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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Synchronization of magnetic stars in binary systems

Asynchronous rotation of magnetic stars in close binary systems drives substantial field-aligned electrical currents between the magnetic star and its companion. The resulting magnetohydrodynamic torque is able to account for the heretofore unexplained synchronous rotation of the strongly magnetic degenerate dwarf component in systems like AM Her, VV Pup, AN UMa, and EF Eri as well as the magnetic A type component in systems like HD 98088 and 41 Tauri. The electric fields produced by even a small asynchronism are large and may accelerate some electrons to high energies, producing radio emission. The total energy dissipation rate in systems with degenerate dwarf spin periods as short as 1 minute may reach 10 to the 33rd ergs/s. Total luminosities of this order may be a characteristic feature of such systems.

Lamb, F. K.↗
DOE OSTI2021

Dynamic Symmetry Breaking in Chiral Magnetic Systems

The Dzyaloshinskii–Moriya interaction (DMI) in magnetic systems stabilizes spin textures with preferred chirality, applicable to next-generation memory and computing architectures. In perpendicularly magnetized heavy-metal/ferromagnet films, the interfacial DMI originating from structural inversion asymmetry and strong spin-orbit coupling favors chiral Néel-type domain walls (DWs) whose energetics and mobility remain at issue. Thus, a new effect is characterized in which domains expand unidirectionally in response to a combination of out-of-plane and in-plane magnetic fields, with the growth direction controlled by the in-plane field strength. These growth directionalities and symmetries with applied fields cannot be understood from static treatments alone. The authors theoretically demonstrate that perpendicular field torques stabilize steady-state magnetization profiles highly asymmetric in elastic energy, resulting in a dynamic symmetry breaking consistent with the experimental findings. This phenomenon sheds light on the mechanisms governing the dynamics of Néel-type DWs and expands the utility of field-driven DW motion to probe and control chiral DWs.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Induced Anisotropy in FeCo-Based Nanocrystalline Ferromagnetic Alloys (HITPERM) by Very High Field Annealing

Very high magnetic field annealing is shown to affect the magnetic anisotropy in FeCo-base nanocrystalline soft ferromagnetic alloys. Alloys of composition Fe(44.5)Co(44.5)Zr(7)B(4) were prepared by melt spinning into amorphous ribbons, then wound to form toroidal bobbin cores. One set of cores was crystallized in a zero field at 600 deg. C for 1 h, then, field annealed at 17 tesla (T) at 480 deg. C for 1 h. Another set was crystallized in a 17-T field at 480 deg. C for 1 h. Field orientation was transverse to the magnetic path of the toroidal cores. An induced anisotropy is indicated by a sheared hysteresis loop. Sensitive torque magnetometry measurements with a Si cantilever sensor indicated a strong, uniaxial, longitudinal easy axis in the zero-field-crystallized sample. The source is most likely magnetoelastic anisotropy, caused by the residual stress from nanocrystallization and the nonzero magnetostriction coefficient for this material. The magnetostrictive coefficient lambda(5) is measured to be 36 ppm by a strain gage technique. Field annealing reduces the magnitude of the induced anisotropy. Core loss measurements were made in the zero-field-crystallized, zero-field-crystallized- than-field-annealed, and field-crystallized states. Core loss is reduced 30%-50% (depending on frequency) by field annealing. X-ray diffraction reveals no evidence of crystalline texture or orientation that would cause the induced anisotropy. Diffusional pair ordering is thought to be the cause of the induced anisotropy. However, reannealing the samples in the absence of a magnetic field at 480 deg. C does not completely remove the induced anisotropy.

FERROMAGNETIC ALLOYS↗
NASA NTRS1979

Flexible stator control on the Galileo spacecraft

Galileo is a dual-spin spacecraft designed to deliver a probe to Jupiter and then orbit the planet. The stator, or despun section, contains four flexible modes below 10 Hz and the despun actuator is separated from the inertial sensors by this flexibility. Control loop separation by bandwidth proved unacceptable due to performance requirements. To obtain the desired performance, a control scheme was devised which consists of three parts. First, flexibility damping and control notch filtering are accomplished by phase locked loop techniques. Second, slewing maneuvers are produced by torque profiles which are nonexcitatory to the structure. Finally, a low bandwidth perturbation controller is supplied to remove spacecraft disturbances.

