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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at NASA’s Marshall Space Flight Center have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. The probe also includes the ability to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL Finite Element Analysis and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller thatmitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

controls↗
NASA NTRSDate not supplied

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere-Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at National Aeronautics and Space Administration’s (NASA’s) Marshall Space Flight Center (MSFC) have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. We have also used high temperature ovens to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL finite element analysis (FEA) and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller that mitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

reaction sphere↗
DOE OSTI2021

Interaction of radio frequency waves with cylindrical density filaments: scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas , vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci. , vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

Physics↗
DOE OSTI2022

Interaction of radio frequency waves with cylindrical density filaments -- scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Nanoscale three-dimensional reconstruction of electric and magnetic stray fields around nanowires

Static electromagnetic stray fields around nanowires (NWs) are characteristic for a number of important physical effects such as field emission or magnetic force microscopy. Consequently, an accurate characterization of these fields is of high interest and electron holographic tomography (EHT) is unique in providing tomographic 3D reconstructions at nm spatial resolution. However, several limitations of the experimental setup and the specimen itself are influencing EHT. Here, we show how a deliberate restriction of the tomographic reconstruction to the exterior of the NWs can be used to mitigate these limitations facilitating a quantitative 3D tomographic reconstruction of static electromagnetic stray fields at the nanoscale. As an example, we reconstruct the electrostatic stray field around a GaAs-AlGaAs core shell NW and the magnetic stray field around a Co{sub 2}FeGa Heusler compound NW.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2013

Strong Casimir force reduction through metallic surface nanostructuring

The Casimir force between bodies in vacuum can be understood as arising from their interaction with an infinite number of fluctuating electromagnetic quantum vacuum modes, resulting in a complex dependence on the shape and material of the interacting objects. Becoming dominant at small separations, the force has a significant role in nanomechanics and object manipulation at the nanoscale, leading to a considerable interest in identifying structures where the Casimir interaction behaves significantly different from the well-known attractive force between parallel plates. Here we experimentally demonstrate that by nanostructuring one of the interacting metal surfaces at scales below the plasma wavelength, an unexpected regime in the Casimir force can be observed. Replacing a flat surface with a deep metallic lamellar grating with sub-100 nm features strongly suppresses the Casimir force and for large inter-surfaces separations reduces it beyond what would be expected by any existing theoretical prediction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Spectrum of relativistic radiation from electric charges and dipoles as they fall freely into a black hole

The motion of electric charges and dipoles falling radially and freely into a Schwarzschild black hole is considered. The inverse effect of the electromagnetic fields on the black hole is neglected. Since the dipole is assumed to be a point particle, the deformation due to the action of tidal forces on it is neglected. According to the theorem stating that 'black holes have no hair', the multipole electromagnetic fields should be completely radiated as a multipole falls into a black hole. The electromagnetic radiation power spectrum for these multipoles (a monopole and a dipole) has been found. Differences have been found in the spectra for different orientations of the falling dipole. A general method has been developed to find the radiated multipole electromagnetic fields for multipoles (including higher-order multipoles-quadrupoles, etc.) falling freely into a black hole. The calculated electromagnetic spectra can be compared with observational data from stellar-mass and smaller black holes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

A computer model of the electrostatic positioning system

Positioning systems based upon electrstatic forces are being developed for the containerless processing of materials that cannot use acoustic or electromagnetic positioning techniques. Currently, electrode configurations for these electrostatic systems are designed on the basis of approximate analytical calculations and past experience. A three dimensional computer model is being developed that will predict the electrostatic fields and forces for a given electrode configuration and will allow for a more rapid evaluation of proposed designs. Early results of this model are presented.

Gutt, G. M.↗
DOE OSTI2022

Noniterative finite amplitude methods for E 1 and M 1 giant resonances

The finite amplitude method (FAM) is a very efficient approach for solving the fully self-consistent random-phase approximation (RPA) equations. We use FAM to rederive the RPA matrices for Skyrme functionals, calculate the electric dipole ( E 1) and the magnetic dipole ( M 1) giant resonances, and compare the results with available experimental and evaluated data. For the E 1 transitions in heavy nuclei, the calculations reproduce well the resonance energy of the photoabsorption cross sections. In the case of M 1 transitions, we show that the residual interaction does not affect the transition strength of double-magic nuclei, which suggests that the spin terms in the Skyrme force currently neglected in the present computation could improve the agreement between FAM and experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Enhancement of EM Pump Performance through Modeling and Testing

