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Results for “Guiding center motion”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Relativistic Guiding-Center Motion: Action Principle, Kinetic Theory and Hydrodynamics

We treat the guiding-center dynamics in a varying external Maxwell field using a relativistically covariant action principle which reproduces the known Vandervoort expression for the drift velocity and extends it to curved spacetime. We derive the corresponding kinetic theory and ideal hydrodynamic theory. In contrast to conventional five-equation hydrodynamics, the guiding-center hydrodynamics needs only three equations due to a constraint on the motion across magnetic field. Furthermore, we argue that such a hydrodynamics is applicable to strongly coupled plasmas where kinetic theory fails.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field

It is pointed out that the conventional Lie transform perturbation theory for the guiding center motion of charged particles in a magnetic field needs to be modified for ordering inconsistency. There are two reasons. First, the ordering difference between the temporal variation of gyrophase and that of the other phase space coordinates needs to be taken into account. Second, it is also important to note that the parametric limit of the derivative of a function is not equivalent to the derivative of the limit function. When these facts are taken into account, the near identity transformation rule for one form related to the Lagrangian is modified. With the modified near identity transformation rule, the drift motion of charged particles can be described in the first order, instead of the second order and beyond through a tedious expansion process as in the conventional formulation. Here, this resolves the discrepancy between the direct and Lie transform treatments in the Lagrangian perturbation theory for charged particle motion in a magnetic field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Response to “Comment on ‘Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field’” [Phys. Plasmas 30 , 104701 (2023)]

Dr. Brizard's comment on my work is based on a conceived procedure that does not come from my work. The defense of his claim that the modification of the so-called standard Lie's transform theory is unnecessary is also unsupported. This response reveals in detail the inconsistency issues in the so-called standard Lie's transform theory by analyzing both its results and root causes. The problem in the so-called standard Lie's transform theory is beyond the issue to take into account the ordering difference between the guiding center motion and gyromotion. Here, the inconsistent commutation of derivative and limit causes another issue. In addition, the so-called standard Lie's transform formulation leads to an unnecessarily lengthy and tedious derivation process for a one or two page task under the singular (or renormalized) formalism described in my paper.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Some mathematics for quasi-symmetry

Quasi-symmetry of a steady magnetic field means integrability of first-order guiding-center motion by a spatial symmetry. Here, we derive many restrictions on the possibilities for a quasi-symmetry. We also derive an analog of the Grad–Shafranov equation for the flux function in a quasi-symmetric magnetohydrostatic field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics

Since variational symplectic integrators for the guiding center was proposed, structure-preserving geometric algorithms have become an active research field in plasma physics. We found that the slow manifolds of the classical Pauli particle enable a family of structure-preserving geometric algorithms for guiding center dynamics with long-term stability and accuracy. This discovery overcomes the difficulty associated with the unstable parasitic modes for variational symplectic integrators when applied to the degenerate guiding center Lagrangian. It is a pleasant surprise that Pauli's Hamiltonian for electrons, which predated the Dirac equation and marks the beginning of particle physics, reappears in classical physics as an effective algorithm for solving an important plasma physics problem. This technique is applicable to other degenerate Lagrangians reduced from regular Lagrangians.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

High order interpolation of magnetic fields with vector potential reconstruction for particle simulations

We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides C(m) continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincaré section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Lastly, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Drift orbit islands of energetic particles due to 3D fields in ITER

In this study, we report a comparative study of the orbit islands formed by the guiding center drift motion of test energetic particles (EPs), including both high-energy deuterium ions and fusion-born α-particles, with respect to the magnetic islands formed by tracing the field lines, for an ITER plasma representing the 15 MA baseline scenario. The particle drift orbit is modified by the presence of static resonant magnetic perturbations (RMPs) of different toroidal mode numbers n (n = 1 and 3 in this study), forming orbit islands in the Poincaré plane by passing EPs. The key findings are as follows. (i) With an n = 1 RMP field, the size of the orbit islands combined with the total RMP field, including the plasma response, is about three times smaller than that obtained by assuming the corresponding vacuum field. (ii) The orbit island size is not sensitive to the EP energy, and is comparable to those of the magnetic islands. (iii) Passing EPs with outward radial orbital drift form orbit islands that shift inward with respect to the corresponding magnetic islands, and vice versa. This radial shift, ΔΨ, measured in the normalized equilibrium poloidal flux, is quantified as ΔΨ ≃ 0.03X for the ITER baseline plasma and assuming n = 1 RMPs, with $X\equiv {(M/{M}_{\mathrm{p}})}^{1/2}{(E[\mathrm{M}\mathrm{e}\mathrm{V}])}^{1/2}{Z}^{-1}$, where M is the particle mass, Mp is the proton mass, E is the particle energy, and Z is the particle charge number. (iv) Trapped EPs do not form drift orbit islands, even in the presence of the 3D fields produced by the 90 kAt ELM control coil current in ITER, and thus possess good confinement properties. Nevertheless, the deformation of the trapped particle drift orbits in the Poincaré plane shows that the canonical toroidal angular momentum of EPs is no longer conserved in the presence of the RMP fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Spatially dependent modeling and simulation of runaway electron mitigation in DIII-D

