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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Quasi-seasonal variation in the sun

The results of an investigation on the effects of earth seasonal changes on solar activity, particularly sunspots, are given. These results show corpuscular and electromagnetic activity increased during the equinoctial months. In addition the electromagnetic aspect tends to increase during the winter months. It was suggested that seasonal changes in sunspot numbers may be caused by the tidal forces and the processional torques exerted by the various planets in the solar atmosphere.

Chandra, S.↗
NASA NTRS1986

Physics through the 1990s: Elementary-particle physics

The volume begins with a non-mathematical discussion of the motivation behind, and basic ideas of, elementary-particle physics theory and experiment. The progress over the past two decades with the quark model and unification of the electromagnetic and weak interactions is reviewed. Existing theoretical problems in the field, such as the origin of mass and the unification of the fundamental forces, are detailed, along with experimental programs to test the new theories. Accelerators, instrumentation, and detectors are described for both current and future facilities. Interactions with other areas of both theoretical and applied physics are presented. The sociology of the field is examined regarding the education of graduate students, the organization necessary in large-scale experiments, and the decision-making process involved in high-cost experiments. Finally, conclusions and recommendations for maintaining US excellence in theory and experiment are given. Appendices list both current and planned accelerators, and present statistical data on the US elementary-particle physics program. A glossary is included.

Source record↗
NASA NTRS2012

Space Telescopes

Space telescopes have been a dominant force in astrophysics and astronomy over the last two decades. As Lyman Spitzer predicted in 1946, space telescopes have opened up much of the electromagnetic spectrum to astronomers, and provided the opportunity to exploit the optical performance of telescopes uncompromised by the turbulent atmosphere. This special section of Optical Engineering is devoted to space telescopes. It focuses on the design and implementation of major space observatories from the gamma-ray to far-infrared, and highlights the scientific and technical breakthroughs enabled by these telescopes. The papers accepted for publication include reviews of major space telescopes spanning the last two decades, in-depth discussions of the design considerations for visible and x-ray telescopes, and papers discussing concepts and technical challenges for future space telescopes.

Clampin, Mark↗
NASA NTRS2006

Modern Design of Resonant Edge-Slot Array Antennas

Resonant edge-slot (slotted-waveguide) array antennas can now be designed very accurately following a modern computational approach like that followed for some other microwave components. This modern approach makes it possible to design superior antennas at lower cost than was previously possible. Heretofore, the physical and engineering knowledge of resonant edge-slot array antennas had remained immature since they were introduced during World War II. This is because despite their mechanical simplicity, high reliability, and potential for operation with high efficiency, the electromagnetic behavior of resonant edge-slot antennas is very complex. Because engineering design formulas and curves for such antennas are not available in the open literature, designers have been forced to implement iterative processes of fabricating and testing multiple prototypes to derive design databases, each unique for a specific combination of operating frequency and set of waveguide tube dimensions. The expensive, time-consuming nature of these processes has inhibited the use of resonant edge-slot antennas. The present modern approach reduces costs by making it unnecessary to build and test multiple prototypes. As an additional benefit, this approach affords a capability to design an array of slots having different dimensions to taper the antenna illumination to reduce the amplitudes of unwanted side lobes. The heart of the modern approach is the use of the latest commercially available microwave-design software, which implements finite-element models of electromagnetic fields in and around waveguides, antenna elements, and similar components. Instead of building and testing prototypes, one builds a database and constructs design curves from the results of computational simulations for sets of design parameters. The figure shows a resonant edge-slot antenna designed following this approach. Intended for use as part of a radiometer operating at a frequency of 10.7 GHz, this antenna was fabricated from dimensions defined exclusively by results of computational simulations. The final design was found to be well optimized and to yield performance exceeding that initially required.