Kopf, E. H.↗
NASA NTRS2014

Timing and Flux Evolution of the Galactic Center Magnetar SGR J1745-2900

We present the X-ray timing and spectral evolution of the Galactic Center magnetar SGR J1745-2900 (SGR*) for the first 4 months post-discovery using data obtained with the Nuclear Spectroscopic Telescope Array (NuSTAR) and Swift observatories. Our timing analysis reveals a large increase in the magnetar spin-down rate by a factor of 2.6 plus or minus 0.07 over our data span. We further show that the change in spin evolution was likely coincident with a bright X-ray burst observed in 2013 June by Swift, and if so, there was no accompanying discontinuity in the frequency. We find that the source 3 to 10 kiloelectronvolt flux has declined monotonically by a factor of approximately 2 over an 80-day period post-outburst accompanied by an approximately 20 percent decrease in the source's blackbody temperature, although there is evidence for both flux and kiloteslas having leveled off. We argue that the torque variations are likely to be magnetospheric in nature and will dominate over any dynamical signatures of orbital motion around Sgr A*.

Stars: magnetic field↗
DOE OSTI2021

Surpassing the Energy Resolution Limit with Ferromagnetic Torque Sensors

We discuss the fundamental noise limitations of a ferromagnetic torque sensor based on a levitated magnet in the tipping regime. We evaluate the optimal magnetic field resolution taking into account the thermomechanical noise and the mechanical detection noise at the standard quantum limit. We find that the energy resolution limit, pointed out in recent literature as a relevant benchmark for most classes of magnetometers, can be surpassed by many orders of magnitude. Moreover, similarly to the case of a ferromagnetic gyroscope, it is also possible to surpass the standard quantum limit for magnetometry with independent spins, arising from spin-projection noise. Our finding indicates that magnetomechanical systems optimized for magnetometry can achieve a magnetic field resolution per unit volume several orders of magnitude better than any conventional magnetometer. Here, we discuss possible implications, focusing on fundamental physics problems such as the search for exotic interactions beyond the standard model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

In-flight identification of the Galileo spacecraft flexible mode characteristics

The Galileo scan platform is controlled in two degrees of freedom. A clock (Spin Bearing) actuator controls the relative position between the rotor and stator, and a cone actuator controls the position between the stator and the platform. Instruments on the platform are required to point to 140 micro-rad accuracy and 50 micro-rad per second stability. The system identification objectives were to identify dominant structural resonance frequencies, mode shapes, and damping ratio which exist in the transfer function between the clock actuator and the gyro sensor; and position the notch filter to limit undesirable actuator torque output to ensure stability and performance.

Wong, Edward C.↗
NASA NTRS1986

Semi-analytical theory for long-term rotational motion of uncontrolled satellites

Analytical solutions/integrals of the free rotational motion of uncontrolled satellites which contain spinning rotors are employed in conjunction with a suitable analytical/numerical averaging approach to predict long-term attitude motion. This semi-analytical method of averaging is basically similar to the one used in purely analytical 'general perturbation' theories. However, in view of the complexities involved in analytical treatment of the problem, its application is primarily numerical in character. An example is presented illustrating the use of the theory to predict the attitude motion of an axisymmetric satellite containing symmetrical constant-speed rotors under gravity-gradient torque. The use of the theory is considerably more efficient than straightforward numerical integration of the complete set of equations of motion.