New simulations with the Kinetic Orbit Runaway electron (RE) Code (KORC) show RE deconfinement losses to the wall during plasma scrape off are the primary current dissipation mechanism in DIII-D experiments with high-Z impurity injection, and not collisional slowing down. The majority of simulations also exhibit an increase in the RE beam energy due to acceleration by the induced toroidal electric field, even while the RE beam current is decreasing. In this study, KORC integrates RE orbits using the relativistic guiding center equations of motion and incorporates time-sequenced, experimental reconstructions of the magnetic and electric fields and line integrated electron density to construct spatiotemporal models of electron and partially ionized impurity transport in the companion plasma. Comparisons of experimental current evolution and KORC results demonstrate the importance of including Coulomb collisions with partially ionized impurity physics, initial RE energy, pitch angle, and spatial distributions, and spatiotemporal electron and partially ionized impurity transport. The research presented here provides an initial quantification of the efficacy of RE mitigation via injected impurities and identification of the critical role played by loss of confinement due to plasma scrape off on the inner wall as compared to the relatively slow collisional damping.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Decoherence and Brownian motion of a polarizable particle near a medium

Optically levitated nanoparticles are ideal experimental testbeds for investigating macroscopic superpositions and microscopic thermodynamics. Integrating such levitated nanoparticles with photonic structures can enable strong coupling between their center-of-mass motion and guided photonic modes, facilitating enhanced control and probing of their motion. When coupling a particle to a photonic structure, such as a waveguide, the effects of fluctuations become prominent at nanoscales. In this work, we analyze the classical and quantized center-of-mass motion of a polarizable particle interacting with the fluctuations of the electromagnetic field in the presence of a medium. We derive a position localization master equation for the particle's quantized center of mass, and examine its classical center-of-mass momentum diffusion, elucidating correspondences between classical and quantum Brownian motion of polarizable particles near media. We study the decoherence rate of the particle in the presence of a planar surface as a function of temperature and distance from the surface, comparing it to common sources of decoherence. Our results are pertinent to experiments aimed at preparing levitated nanospheres in macroscopic quantum states and investigating their Brownian dynamics.

Brownian motion↗
DOE OSTI2023

Particle Acceleration by Magnetic Reconnection in Geospace

Particles are accelerated to very high, non-thermal energies during explosive energy-release phenomena in space, solar, and astrophysical plasma environments. While it has been established that magnetic reconnection plays an important role in the dynamics of Earth’s magnetosphere, it remains unclear how magnetic reconnection can further explain particle acceleration to non-thermal energies. Here we review recent progress in our understanding of particle acceleration by magnetic reconnection in Earth’s magnetosphere. With improved resolutions, recent spacecraft missions have enabled detailed studies of particle acceleration at various structures such as the diffusion region, separatrix, jets, magnetic islands (flux ropes), and dipolarization front. With the guiding-center approximation of particle motion, many studies have discussed the relative importance of the parallel electric field as well as the Fermi and betatron effects. However, in order to fully understand the particle acceleration mechanism and further compare with particle acceleration in solar and astrophysical plasma environments, there is a need for further investigation of, for example, energy partition and the precise role of turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Guiding center and gyrokinetic orbit theory for large electric field gradients and strong shear flows

The guiding center and gyrokinetic theory of magnetized particle motion is extended to the regime of large electric field gradients perpendicular to the magnetic field. A gradient in the electric field directly modifies the oscillation frequency and causes the Larmor orbits to deform from circular to elliptical trajectories. In order to retain a good adiabatic invariant, there can only be strong dependence on a single coordinate at lowest order, so that resonances do not generate chaotic motion that destroys the invariant. When the gradient across magnetic flux surfaces is dominant, the guiding center drift velocity becomes anisotropic in response to external forces and additional curvature drifts must be included. The electric polarization density remains gyrotropic, but both the polarization and magnetization are modified by the change in gyrofrequency. The theory can be applied to shear flows that are even stronger than those observed in the edge transport barrier of a high-performance tokamak (H-mode) pedestal, even if the toroidal field is as small as or even smaller than the poloidal field. Yet, the theory retains a mathematical form that is similar to the standard case and can readily be implemented within existing simulation tools.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Guiding center equations for the magnetic dipole

Since the discovery of Van Allen radiation belts in the 1960s, observations of energetic ions trapped in the Earth's dipole magnetic field have illustrated the remarkable confinement properties of this configuration. As such, it has been used for confining a hot plasma for nuclear fusion studies, starting from the pioneering work of Bo Lehnert and Akira Hasegawa, in the Levitated Dipole Experiment (LDX) at MIT until 2011 and in the RT-1 experiment at the University of Tokyo. More recently, the dipole has been subject to a renewed interest for fusion studies by a couple of startups and for smaller applications as a cold plasma source. While the equilibrium and magneto-hydrodynamic stability of the dipole have been investigated quite in detail, neoclassical properties of the dipole are comparatively much less known: the dipole is more known in geophysics than in fusion science. For this reason, in this paper, we propose a set of Hamiltonian, guiding-center equations to describe the motion of electrons and ions in a magnetic dipole configuration. We also developed a code, and we show the main features of particle motion, benchmarking our results with the analytical solutions for the bounce and precession motion, which are well documented in the literature. We also draw some general conclusions for the neoclassical transport in usual toroidal confinement schemes, such as the tokamak and the stellarator, pointing out the unique advantages of the dipole in confining energetic particles.