Gosselin, R. B.↗
NASA NTRSDate not supplied

Magnetohydrodynamics (MHD) Aerocapture System for Enabling Faster-Larger Planetary Science & Human Exploration Missions

Since our completing the NIAC Phase I NIAC on this Advanced Aerocapture System, NASA Langley Research Center has funded or supported a number of studies and code enhancements through its Center Innovation Fund (CIF) and NASA’s NSTGRO and Internship Programs to mature the analysis capabilities and quantify the merits of the MHD Aerocapture System technology. These efforts have resulted in a plug and play analysis capability for assessing MHD aerocapture system performance for arrival at many planetary bodies of interest. Our efforts have especially focused on the potential mass savings for improving the capacity for science observations at Neptune and Triton. A re-cent Forbes article published “‘Orbital mechanics is probably going to decide for us whether we go to Uranus or Neptune because we need to flyby Jupiter,’ said Kunio Sayanagi at Hampton University, Virginia, who also worked on the Neptune Odyssey proposal…. Exactly when a mission can be sent to Uranus, or Neptune, depends on the relative position of Jupiter, which can help give a spacecraft a gravitational slingshot. That drastically shortens the cruise phase.” [1] Since shortening the cruise phase is important for these science missions, any mass savings enabled by the MHD Aerocapture System could be reallocated to increasing Thermal Protection System mass to allow faster arrival speeds and/or for onboarding additional payloads such as science instruments, batteries, or propellant for conducting more science for longer durations in the desired orbits. The analysis steps and codes for conducting trades and sizing vehicles for aerocapture are as follows: Step 1 is to conduct aeroheating analysis using LAURA of the selected entry vehicle shape to identify locations on the forebody where ionization and flow velocity are sufficient for producing Lo-rentz forces. LAURA is a multiblock structured grid finite-volume CFD solver developed at the NASA Langley Research Center. [2] LAURA has been used for aerothermal analysis support of the entry, de-scent and landing (EDL) phase of interplanetary missions over the last three decades [3-7]. Step 2 is to port the LAURA results into CFDWARP to calcu-late electrical and thermal conductivities of ionized flow for sizing MHD patch system and calculating Lorentz forces needed for controls analysis. CFDWARP is a CFD code that uses advanced nu-merical methods that enable the simulation of the full coupling between the aerodynamics, the magne-tohydrodynamics, and the non-neutral plasma sheaths. CFDWARP has the unique capability to simulate efficiently the non-neutral sheaths (near the electrodes) in coupled form with the quasi-neutral bulk MHD flow [8-11]. Step 3 is to link re-sults from LAURA and CFDWARP into POST2 for calculating entry trajectories and comparing MHD control results with other aerodynamic control strategies. The Program to Optimize Simulated Tra-jectories II (POST2) is a generalized point mass, discrete parameter targeting and optimization pro-gram. POST2 provides the capability to target and optimize point mass trajectories for multiple pow-ered or un-powered vehicles near an arbitrary rotat-ing, oblate planet [12]. Step 4: TPS sizing was per-formed using the Fully Implicit Ablation and Ther-mal-response code (FIAT) tool which computes the transient one-dimensional thermal response and surface thermochemistry of a multilayer stackup of thermal protection, bonding, and structural materi-als subject to aeroheating on one surface [13]. The sizing and margining methodology used was based on the approach documented by Mahzari and Milos [14] for the dual-layered heatshield for extreme entry environment technology (DL-HEEET) TPS concept. TPS analysis utilizes trajectory information from POST2. Using this step-wise plug and play MHD Aerocapture performance assessment process, our analysis targets a Neptune aerocapture trajectory that will place the spacecraft in an observation orbit for Triton. [15]. Magnetohydrodynamic (MHD) control of a 4.5-meter diameter MSL-style capsule resulted in TPS mass savings of nearly 2000 kg when using an MHD system mass of under 200 kg. The flight path for a vehicle using the MHD control strategy has a much lower heat rate and heat load compared to the conventional aerodynamic aerocapture strategies known as bank angle con-trolled (BAC) and direct force controlled (DFC). Both BAC and DFC have heat rates significantly greater than 1500 W/cm2 typically used as an upper limit for PICA. Thus, DL-HEEET TPS concept was required for the BAC and DFC control strategies. However, considering the more benign environ-ments for the MHD case, additional TPS concepts with improved mass efficiency were also assessed. PICA was considered for the MHD controlled strat-egy since the maximum heat rate was well within the limits (<1500 W/cm2) of PICA. TPS sizing re-sulted in a significant mass reduction. The PICA layer for this sizing case was about 7.8 cm. As a point of reference, the Mars 2020 mission, which used this same PICA concept, had a PICA thickness of 3.18 cm [16]. The trajectories used for the TPS sizing originat-ed from the POST2 simulations. The current, I, to an electromagnet configuration can be manipulated to allow for active control of the vehicle. Manipula-tion of the current, I, changes the magnetic field, B, which affects the Lorentz force and therefore the MHD drag force on the vehicle. Our analysis in-cluded both open-loop and close-loop control. Closed-loop control will enable improved overall performance when taking into account mission level uncertainties, such as interplanetary delivery errors and atmospheric modeling uncertainties. The open-loop and closed-loop MHD control cases do not dip as deep into the atmosphere as the aerodynamic cases. Three types of aerodynamic-only approach-es are investigated: bank angle modulation (BAM), director force control (DFC), and Drag Modulated. BAM and DFC make use of vehicle aerodynamic angles to steer the vehicle. Thus, changing the aer-odynamic forces acting on the vehicle for control, aerodynamic drag modulated case requires a vary-ing drag area to modulate the drag force. The MHD drag modulated case modulates MHD generated drag force that adds to the aerodynamic drag. This higher atmospheric activation of drag forces by the MHD patch results in significantly less heat flux on the vehicle. The MHD technology will enable shorter cruise times and deceleration of larger payloads for increasing the capacity for science at the Ice Giants or for returning astronauts to Earth from cislunar space or from Mars. The purpose of this presentation is to provide more details about this work and to highlight plans for further research and development including a flight demonstration.