Lahr, B. S.↗
DOE OSTI2023

Mechanical Analysis of Carbon Fiber Retaining Sleeve for A High-speed Outer Rotor SPM Electric Motor Design

Outer rotor motors can be designed with a larger airgap diameter than inner rotor motors for the same overall diameter and therefore provide higher torque which makes them ideal for high torque space constrained applications. This advantage fits well with the increasing demand of high-speed electric machines in many applications due to their inherent high-power density. However, increasing the motor speed results in significant centrifugal loads for the outer rotor motor design. Layers of carbon fiber sleeve winding on the rotor outer surface is necessary to guarantee its structural integrity without introducing too much weight on the motor itself. In this paper, we studied the mechanical stress of a carbon fiber retaining sleeve in a surface permanent magnet outer rotor motor that spins up to 20,000 RPM. Analytical results from finite element method (FEM) confirmed that the maximum stress experienced by the carbon fiber sleeve was under the material’s yield strength. The proposed sleeve will allow this outer rotor motor to operate at high speeds.

Lin, Lianshan↗
DOE OSTI2020

Optical matter machines: angular momentum conversion by collective modes in optically bound nanoparticle arrays

The creation of optically powered self-assembling nano-to-meso-scale machines that do work is a long-standing goal in photonics. We demonstrate an optical matter (OM) machine that converts the spin angular momentum (SAM) of light into orbital angular momentum (OAM) to do mechanical work. The specific OM machine we study is based on a sixfold symmetric hexagonally ordered nanoparticle array that operates as an OM “gear” that is assembled and made to rotate in a circularly polarized Gaussian beam. The rotational symmetry of the OM gear leads to a selection rule for the allowed scattering modes based on their angular momentum. Electrodynamics calculations show that the collective scattering modes with the largest angular momentum scatter strongly in the transverse direction. Simulations and experiments show that the angular momentum that accompanies the scattered light causes a “negative torque” response on the OM gear and drives a “probe” particle placed outside the OM gear around the gear in an asymmetric force field analogously to Brownian ratchets. The gear–probe OM machine concept can be expanded to applications in nanofluidics and particle sorting.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2001

SRS Computer Animation and Drive Train System

The spinning rocket simulator (SRS) is an ongoing project at Oral Roberts University. The goal of the SRS is to gather crucial data concerning a spinning rocket under thrust for the purpose of analysis and correction of the coning motion experienced by this type of spacecraft maneuver. The computer animation simulates a virtual, scale model of the component of the SRS that represents the spacecraft itself. This component is known as the (VSM), or virtual spacecraft model. During actual physical simulation, this component of the SRS will experience a coning. The goal of the animation is to cone the VSM within that range to accurately represent the motion of the actual simulator. The drive system of the SRS is the apparatus that turns the actual simulator. It consists of a drive motor, motor mount and chain to power the simulator into motion. The motor mount is adjustable and rigid for high torque application. A digital stepper motor controller actuates the main drive motor for linear acceleration. The chain transfers power from the motor to the simulator via sprockets on both ends.

Arthun, Daniel↗
NASA NTRS2002

Spin-Up Instability of a Levitated Molten Drop in MHD-Flow Transition to Turbulence

When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. In this work, a background of these set of observations will be given followed by a presentation of our results on the digital particle tracking analysis that has been performed on a number of available videos. The analysis indicates that the levitated drop attains a constant rotational speed during the melting phase and formation of the co-rotating axi-symmetric laminar toroidal structures. However, the rate of axial rotation increases dramatically during the deformation of the toroidal structures anti their breakup into chaotic entities. This new data suggests an interaction between the flow inside the levitated molten drop and the driving coils in the experiments. Possible mechanisms for this interaction will be reviewed. The data will also be used to make an assessment of existing theories on droplet rotation.

