 due to reconnection near the footpoints of a magnetic cloud (i.e., between 1 and 5 solar radii). These signatures include: (1) an internal shock traveling approximately along the axis of the magnetic cloud, (2) a simple compression of the magnetic field consistent with the footpoint magnetic fields being thrust outwards at speeds much greater than the solar wind speed, (3) an electron heat flux dropout occurring within minutes of the shock indicating a topological change resulting from disconnection from the solar surface, (4) a very cold 5 keV proton beam and (5) an associated monochromatic wave. We expect that, given observations of enough magnetic clouds, Wind and other spacecraft will see signatures similar to the ones reported here indicating reconnection. However, these observations require the spacecraft to be fortuitously positioned to observe the passing shock and other signatures and will therefore be associated with only a small fraction of magnetic clouds. Consistent with this, a few magnetic clouds observed by Wind have been found to possess internal shock waves.

Collier, Michael R.↗
NASA NTRS1999

Magnetometer Data Tests Models for the Origin of the Martian Crustal Dichotomy; Dichotomy Models Constrain Timing of Martian Magnetic Field

Measurements recently supplied by the MGS Magnetometer/Electron Reflectometer (MAG/ER) on MGS can be applied to test theories of the origin of the martian crustal dichotomy. Strong (+/- 1500 nT) magnetic anomalies are observed in the Martian crust. The observations can be summarized as follows: 1) strong crustal magnetic sources are generally confined to the southern highlands, although weaker (approx. 40 nT) anomalies were observed during close periapsis; 2) strong magnetic anomalies are absent in the vicinity of Hellas and Argyre; 3) the anomalies in the region 0 deg to 90 deg S, 120 deg to 240 deg west have a linear geometry, strike generally east west for 1000s km, and show several reversals. This latter point has led to the suggestion that some form of lateral plate tectonics may have been operative in the southern highlands of Mars. These observations have led previous workers to hypothesize that the magnetic anomalies were present prior to and were destroyed by the formation of Hellas and Argyre. As such large impacts are confined to the era of heavy bombardment, this places the time of formation of large magnetic anomalies prior to approx. 3.9 Ga. One obvious extension of this is that the northern lowlands lack significant anomalies because they were erased by impacts and/or the northern lowlands represent crust completely reheated above the Curie temperature. Preliminary observations of the distributions of the large crustal magnetic anomalies show that many of them extend continuously over the highland lowland boundary. This occurs particularly north of the boundary between 30 deg W and 270 deg W, corresponding to northern Arabia, but also occurs in southern Elysium (approx. 10 deg S, 200 deg) and the SW portion of Tharsis (approx. 15 deg S, 140 deg). This suggests that, in these areas, Noachian crust containing the greater than 3.9 Ga magnetic signature, lies beneath the northern highlands. This geometry can be used to test models for the formation of the martian crustal dichotomy. Additional information is contained in the original extended abstract.

Gilmore, M. S.↗
NASA NTRS2001

Magnetic Field Structure of Pressure Balanced Structures from Ulysses High Latitudes Observations

Ulysses observations showed that pressure balance structures (PBSs) are a common feature in the high-latitude solar winds near the solar minimum. On the other hand, coronal plumes are common in polar coronal holes near the solar minimum. It is therefore considered that the PBSs would be remnants of plumes. Several detailed studies of the PBSs have been made from Ulysses/SWOOPS observations, but study of their magnetic structures has not yet been done. The study of the magnetic structure is important because previous observations and theoretical models of plumes indicate that they are related to the network activity such as magnetic reconnection on the photosphere. We have investigated the magnetic structures of the PBSs with Ulysses magnetometer and SWOOPS data. We have found that magnetic reversals in radial magnetic field take place while the spacecraft passes through most of the PBSs These magnetic reversals have been interpreted as large amplitude Alfv/'enic fluctuations but our results suggest that Ulysses is also traversing current sheets of plasmoids associated with network activity at the base of plumes.

Yamauchi, Y.↗
NASA NTRS2001

Flightweight Electro-Magnet Systems

NASA has a need for lightweight high performance magnets to be used in propulsion systems involving plasmas. We report the design, construction, and testing of a six inch diameter by twelve inch long solenoid using high purity aluminum wire operating at a temperature of 77 Kelvin (K) for the current carrying element. High purity aluminum is the material of choice because of three properties that make it optimal for magnetic construction. At 77 K high purity aluminum has one of the lowest resistivities at 77 K of any metal (p = 0.254 muOMEGA-cm), thus reducing the power requirements for creating magnetic fields. Aluminum is a low-density (2.6989 g/cc) material and the end product magnet will be of low total mass compared to similar designs involving copper or other elements. The magneto-resistance of aluminum saturates at low magnetic fields and does not increase indefinitely as is the case in copper. The magnet consists of four layers of closely wound wire and is approximately 150 mm in diameter by 300 mm long. A cylinder made from G - 10 was machined with a spiral groove to hold the high purity Al wire and the wire wound on it. Following the winding, each layer was potted in STYCAST high thermal conductivity epoxy to provide insulation between the turns of the coil and mechanical strength. The magneto-resistance of the coil has been measured at the National High Magnetic Field Laboratory (NHMFL), Tallahassee, FL in externally applied fields to 10 tesla. Following these tests it was energized to the full 2 tesla field it can produce using the facilities of the NHMFL at the Los Alamos National Laboratory. The results of all of these tests will be presented.