R. W. Moses↗
DOE OSTI2015

Silver nanoparticles on nanopatterned LiF(110) surface studied by extreme ultraviolet light scattering

A LiF(110) surface featuring a ridge-and-valley nanopatterned structure periodic along the [−1,1,0] direction (period and height of the order of 30 nm and 10 nm, respectively) formed by [001] macrosteps exposing (100) and (010) facets was functionalized by rows of Ag nanoparticles and studied by elastic light scattering in the energy range 50–100 eV. Families of diffraction efficiencies curves were taken at grazing incidence angle and fixed photon energy as a function of scattering angle, and elastic scattering curves were taken at fixed scattering angle as a function of energy. The scattering curves presented well-defined features ascribable to the periodicities of the surface, or equivalently to the reciprocal q{sub X} vectors correlated with the power spectral density features of topological images of atomic force microscopy. Other characteristics of the functionalized surface, including the height of ridge-valley profile, the Ag nanoparticle dimensions, and the material distribution in the scattering plane, were obtained by fitting the experimental zero and first order efficiency curves to simulation results of a parameterized model. The simulations were carried out adapting an in-house code based on the electromagnetic differential method, and the different material properties were taken into account by a space dependent complex dielectric constant. Information along the direction perpendicular to the scattering plane was not accessible but morphological insights were obtained combining light diffraction with atomic force microscopy. The results indicate nanoparticles with a quasi-ellipsoidal shape prolate along the ridge direction with minor and major axes of ∼12 nm and ∼21 nm, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Transport phenomena in electrolyte solutions: Nonequilibrium thermodynamics and statistical mechanics

The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and nonequilibrium thermodynamics. The governing equations of irreversible thermodynamics, including balance laws, Maxwell's equations, internal entropy production, and linear laws relating the thermodynamic forces and fluxes, are derived. Green–Kubo relations for the transport coefficients connecting electrochemical potential gradients and diffusive fluxes are obtained in terms of the flux–flux time correlations. Furthermore, the relationship between the derived transport coefficients and those of the Stefan–Maxwell and infinitely dilute frameworks are presented, and the connection between the transport matrix and experimentally measurable quantities is described. To exemplify the application of the derived Green–Kubo relations in molecular simulations, the matrix of transport coefficients for lithium and chloride ions in dimethyl sulfoxide is computed using classical molecular dynamics and compared with experimental measurements.