Abedian, B.↗
NASA NTRS2001

Large Aperture Scanning Lidar Based on Holographic Optical Elements

Lidar remote sensing instruments can make a significant contribution to satisfying many of the required measurements of atmospheric and surface parameters for future spaceborne platforms, including topographic altimeters, atmospheric profiles of, wind, humidity, temperature, trace molecules, aerosols, and clouds. It is highly desirable to have wide measurement swaths for rapid coverage rather than just the narrow ribbon of data that is obtained with a nadir only observation. For most applications global coverage is required, and for wind measurements scanning or pointing is required in order to retrieve the full 3-D wind vector from multiple line-of-sight Doppler measurements. Conventional lidar receivers make up a substantial portion of the instrument's size and weight. Wide angle scanning typically requires a large scanning mirror in front of the receiver telescope, or pointing the entire telescope and aft optics assembly, Either of these methods entails the use of large bearings, motors, gearing and their associated electronics. Spaceborne instruments also need reaction wheels to counter the torque applied to the spacecraft by these motions. NASA has developed simplified conical scanning telescopes using Holographic Optical Elements (HOEs) to reduce the size, mass, angular momentum, and cost of scanning lidar systems. NASA has developed two operating lidar systems based on 40 cm diameter HOEs. The first such system, named Prototype Holographic Atmospheric Scanner for Environmental Remote Sensing (PHASERS) was a joint development between NASA Goddard Space Flight Center (GSFC) and the University of Maryland College Park. PHASERS is based on a reflection HOE for use at the doubled Nd:YAG laser wavelength of 532 nm and has recently undergone a number of design changes in a collaborative effort between GSFC and Saint Anselm College in New Hampshire. The next step was to develop IR transmission HOEs for use with the Nd:YAG fundamental in the Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE). The HOE spins like a compact disk in a large ring ball bearing. In an aircraft the HOE faces down, looking out through a window at an angle of 45 degrees off-nadir. The HOE diffracts 85% of the incident 532 nm light into a 160 micron spot at a focal length of 1 meter. HARLIE is a field deployable lidar measuring aerosol, cloud, and boundary layer backscatter for atmospheric research. It has flown several times and is also used from a ground-based trailer in an upward-looking mode. The HOE generates a 45 degree conical scan pattern by rotating at speeds up to 30 rpm. Like PHASERS, the HOE in HARLIE serves both as the laser collimating lens as well as the receiver telescope primary optic. The telescope is coupled to the receiver package via fiber optic. The transmitter is a diode pumped Nd:YAG laser operating at 1064 nm, delivering 1 mJ pulses at a 5 KHz rep-rate. The receiver has a 200 microradian field-of-view and a 0.5 nm optical bandpass. The photon counting data system utilizes a single Geiger-mode silicon avalanche photodiode detector, This new technology has also presented us with new data visualization challenges as well as new measurement techniques. The backscatter data obtained from a stationary (i.e. ground-based) scanning HOE lidar is on the surface of a cone, which when viewed over many consecutive scans can reveal atmospheric motions on this surface over time as the atmosphere advects over the site. In a moving platform such as an airplane or satellite, the data from consecutive scans cover different areas under the flight path, revealing atmospheric structure in 3-dimensions. An example of a visualization of HARLIE ground-based data is presented, showing aerosol backscatter on a 90 degree conical surface generated from one 360 degree scan of the lidar during the HOLO-1 field campaign on the afternoon of 10 March 1999. Higher backscatter levels are rendered as lighter signal against a dark background. Breaking Kelvin-Helmholtz waves are evident on the north side of the scan at an altitude of 10-11 km. Time series of successive scans made at regular intervals render unique views of atmospheric motions, from which vertical profiles of atmospheric wind vectors can be obtained using a unique data analysis approach. Wind vectors obtained from the lidar were compared with co-located radiosonde wind profiles during an intensive operating period in September-October 2000 at the Atmospheric Radiation Measurement Program's Southern Great Plains Central Facility.

Schwemmer, Geary K.↗
DOE OSTI2022

Magnetoquantum oscillations in the specific heat of a topological Kondo insulator

Surprisingly, magnetoquantum oscillations (MQOs) characteristic of a metal with a Fermi surface have been observed in measurements of the topological Kondo insulator SmB 6 . As these MQO have only been observed in measurements of magnetic torque (dHvA) and not in measurements of magnetoresistance (SdH), a debate has arisen as to whether the MQO are an extrinsic effect arising from rare-earth impurities, defects, and/or aluminum inclusions or an intrinsic effect revealing the existence of charge-neutral excitations. In this work, we report the first observation of MQO in the low-temperature specific heat of SmB 6 . The observed frequencies and their angular dependence for these flux-grown samples are consistent with previous results based on magnetic torque for SmB 6 but the inferred effective masses are significantly larger than previously reported. Such oscillations can only be observed if the MQO are of bulk thermodynamic origin; the measured magnetic-field dependent oscillation amplitude and effective mass allow us to rule out suggestions of an extrinsic, aluminum inclusion-based origin for the MQO.