Liquid sodium has seen development as a nuclear reactor coolant in the United States for over 50 years. While sodium has many desirable characteristics as a heat transfer fluid, its reactivity poses numerous engineering challenges for even the most basic plant components like pumps. Despite the challenges, mechanical pumps have seen success in sodium service albeit at the expense of simplicity and flexibility. In fact, significant failures of these pumps have been recorded which can be attributed to their complexity. Notwithstanding the complexity, mechanical pumps are still widely proposed for the main circuit pump of sodium cooled reactors. However, an alternative to mechanical pumps are Electromagnetic Induction Pumps (EMIPs) which use the principle of the Lorentz Force. EMIPs avoid mechanically moving parts in contact with sodium which simplifies the design by avoiding mechanical wear and seals. Therefore, these pumps are generally safer and more reliable than their mechanical counterparts. That being said, EMIPs suffer from relatively low efficiencies that range from 5% to 45%. Some of the inefficiencies are inherent to the EMIPs pumps; namely, inefficiencies arise in the form of resistive heating losses in the fluid itself. However, other inefficiencies arise from Edge Effects which include Finite Length and Finite Width effects. Due to the significant safety advantages EMIPs have compared to mechanical pumps, there is a strong motivation to integrate these technologies into the design of Generation IV liquid-metal-cooled nuclear power plants. However, EMIPs have low efficiencies partly attributed to Edge Effects. Much of the literature focusing on Edge Effects is dated or simply does not exist in the public domain. More recently, numerical models of EMIPs have shown promising results. However, these models are often custom solvers or use complex software suits which limit their application. This report describes the work completed to understand Edge Effects in two EMIPs designs. These designs are the Annular Linear Induction Pump (ALIP) and Permanent Magnet Induction Pump (PMIP) also known as a Moving Magnet Pump (MMP). The methodology developed during this project aim at measuring key performance parameters (pressure-flowrate and efficiency-slip performance) using high temperature liquid-sodium. Baseline experimental measurements were then used to verify the accuracy of numerical models developed in the software suit ANSYS/FLUENT. On the experimental side, instrumentation was developed to characterize the pressure-flowrate and efficiency-slip performance of both the ALIP and PMIP in high-temperature liquid-sodium. Additionally, instrumentation was developed to measure potential output pressure pulsations and the magnetic field distributions. Moreover, a specialized ALIP was constructed to study the impacts magnetic field tapering, also known as coil grading, on the Finite Length Effect. Lastly, experimental performance curves of the PMIP were collected at 300 oC and 600 oC and compared to analytical theory which accounted for Finite Width Effects. These results showed that the Finite Width Effect and non-uniform magnetic field in a PMIP impact the performance. On the numerical side, models were developed using the software suit FLUENT/ANSYS. These methods were initially compared against a simple MHD flow in a Permanent Magnet Electromagnet Flowmeter (PMEMFM). The results were significant in that they showed agreeance between the numerical model and demonstrated that PMEMFM’s could be calibrated numerically. These modeling methods were then applied to a prototypic PMIP. Results showed that this simple model provided reasonably accurate results of the PMIP p-Q performance.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2012

Photonic band gaps in one-dimensional magnetized plasma photonic crystals with arbitrary magnetic declination

In this paper, the properties of photonic band gaps and dispersion relations of one-dimensional magnetized plasma photonic crystals composed of dielectric and magnetized plasma layers with arbitrary magnetic declination are theoretically investigated for TM polarized wave based on transfer matrix method. As TM wave propagates in one-dimensional magnetized plasma photonic crystals, the electromagnetic wave can be divided into two modes due to the influence of Lorentz force. The equations for effective dielectric functions of such two modes are theoretically deduced, and the transfer matrix equation and dispersion relations for TM wave are calculated. The influences of relative dielectric constant, plasma collision frequency, incidence angle, plasma filling factor, the angle between external magnetic field and +z axis, external magnetic field and plasma frequency on transmission, and dispersion relation are investigated, respectively, and some corresponding physical explanations are also given. From the numerical results, it has been shown that plasma collision frequency cannot change the locations of photonic band gaps for both modes, and also does not affect the reflection and transmission magnitudes. The characteristics of photonic band gaps for both modes can be obviously tuned by relative dielectric constant, incidence angle, plasma filling factor, the angle between external magnetic field and +z axis, external magnetic field and plasma frequency, respectively. These results would provide theoretical instructions for designing filters, microcavities, and fibers, etc.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1986

Electromagnetic Hammer for Metalworking

High eddy currents apply pressure for cold-forming. Coil housing constructed for mechanical strength to hold coil against magnetic force, to maintain electrical contact with coil ends, and to maintain insulation between coil turns. Drilled holes placed to facilitate release of bubbles during potting. In contrast with mechanical hammers, electromagnetic hammer requires no dynamic material contact with workpiece; consequently, produces almost no change in metal grain structure.