Hamiltonian mechanics↗
DOE OSTI2025

Nonperturbative Guiding Center Model for Magnetized Plasmas

Perturbative guiding center theory adequately describes the slow drift motion of charged particles in the strongly magnetized regime characteristic of thermal particle populations in various magnetic fusion devices. However, it breaks down for particles with large-enough energy. Here, we report on a data-driven method for learning a nonperturbative guiding center model from full-orbit particle simulation data. We show the data-driven model significantly outperforms traditional asymptotic theory in magnetization regimes appropriate for fusion-born α particles in stellarators, thus opening the door to nonperturbative guiding center calculations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Verification of nonperturbative guiding center theory in symmetric fields

We verify a recently-developed nonperturbative guiding center formalism to charged particle dynamics in fields with two-parameter continuous symmetry groups. This entails finding exact constants of motion, valid in the nonperturbative regime, that agree with Kruskal’s adiabatic invariant series to all orders in the perturbative regime, when the field scale length is large compared with a typical gyroradius. We demonstrate that the nonperturbative guiding center model makes exact predictions in these cases, even though it eliminates the cyclotron timescale, thereby establishing a theoretical baseline for performance of the nonperturbative formalism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Effects of Radiation Reaction Physics on High-Current Power Flow

In this study, we examine the effects of the radiation reaction force on electrons in a radial magnetically insulated transmission line (MITL) near a load with peak currents of 60+ MA. More specifically, we study the differences in electron motion and kinetic energy with or without radiation reaction physics using a novel guiding center drift approach that incorporates E $\times$ B and ∇B drifts. A key finding of this study is that an electron's magnetic moment, which would be conserved when radiation reaction physics is not incorporated, can be significantly reduced in magnetic fields on the order of 10,000's T when radiation reaction is included. The reduction of magnetic moment gives rise to a significant reduction in cycloidal kinetic energy as well as a reduction in the electron's ∇B drift.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

An energy-conserving and asymptotic-preserving charged-particle orbit implicit time integrator for arbitrary electromagnetic fields

Here we present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit motion in the small time-step limit, but also recovers all the first-order guiding center drifts as well as the correct gyroradius when stepping over the gyration time-scale. In contrast to previous efforts in this direction, the new scheme also features exact energy conservation. In the derivation of the scheme, we find that a new numerical time-scale is introduced. This scale is analyzed and the resulting restrictions on time-step are derived. Based on this analysis, we develop an adaptive time-stepping strategy the respects these constraints while stepping over the gyration scale when physically justified. It is shown through numerical tests on single-particle motion that the scheme's energy conservation property results in tremendous improvements in accuracy, and that the scheme is able to transition smoothly between magnetized and unmagnetized regimes as a result of the adaptive time-stepping.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Information-Guided Dynamic Nuclear Polarization

A spin ensemble in thermal equilibrium continuously undergoes random fluctuations analogous to those observed in Brownian motion, a process known as spin noise. Here, we investigate the dynamics of a system comprising a spin-1 paramagnetic center and a hyperfine-coupled spin-1/2 nucleus in the vicinity of a level crossing. We theoretically show that nuclear spins polarize efficiently under the combined action of thermal fluctuations and a closed-loop feedback protocol. The latter articulates periodic observations of the electronic magnetization and radio-frequency pulses connecting hybrid states with opposite nuclear spin alignment. Since nuclear polarization emerges from electronic spin fluctuations, not spin order, this microwave-free technique generically benefits from warmer, not colder, operation temperatures. Furthermore, because the spin dynamics at play near a level crossing is rather insensitive to the absolute value of the magnetic field, our work promises opportunities for high-field dynamic nuclear polarization, which is difficult to attain through present methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Electron Dynamics Within a MITL Containing a Load

In this paper, we derive the vacuum electric fields within specific cylindrically symmetric magnetically insulated transmission lines (MITLs) in the limit of an infinite speed of light for an arbitrary time-dependent current. We focus our attention on two types of MITLs: the radial MITL and a spherically curved MITL. We then simulate the motion of charged particles, such as electrons, present in these MITLs due to the vacuum fields. In general, the motion of charged particles due to the vacuum fields is highly nonlinear since the fields are nonlinear functions of spatial coordinates and depend on an arbitrary time-dependent current drive. Using guiding center theory, however, one can describe the gross particle kinetics using a combination of $\textbf {E} \times \textbf {B}$ and $\nabla B$ drifts. In addition, we compare our approximate inner MITL field models and particle kinetics with those from a fully electromagnetic simulation code. We find that the agreement between the approximate model and the electromagnetic simulations is excellent.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