42 ENGINEERING↗
DOE OSTI2019

Higgs Parity, strong CP and dark matter

An exact spacetime parity replicates the $SU(2) \times U(1)$ electroweak interaction, the Higgs boson $H$, and the matter of the Standard Model. This "Higgs Parity" and the mirror electroweak symmetry are spontaneously broken at scale $v' = \left\langle{H'} \right\rangle \gg \left\langle{H}\right\rangle$, yielding the Standard Model below $v'$ with a quartic coupling that essentially vanishes at $v'$: $\lambda_{SM}(v') \sim 10^{-3}$. The strong CP problem is solved as Higgs parity forces the masses of mirror quarks and ordinary quarks to have opposite phases. Dark matter is composed of mirror electrons, $e'$, stabilized by unbroken mirror electromagnetism. These interact with Standard Model particles via kinetic mixing between the photon and the mirror photon, which arises at four-loop level and is a firm prediction of the theory. Physics below $v'$, including the mass and interaction of $e'$ dark matter, is described by $\textit{one fewer parameter}$ than in the Standard Model. The allowed range of $m_{e'}$ is determined by uncertainties in $(\alpha_s, m_t, m_h)$, so that future precision measurements of these will be correlated with the direct detection rate of $e'$ dark matter, which, together with the neutron electric dipole moment, will probe the entire parameter space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Cartan gravity, matter fields, and the gauge principle

Gravity is commonly thought of as one of the four force fields in nature. However, in standard formulations its mathematical structure is rather different from the Yang–Mills fields of particle physics that govern the electromagnetic, weak, and strong interactions. This paper explores this dissonance with particular focus on how gravity couples to matter from the perspective of the Cartan-geometric formulation of gravity. There the gravitational field is represented by a pair of variables: (1) a ‘contact vector’ V{sup A} which is geometrically visualized as the contact point between the spacetime manifold and a model spacetime being ‘rolled’ on top of it, and (2) a gauge connection A{sub μ}{sup AB}, here taken to be valued in the Lie algebra of SO(2,3) or SO(1,4), which mathematically determines how much the model spacetime is rotated when rolled. By insisting on two principles, the gauge principle and polynomial simplicity, we shall show how one can reformulate matter field actions in a way that is harmonious with Cartan’s geometric construction. This yields a formulation of all matter fields in terms of first order partial differential equations. We show in detail how the standard second order formulation can be recovered. In particular, the Hodge dual, which characterizes the structure of bosonic field equations, pops up automatically. Furthermore, the energy–momentum and spin-density three-forms are naturally combined into a single object here denoted the spin-energy–momentum three-form. Finally, we highlight a peculiarity in the mathematical structure of our first-order formulation of Yang–Mills fields. This suggests a way to unify a U(1) gauge field with gravity into a SO(1,5)-valued gauge field using a natural generalization of Cartan geometry in which the larger symmetry group is spontaneously broken down to SO(1,3)×U(1). The coupling of this unified theory to matter fields and possible extensions to non-Abelian gauge fields are left as open questions. -- Highlights: •Develops Cartan gravity to include matter fields. •Coupling to gravity is done using the standard gauge prescription. •Matter actions are manifestly polynomial in all field variables. •Standard equations recovered on-shell for scalar, spinor and Yang–Mills fields. •Unification of a U(1) field with gravity based on the orthogonal group SO(1,5)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

A review of high magnetic moment thin films for microscale and nanotechnology applications

Here, the creation of large magnetic fields is a necessary component in many technologies, ranging from magnetic resonance imaging, electric motors and generators, and magnetic hard disk drives in information storage. This is typically done by inserting a ferromagnetic pole piece with a large magnetisation density M S in a solenoid. In addition to large M S , it is usually required or desired that the ferromagnet is magnetically soft and has a Curie temperature well above the operating temperature of the device. A variety of ferromagnetic materials are currently in use, ranging from FeCo alloys in, for example, hard disk drives, to rare earth metals operating at cryogenic temperatures in superconducting solenoids. These latter can exceed the limit on M S for transition metal alloys given by the Slater-Pauling curve. This article reviews different materials and concepts in use or proposed for technological applications that require a large M S , with an emphasis on nanoscale material systems, such as thin and ultra-thin films. Attention is also paid to other requirements or properties, such as the Curie temperature and magnetic softness. In a final summary, we evaluate the actual applicability of the discussed materials for use as pole tips in electromagnets, in particular, in nanoscale magnetic hard disk drive read-write heads; the technological advancement of the latter has been a very strong driving force in the development of the field of nanomagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Sub-photospheric Shocks in Relativistic Explosions