Goodrich, Roy G.↗
NASA NTRS2001

A 3-D Magnetic Analysis of a Stirling Convertor Linear Alternator Under Load

The NASA Glenn Research Center (GRC), the Department of Energy (DOE), and the Stirling Technology Company (STC) are developing Stirling convertors for Stirling Radioisotope Power Systems (SRPS) to provide electrical power for future NASA deep space missions. STC is developing the 55-We Technology Demonstration Convertor (TDC) under contract to DOE. Of critical importance to the successful development of the Stirling convertor for space power applications is the development of a lightweight and highly efficient linear alternator. This paper presents a 3-dimensional finite element method (FEM) approach for evaluating Stirling convertor linear alternators. The model extends a magnetostatic analysis previously reported at the 35th Intersociety Energy Conversion Engineering Conference (IECEC) to include the effects of the load current. STC's 55-We linear alternator design was selected to validate the model. Spatial plots of magnetic field strength (H) are presented in the region of the exciting permanent magnets. The margin for permanent magnet demagnetization is calculated at the expected magnet operating temperature for the near earth environment and for various average magnet temperatures. These thermal conditions were selected to represent a worst-case condition for the planned deep space missions. This paper presents plots that identify regions of high H where the potential to alter the magnetic moment of the magnets exists.

Geng, Steven M.↗
NASA NTRS2001

Continuous Magnetic Refrigerators for Cooling in the 0.05 to 10 K Range

Low temperature refrigeration is an increasingly vital technology for NASA's Space Science program since most detectors being developed for x-ray, IR and sub-millimeter missions must be cooled to below 100 mK in order to meet the requirements for energy and spatial resolution. For space applications, magnetic refrigeration has an inherent advantage over alternative techniques because it does not depend on gravity. Adiabatic demagnetization refrigerators, or ADRs, are relatively simple, solid state devices. The basic elements are a magnetocaloric refrigerant (usually an encapsulated paramagnetic salt) located in the bore of a superconducting magnet, and a heat switch linking the salt to a heat sink. The alignment of magnetic spins with the magnetic field causes the refrigerant to warm as the magnetic field increases and cool as the field decreases. Thus the simple process of magnetizing the refrigerant to high field with the heat switch closed, then demagnetizing it with the heat switch open allows one to obtain temperatures well below 100 mK using a heat sink as warm as 4.2 K. The refrigerant can maintain a low temperature for a length of time depending on the applied and parasitic heat loads, its mass, and the initial magnetic field strength. Typically ADRs are designed for 12-24 hours of hold time, after which they must be warmed up and recycled.

Shirron, Peter↗
NASA NTRS2001

Dynamic Magnetic Field Applications for Materials Processing

Magnetic fields, variable in time and space, can be used to control convection in electrically conducting melts. Flow induced by these fields has been found to be beneficial for crystal growth applications. It allows increased crystal growth rates, and improves homogeneity and quality. Particularly beneficial is the natural convection damping capability of alternating magnetic fields. One well-known example is the rotating magnetic field (RMF) configuration. RMF induces liquid motion consisting of a swirling basic flow and a meridional secondary flow. In addition to crystal growth applications, RMF can also be used for mixing non-homogeneous melts in continuous metal castings. These applied aspects have stimulated increasing research on RMF-induced fluid dynamics. A novel type of magnetic field configuration consisting of an axisymmetric magnetostatic wave, designated the traveling magnetic field (TMF), has been recently proposed. It induces a basic flow in the form of a single vortex. TMF may find use in crystal growth techniques such as the vertical Bridgman (VB), float zone (FZ), and the traveling heater method. In this review, both methods, RMF and TMF are presented. Our recent theoretical and experimental results include such topics as localized TMF, natural convection dumping using TMF in a vertical Bridgman configuration, the traveling heater method, and the Lorentz force induced by TMF as a function of frequency. Experimentally, alloy mixing results, with and without applied TMF, will be presented. Finally, advantages of the traveling magnetic field, in comparison to the more mature rotating magnetic field method, will be discussed.