topological materials↗
DOE OSTI2024

"Hall" transport of liquid crystal solitons in Couette flow

Topology establishes a unifying framework for a diverse range of scientific areas including particle physics, cosmology, and condensed matter physics. One of the most fascinating manifestations of topology in the context of condensed matter is the topological Hall effect, and its relative: the Skyrmion Hall effect. Skyrmions are stable vortex-like spin configurations in certain chiral magnets, and when subject to external electric currents can drift in the transverse direction to the current. These quasi-particles are characterised by a conserved topological charge which in the Skyrmion Hall effect plays the role of electric charges in the ordinary Hall effect. Recently, it has been shown that liquid crystals endowed with chiral properties serve as an ideal testbed for the fundamental investigation of topological solitons, including their two- and three-dimensional realisations. Here, we show experimentally and numerically that three-dimensional solitons aka "torons" exhibit a Hall-like effect when driven by shear flows: the torons are deflected in the direction perpendicular to the shear plane. The experimental results are rationalised in terms of the dynamic Ericksen-Leslie equations, which predict the emergence of the transverse component of the net mass flow, the magnitude of which scales as the 3rd power of the shear rate. The perturbation analysis highlights an interplay of the viscous and chiral elastic torques as the mechanism for the emergence of net transverse currents. Numerical simulations demonstrate, however, that torons are not merely dragged by the flow but move with their own transverse speed, much larger than the average flow velocity in the transverse direction. Our findings may enable responsive microfluidic applications relying on soft topological solitons.

FOS: Physical sciences↗
NASA NTRS1972

The stability of motion of satellites with flexible appendages

The mathematical formulation associated with the problem of stability of motion of a satellite consisting of a main rigid body and three (or less) pairs of flexible rods is presented. The rods are capable of flexure in two orthogonal directions. Whereas the rotational motion of the body is described by generalized coordinates depending on time alone, the elastic displacements of the rods depend both on spatial position and time. Assuming no external torques, there exist motion integrals in the form of momentum integrals. These integrals can be regarded as constraint equations relating the system velocities, and used to reduce the number of variables describing the motion. The stability analysis has been carried out by means of an extension of the Liapunov direct method. Since the elastic vibrations result in energy dissipation, it is shown that the equilibrium position is asymptotically stable if the Hamiltonian is positive definite and unstable if it can take negative values in the neighborhood of the equilibrium. Determining the sign definiteness of the Hamiltonian is complicated by the fact that it contains spatial derivatives of the elastic displacements. Two methods are presented to cope with this problem. The first, the standard modal analysis in conjunction with series truncation, develops criteria in terms of infinite series associated with the natural modes and frequencies of the elastic rods. The second, the method of integral coordinates, yields closed-form stability criteria involving the system parameters, such as the body moments of inertia, the length and mass distribution of the rods, the lowest natural frequencies of the rods, and the satellite spin velocity.