This paper examines the mechanism of internal shocks in opaque relativistic outflows, in particular in cosmological gamma-ray bursts. The shocks produce neutrino emission and affect the observed photospheric radiation from the explosion. They develop from internal compressive waves and can be of different types depending on the composition of the outflow. (1) Shocks in “photon gas,” with negligible plasma inertia, have a unique structure determined by the force-free condition—zero radiation flux in the plasma rest frame. Radiation dominance over plasma inertia suppresses the formation of collisionless shocks mediated by collective electromagnetic fields. (2) If the outflow is sufficiently magnetized, a strong collisionless subshock develops, which is embedded in a thicker radiation-mediated structure. (3) Waves in outflows with a free neutron component lead to dissipation through nuclear collisions. At large optical depths, shocks have a thickness comparable to the neutron free path, with embedded radiation-mediated and collisionless subshocks. The paper also presents first-principles simulations of magnetized flows filled with photons, demonstrating the formation of shocks and their structure. Simple estimates show that magnetized sub-photospheric shocks are efficient producers of photons and have a great impact on the observed photospheric radiation. The shock structure changes as the outflow expands toward its photosphere. The dissipation is accompanied by strong e{sup ±} pair creation, and the e{sup ±}-dressed shock carries the photosphere with it up to two decades in radius, emitting a strong pulse of nonthermal radiation.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

A new hydrodynamic analysis of double layers

A genuine two-fluid model of plasmas with collisions permits the calculation of dynamic (not necessarily static) electric fields and double layers inside of plasmas including oscillations and damping. For the first time a macroscopic model for coupling of electromagnetic and Langmuir waves was achieved with realistic damping. Starting points were laser-produced plasmas showing very high dynamic electric fields in nonlinear force-produced cavitous and inverted double layers in agreement with experiments. Applications for any inhomogeneous plasma as in laboratory or in astrophysical plasmas can then be followed up by a transparent hydrodynamic description. Results are the rotation of plasmas in magnetic fields and a new second harmonic resonance, explanation of the measured inverted double layers, explanation of the observed density-independent, second harmonics emission from laser-produced plasmas, and a laser acceleration scheme by the very high fields of the double layers.

Hora, Heinrich↗
NASA NTRS2002

Engines for the Cosmos

Galactic forces spiral across the cosmos fueled by nuclear fission and fusion and atoms in plasmatic states with throes of constraints of gravitational forces and magnetic fields, In their wanderings these galaxies spew light, radiation, atomic and subatomic particles throughout the universe. Throughout the ages of man visions of journeying through the stars have been wondered. If humans and human devices from Earth are to go beyond the Moon and journey into deep space, it must be accomplished with like forces of the cosmos such as electrical fields, magnetic fields, ions, electrons and energies generated from the manipulation of subatomic and atomic particles. Forms of electromagnetic waves such as light, radio waves and lasers must control deep space engines. We won't get far on our Earth accustomed hydrocarbon fuels.

Rodgers, Stephen L.↗
NASA NTRS2013

Doppler Lidar System Design via Interdisciplinary Design Concept at NASA Langley Research Center - Part I

Optimized designs of the Navigation Doppler Lidar (NDL) instrument for Autonomous Landing Hazard Avoidance Technology (ALHAT) were accomplished via Interdisciplinary Design Concept (IDEC) at NASA Langley Research Center during the summer of 2013. Three branches in the Engineering Directorate and three students were involved in this joint task through the NASA Langley Aerospace Research Summer Scholars (LARSS) Program. The Laser Remote Sensing Branch (LRSB), Mechanical Systems Branch (MSB), and Structural and Thermal Systems Branch (STSB) were engaged to achieve optimal designs through iterative and interactive collaborative design processes. A preliminary design iteration was able to reduce the power consumption, mass, and footprint by removing redundant components and replacing inefficient components with more efficient ones. A second design iteration reduced volume and mass by replacing bulky components with excessive performance with smaller components custom-designed for the power system. Mechanical placement collaboration reduced potential electromagnetic interference (EMI). Through application of newly selected electrical components and thermal analysis data, a total electronic chassis redesign was accomplished. Use of an innovative forced convection tunnel heat sink was employed to meet and exceed project requirements for cooling, mass reduction, and volume reduction. Functionality was a key concern to make efficient use of airflow, and accessibility was also imperative to allow for servicing of chassis internals. The collaborative process provided for accelerated design maturation with substantiated function.