Mazuruk, K.↗
NASA NTRS2001

High Power Thruster Based on Inductive Magnetized Plasmoid Acceleration

Regardless of the power source, deep space missions will require both high specific impulse (greater than 500 s) and high thrust power (greater than 100kW). These high Isp thrusters will need to have high electrical efficiency (approx. 90%) and low specific mass (alpha approximately less than 10 kg/kW) as well. Additionally they should have high thrust to allow greater mission flexibility. All these requirements can potentially be achieved with the pulsed formation and acceleration of magnetically self-confined plasmoids commonly referred to as compact toroids (CTs). An electromagnetic plasma thruster based on CT acceleration makes an ideal candidate for a high power, high Isp thruster, since the CT is magnetically isolated from the accelerator so that there is no contact between the propellant and the accelerator. The transfer of momentum to the CT occurs through an electromagnetic interaction with the magnetic field. By maintaining an axial magnetic field gradient across it, the directed velocity of the CT can be increased indefinitely. In previous experiments carried out at the University of Washington, CT's of near milligram mass were accelerated to velocities of 250 km/s in a single pulse. The ejection of the plasmoid by an external axial field also avoids the serious problem of detachment, which would occur in thrusters that employ a magnetic mirror or magnetic nozzle. To employ the CT for propulsion, one must design, construct and test a plasma source that is capable of generating a self-confined plasma inductively, and to do it repeatedly at a sufficiently high rep rate. A repetitively pulsed 100 kW level FRC thruster was built and was operated for short bursts at a 10 kHz rep rate and will be described. Another regime for the FRC thruster however is to produce an FRC in a more conventional manner at high voltage and magnetic field. With the large energy transfer with each pulse, the rep rate for this approach is much lower (approximately 100 Hz). This is the approach that is being evaluated at MSFC in the FAST experiment. The purpose of this experiment is to build an FRC thruster, measure its performance characteristics e.g. specific impulse, thrust, and efficiency. This experiment will also be described as well as various mission scenarios that that are well matched for this type of propulsion.

Slough, John↗
NASA NTRS1999

Tail Lobe Revisited: Magnetic Field Modeling Based on Plasma Data

Plasma data from the ISEE-1 and -2 spacecraft during 1977-1980 have been used to determine the distribution of data points in the magnetotail in the range of distances -20 < XGSM < --15, i.e. which of the records that were located in the current sheet, in the tail lobe, in the magnetosheath and in the boundary layers respectively. The ISEE-1 and -2 magnetic field data for the records in the tail lobe were then used to model the tail lobe magnetic field dependence on the solar wind dynamic pressure, on the Interplanetary Magnetic Field (IMF) and on the Dst index. The tail lobe magnetic field was assumed to be dependent on the square root of the dynamic pressure based on the balance between the total magnetic pressure in the tail lobes and the dynamic pressure of the solar wind. The IMF dependent terms, added to the pressure term, were sought in many different forms while the Dst dependence of the tail lobe magnetic field was assumed to be linear. The field shows a strong dependence on the square root of the dynamic pressure and the different IMF dependent terms all constitute a significant contribution to the total field. However, the dependence on the Dst index turned out to be very weak at those down-tail distances. The results of this study are intended to be used for parameterizing future versions of the data-based models of the global magnetospheric magnetic field.

Karlsson, S. B. P.↗
NASA NTRS2002

Interchange Method in Compressible Magnetized Couette Flow: Magnetorotational and Magnetoconvective Instabilities

We obtain the general forms of the axisymmetric stability criteria in a magnetized compressible Couette flow using an energy variational principle, the so-called interchange or Chandrasekhar s met hod, which we applied successfully in the incompressible case. This formulation accounts for the simultaneous presence of gravity, rotation, a toroidal magnetic field, a weak axial magnetic field, entropy gradients, and density gradients in the initial equilibrium state. The power of the method lies in its simplicity which allows us to derive extremely compact and physically clear expressions for the relevant stability criteria despite the inclusion of so many physical effects. In the implementation of the method, all the applicable conservation laws are explicitly taken into account during the variations of a quantity with dimensions of energy which we call the free energy function. As in the incompressible case, the presence of an axial field invalidates the conservation laws of angular momentum and azimuthal magnetic flux and introduces instead isorotation and axial current conservation along field lines. Our results are therefore markedly different depending on whether an axial magnetic field is present, and generalize in two simple expressions all previously known, partial stability criteria for the appearance of magnetorotational instability. Furthermore, the coupling between magnetic tension and buoyancy and its influence to the dynamics of nonhomoentropic magnetized flows becomes quite clear from our results. In the limits of plane-parallel atmospheres and homoentropic flows, our formulation easily recovers the stability criteria for suppression of convective and Parker instabilities, as well as some related special cases studied over 40 years ago by Newcomb and Tserkovnikov via laborious variational techniques.

Christodoulou, Dimitris M.↗