Meirovitch, L.↗
NASA NTRS2013

The Complex Spin State of 103P-Hartley 2: Kinematics and Orientation in Space

We derive the spin state of the nucleus of Comet 103P/Hartley 2, its orientation in space, and its short-term temporal evolution from a mixture of observations taken from the DIXI (Deep Impact Extended Investigation) spacecraft and radar observations. The nucleus is found to spin in an excited long-axis mode (LAM) with its rotational angular momentum per unit mass, M, and rotational energy per unit mass, E, slowly decreasing while the degree of excitation in the spin increases through perihelion passage. M is directed toward (RA, Dec; J2000) = 8+/-+/- 4 deg., 54 +/- 1 deg. (obliquity = 48 +/- 1 deg.). This direction is likely changing, but the change is probably <6 deg. on the sky over the approx. 81.6 days of the DIXI encounter. The magnitudes of M and E at closest approach (JD 2455505.0831866 2011-11-04 13:59:47.310) are 30.0 +/- 0.2 sq. m/s and (1.56 +/- 0.02) X 10(exp -3) sq. m /sq. s respectively. The period of rotation about the instantaneous spin vector, which points in the direction (RA, Dec; J2000) = 300 +/- 3.2deg., 67 +/- 1.3 deg. at the time of closest approach, was 14.1 +/- 0.3 h. The instantaneous spin vector circulates around M, inclined at an average angle of 33.2 +/- 1.3 deg. with an average period of 18.40 +/- 0.13 h at the time of closest approach. The period of roll around the principal axis of minimum inertia (''long'' axis) at that time is 26.72 +/- 0.06 h. The long axis is inclined to M by approx. 81.2 +/- 0.6 deg. on average, slowly decreasing through encounter. We infer that there is a periodic nodding motion of the long axis with half the roll period, i.e., 13.36+/- 0.03 h, with amplitude of 1 again decreasing through encounter. The periodic variability in the circulation and roll rates during a cycle was at the 2% and 10-14% level respectively. During the encounter there was a secular lengthening of the circulation period of the long axis by 1.3 +/- 0.2 min/d, in agreement with ground-based estimates, while the period of roll around the long axis changed by approx. -4.4 min/d at perihelion. M decreased at a rate of 0.038 (sq m/s) per day in a roughly linear fashion. Assuming a bulk density between 230-300 kg/m3 and a total volume for the nucleus of 8.09 X 10(exp 8) cubic m, the net torque acting on the nucleus was in the range 0.8-1.1 X 10(exp 5) kg m(exp 2) /s(exp 2). In order to bring the spacecraft photometric and imaging data into alignment on the direction of M, the directions of the intermediate and short principal axes of inertia had to be adjusted by 33 deg (on the sky) from the values indicated by the shape model with an assumed homogeneous interior. The adjusted direction of the intermediate axis is RA, Dec = 302 deg., -16.5 deg.. The morning and evening terminators in the images are identified, and the variation of the insolation at three regions on the nucleus associated with active areas calculated. The plume of water vapor observed in the inner coma is found to be directed close to the direction of local gravity over the sub-solar region for a range of reasonable bulk densities. The plume does not follow the projected normal to the surface at the sub-solar point.

Comets↗
NASA NTRS1995

Double core evolution. 7: The infall of a neutron star through the envelope of its massive star companion

Binary systems with properties similar to those of high-mass X-ray binaries are evolved through the common envelope phase. Three-dimensional simulations show that the timescale of the infall phase of the neutron star depends upon the evolutionary state of its massive companion. We find that tidal torques more effectively accelerate common envelope evolution for companions in their late core helium-burning stage and that the infall phase is rapid (approximately several initial orbital periods). For less evolved companions the decay of the orbit is longer; however, once the neutron star is deeply embedded within the companion's envelope the timescale for orbital decay decreases rapidly. As the neutron star encounters the high-density region surrounding the helium core of its massive companion, the rate of energy loss from the orbit increases dramatically leading to either partial or nearly total envelope ejection. The outcome of the common envelope phase depends upon the structure of the evolved companion. In particular, it is found that the entire common envelope can be ejected by the interaction of the neutron star with a red supergiant companion in binaries with orbital periods similar to those of long-period Be X-ray binaries. For orbital periods greater than or approximately equal to 0.8-2 yr (for companions of mass 12-24 solar mass) it is likely that a binary will survive the common envelope phase. For these systems, the structure of the progenitor star is characterized by a steep density gradient above the helium core, and the common envelope phase ends with a spin up of the envelope to within 50%-60% of corotation and with a slow mass outflow. The efficiency of mass ejection is found to be approximately 30%-40%. For less evolved companions, there is insufficient energy in the orbit to unbind the common envelope and only a fraction of it is ejected. Since the timescale for orbital decay is always shorter than the mass-loss timescale from the common envelope, the two cores will likely merge to form a Thorne-Zytkow object. Implications for the origin of Cyg X-3, an X-ray source consisting of a Wolf-Rayet star and a compact companion, and for the fate of the remnant binary consisting of a helium star and a neutron star are briefly discussed.

Terman, James L.↗