Boyer, Charles M.↗
DOE OSTI2015

SU-E-E-08: Applications of the Quantization of Coupled Circuits in Radiation Physics (design of Klystron, Bremsstrahlung, Synchrotron)

Purpose: During the past decade the quantization of coupled/forced electromagnetic circuits with or without Ohm’s resistance has gained the subject of some fundamental studies, since even problems of quantum electrodynamics can be solved in an elegant manner, e.g. the creation of quantized electromagnetic fields. In this communication, we shall use these principles to describe optimization procedures in the design of klystrons, synchrotron irradiation and high energy bremsstrahlung. Methods: The base is the Hamiltonian of an electromagnetic circuit and the extension to coupled circuits, which allow the study of symmetries and perturbed symmetries in a very apparent way (SU2, SU3, SU4). The introduction resistance and forced oscillators for the emission and absorption in such coupled systems provides characteristic resonance conditions, and atomic orbitals can be described by that. The extension to virtual orbitals leads to creation of bremsstrahlung, if the incident electron (velocity v nearly c) is described by a current, which is associated with its inductivitance and the virtual orbital to the charge distribution (capacitance). Coupled systems with forced oscillators can be used to amplify drastically the resonance frequencies to describe klystrons and synchrotron radiation. Results: The cross-section formula for bremsstrahlung given by the propagator method of Feynman can readily be derived. The design of klystrons and synchrotrons inclusive the radiation outcome can be described and optimized by the determination of the mutual magnetic couplings between the oscillators induced by the currents. Conclusions: The presented methods of quantization of circuits inclusive resistance provide rather a straightforward way to understand complex technical processes such as creation of bremsstrahlung or creation of radiation by klystrons and synchrotrons. They can either be used for optimization procedures and, last but not least, for pedagogical purposes with regard to a qualified understanding of radiation physics for students.

43 PARTICLE ACCELERATORS↗
NASA NTRS1996

Design of a Long-Stroke Noncontact Electromagnetic Actuator for Active Vibration Isolation

A long-stroke moving coil Lorentz Actuator was designed for use in a microgravity vibration isolation experiment. The final design had a stroke of 5.08 cm (2 in) and enough force capability to isolate a mass of the order of 22.7-45.4 kg. A simple dynamic magnetic circuit analysis, using an electrical analog, was developed for the initial design of the actuator. A neodymium-iron-boron material with energy density of 278 T-kA/m (35 MGOe) was selected to supply the magnetic field. The effect of changes in the design parameters of core diameter, shell outer diameter, pole face length, and coil wire layers were investigated. An extensive three-dimensional finite element analysis was carried out to accurately determine linearity with regard to axial position of the coil and coil current levels. The actuator was constructed and tested on a universal testing machine. Example plots are shown, indicating good linearity over the stroke of approximately 5.08 cm (2 in) and a range of coil currents from -1.5 A to +1.5 A. The actuator was then used for the microgravity vibration isolation experiments, described elsewhere.

Banerjee, Bibhuti↗
DOE OSTI2020

Transformation of Spinors in Accelerators and Beam Transfer Lines

The stable spin direction and the spin tune are two important concepts used when polarized beams are transferred along beam lines or circulating in an accelerator. One of the methods to calculate the stable spin direction and the spin tune of the reference particle of a polarized beam bunch is by integrating simultaneously the Lorentz Force $\vec{F}$ = q($\vec{E}$ +$\vec{v}$ x $\vec{B}$) and the BMT equation of the reference particle as it is transported by the magnets of a beam line or accelerator. A modified version of the Raytrace code was used to integrate the Lorentz equation and the BMT equation. Using the spin motion which is governed by the BMT equation one can compute both, the stable spin direction of the reference particle at any point along the reference orbit of an accelerator or a beam line, and the spin tune of the closed orbit in an accelerator. The simultaneous integration of the Lorentz force and of the BMT equation is the most accurate method to calculate the trajectory and the spin motion of a charged particle moving in an electromagnetic field, however this method requires the accurate description of the electromagnetic fields of the elements in which the charged particles are moving. An alternative method of calculating the stable spin direction and the spin tune of spin ½ charged particles along the reference trajectory of a beam line or an accelerator is the transformation of the spinor which is the wavefunction of spin ½ particles. This method requires the knowledge of the stable spin direction of each element of the beam line or the accelerator. This technical note describes the “spinor-method” to calculate the stable-spin- direction and the spin-tune of a spin ½ particle moving along the reference trajectory of a beam line or an accelerator.

43 PARTICLE ACCELERATORS↗