Anderson, S. A.↗
DOE OSTI2023

Coulomb-free 1S0 p − p scattering length from the quasi-free p + d → p + p + n reaction and its relation to universality

Abstract The Coulomb-free 1 S 0 proton-proton ( p - p ) scattering length relies heavily on numerous and distinct theoretical techniques to remove the Coulomb contribution. Here, it has been determined from the half-off-the-energy-shell p - p scattering cross section measured at center-of-mass energies below 1 MeV using the quasi-free p + d → p + p + n reaction. A Bayesian data-fitting approach using the expression of the s-wave nucleon-nucleon scattering cross section returned a p - p scattering length $${a}_{pp}=-18.1{7}_{-0.58}^{+0.52}{| }_{stat}\pm 0.0{1}_{syst}$$ a p p = − 18.1 7 − 0.58 + 0.52 ∣ s t a t ± 0.0 1 s y s t fm and effective range r 0 = 2.80 ± 0.05 s t a t ± 0.001 s y s t fm. A model based on universality concepts has been developed to interpret this result. It accounts for the short-range interaction as a whole, nuclear and residual electromagnetic, according to what the s-wave phase-shift δ does in the description of low-energy nucleon-nucleon scattering data. We conclude that our parameters are representative of the short-range physics and propose to assess the charge symmetry breaking of the short-range interaction instead of just the nuclear interaction. This is consistent with the current understanding that the charge dependence of nuclear forces is due to different masses of up-down quarks and their electromagnetic interactions. This achievement suggests that these properties have a lesser than expected impact in the context of the charge symmetry breaking.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Towards modelling AR Sco: generalized particle dynamics and strong radiation-reaction regimes

Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is especially highlighted in pulsar modelling due to the extreme associated electromagnetic fields and particle Lorentz factors. Including the radiation-reaction force in the particle dynamics adds even more complexity to the problem, but is crucial for such extreme astrophysical sources. We have also realized the need for such modelling concerning magnetic mirroring and particle injection models proposed for AR Sco, the first white dwarf pulsar. This paper demonstrates the benefits of using higher-order explicit numerical integrators with adaptive time-step methods to solve the full particle dynamics with radiation-reaction forces included. We show that for standard test scenarios, namely various combinations of uniform E- and B-fields and a static dipole B-field, the schemes we use are equivalent to and in extreme field cases outperform standard symplectic integrators in accuracy. We show that the higher-order schemes have massive computational time improvements due to the adaptive time-steps we implement, especially in non-uniform field scenarios and included radiation reaction where the particle gyro-radius rapidly changes. When balancing accuracy and computational time, we identified the adaptive Dormand–Prince eighth-order scheme to be ideal for our use cases. The schemes we use maintain accuracy and stability in describing the particle dynamics and we indicate how a charged particle enters radiation-reaction equilibrium and conforms to the analytical Aristotelian Electrodynamics expectations.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2002

Integration and Test Flight Validation Plans for the Pulsed Plasma Thruster Experiment on EO- 1

The Pulsed Plasma Thruster (PPT) Experiment on the Earth Observing One (EO-1) spacecraft has been designed to demonstrate the capability of a new generation PPT to perform spacecraft attitude control. The PPT is a small, self-contained pulsed electromagnetic propulsion system capable of delivering high specific impulse (900-1200 s), very small impulse bits (10-1000 uN-s) at low average power (less than 1 to 100 W). Teflon fuel is ablated and slightly ionized by means of a capacitative discharge. The discharge also generates electromagnetic fields that accelerate the plasma by means of the Lorentz Force. EO-1 has a single PPT that can produce thrust in either the positive or negative pitch direction. The flight validation has been designed to demonstrate of the ability of the PPT to provide precision pointing accuracy, response and stability, and confirmation of benign plume and EMI effects. This paper will document the success of the flight validation.

Zakrzwski, Charles↗
DOE OSTI2021

Measurement of Parity Violating Asymmetry in Elastic Electron Scattering off 48Ca

Atomic nuclei are composed of nucleons governed by the strong nuclear force. Although the proton distributions in nuclei are well measured with electromagnetic probes, the neutron distributions are relatively unconstrained. The nuclear symmetry energy governs the distribution of the excess neutrons in asymmetric nuclei, as well as the dynamics of neutron-rich nuclear matter up to the scale of neutron stars….

Clarke, Cameron↗
NASA NTRS1987

Shear flow instability generated by non-homogeneous external forcing

An experiment has been designed and conducted in order to ascertain whether instability waves can be generated by nonhomogeneous forcing, using a biconvex vane located outside the mixing layer whose oscillation was induced by an electromagnetic shaker through a linkage. The vane was oscillated at 20 Hz, and the resulting spectra were computed by a spectrum analyzer. The data are judged to provide an example of instability waves generated solely through nonhomogeneous forcing.

Durbin, P. A.↗
DOE OSTI2016

A field theory approach to the evolution of canonical helicity and energy

A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