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Results for “adiabatic invariant”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
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 OSTI2023

Isodrastic magnetic fields for suppressing transitions in guiding-centre motion

In a magnetic field, transitions between classes of guiding-centre motion can lead to cross-field diffusion and escape. We say a magnetic field is isodrastic if guiding centres make no transitions between classes of motion. This is an important ideal for enhancing confinement. First, we present a weak formulation, based on the longitudinal adiabatic invariant, generalising omnigenity. To demonstrate that isodrasticity is strictly more general than omnigenity, we construct weakly isodrastic mirror fields that are not omnigenous. Then we present a strong formulation that is exact for guiding-centre motion. We develop a first-order treatment of the strong version via a Melnikov function and show that it recovers the weak version. The theory provides quantification of deviations from isodrasticity that can be used as objective functions in optimal design. The theory is illustrated with some simple examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Energetic particle loss mechanisms in reactor-scale equilibria close to quasisymmetry

Abstract Collisionless physics primarily determines the transport of fusion-born alpha particles in 3D equilibria. Several transport mechanisms have been implicated in stellarator configurations, including stochastic diffusion due to class transitions, ripple trapping, and banana drift-convective orbits. Given the guiding center dynamics in a set of six quasihelical and quasiaxisymmetric equilibria, we perform a classification of trapping states and transport mechanisms. In addition to banana drift convection and ripple transport, we observe substantial non-conservation of the parallel adiabatic invariant which can cause losses through diffusive banana tip motion. Furthermore, many lost trajectories undergo transitions between trapping classes on longer time scales, either with periodic or irregular behavior. We discuss possible optimization strategies for each of the relevant transport mechanisms. We perform a comparison between fast ion losses and metrics for the prevalence of mechanisms such as banana-drift convection (Velasco et al 2021 Nucl. Fusion 61 116059), transitioning orbits, and wide orbit widths. Quasihelical configurations are found to have natural protection against ripple-trapping and diffusive banana tip motion leading to a reduction in prompt losses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Energetic particle optimization of quasi-axisymmetric stellarator equilibria

Abstract An important goal of stellarator optimization is to achieve good confinement of energetic particles such as, in the case of a reactor, alphas created by deuterium–tritium fusion. In this work, a fixed-boundary stellarator equilibrium was re-optimized for energetic particle confinement via a two-step process: first, by minimizing deviations from quasi-axisymmetry (QA) on a single flux surface near the mid-radius, and secondly by maintaining this improved QA while minimizing the analytical quantity Γ C , which represents the angle between magnetic flux surfaces and contours of J | | , the second adiabatic invariant. This was performed multiple times, resulting in a group of equilibria with significantly reduced energetic particle losses, as evaluated by Monte Carlo simulations of alpha particles in scaled-up versions of the equilibria. This is the first time that energetic particle losses in a QA stellarator have successfully been reduced by optimizing Γ C . The relationship between energetic particle losses and metrics such as QA error ( E q a ) and Γ C in this set of equilibria were examined via statistical methods and a nearly linear relationship between volume-averaged Γ C and prompt particle losses was found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Adiabatic behavior of an elliptical vortex in a time-dependent external strain flow

The adiabatic behavior of two-dimensional (2D) fluid vortices subject to slowly varying, time-dependent external strain flows is studied theoretically, and experimentally using magnetized non-neutral electron plasmas. Here the E × B drift dynamics of the electrons perpendicular to the magnetic field are analogous to the motion of fluid vorticity under the 2D Euler equations describing ideal fluids. A low-dimensional elliptical vortex patch model is used along with a WKB approximation to derive a formula for the breaking of an adiabatic invariant due to the changing external flow. The invariant is interpreted as the amplitude of a perturbative oscillation about a stable fixed point corresponding to a steady elliptical vortex. Smooth, hyperbolic tangent and piecewise linear ramp functions are considered for the external strain time dependence. Standard exponential breaking is observed in the former case, whereas the latter exhibits a power-law breaking curve with periodic modulation. It is found that a driving term in the equations of motion contributes the majority of the breaking whereas the frequency variation plays a weaker, but significant role. The experimental data agree closely with the theoretical model. The most significant deviation is due to inviscid damping behavior associated with the smooth edges of the experimental vortices, which tends to reduce the amplitude of the oscillation. Finally, the results are compared and contrasted with other related experimental, numerical, and theoretical work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1966

Source of outer zone protons.

Acceleration processes of outer zone protons investigated, using Kellogg hypothesis of radiation belt formation through magnetic disturbances where third adiabatic invariant is violated

OUTER RADIATION BELT↗
NASA NTRS1971

Hamiltonian formulation of guiding center motion

The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.

Stern, D. P.↗
NASA NTRS1972

The effect of Jupiter's satellites on the diffusion of protons

Proton diffusion data are calculated for the Jovian satellites Amalthea, Io, Europa, Ganymede, and Callisto, assuming an equatorial magnetic field at Jupiter's surface of 10 gauss. The cyclotron radius, bounce period, and drift period are calculated for 1 MeV protons. These characteristics and the proton energy at the satellite, mean life near the satellite before impact, and diffusion time are also calculated for 100 MeV protons which conserve their first adiabatic invariant. The longitudinal distance between successive bounces is of the order of a few satellite radii.

Mead, G. D.↗
NASA NTRS1972

Analysis of inner and outer zone: OGO-1 and OGO-2 electron spectrometer and ion chamber data

The dynamic processes governing the acceleration and loss of electrons in the radiation zones are investigated. The radial diffusion coefficient was determined for a McIlwain parameter between 1.6 and 2.2 for electrons having a first adiabatic invariant of 12 MeV/gauss. The coefficient is larger than earlier values and suggests that there exists a lower limit to the fluxes in the inner zone. The agreement between observed and calculated magnetic fields and particle fluxes is improved by using solar wind pressure as input to the magnetic field models. Changes in the plasma pressure can cause apparent local time asymmetries in particle flux. A comparison of the magnetic field models with observed location of the trapping boundary also indicates the need for including distributed currents within the magnetosphere. The high latitude trapping boundary is only weakly dependent on A sub p, and the trapping boundary data are improved by including in the models a stand-off distance which varies with the plasma pressure.

Pfitzer, K. A.↗
NASA NTRS1971

Source and loss processes of protons of the inner radiation belt.

The adequacy of the known source and loss processes to populate the inner radiation belt with protons is examined by calculating the equilibrium trapped-proton distribution, which would result from decay of albedo neutrons, energy-loss collisions, and radial diffusion by changes in the third adiabatic invariant. The strength of the neutron source and the rates of atmospheric energy loss are obtained from available theoretical and experimental data, and the radial-diffusion coefficient is adjusted to give agreement between theory and experiment for equatorially trapped protons with first invariants between 200 and 3000 MeV gauss. The flux intensities, energy spectrums, and radial distributions obtained by the theory are in good agreement with observations, and the radial diffusion coefficient required is consistent with dif*usion coefficients derived by a variety of other methods.-

Farley, T. A.↗
NASA NTRS1973

Jupiter's radiation belts.

A model for the production and loss of energetic electrons in Jupiter's radiation belt is presented. It is postulated that the electrons originate in the solar wind and are diffused in toward the planet by perturbations which violate the particles' third adiabatic invariant. At large distances, magnetic perturbations, electric fields associated with magnetospheric convection, or interchange instabilities driven by thermal plasma gradients may drive the diffusion. Inside about 10 Jupiter radii, the diffusion is probably driven by electric fields associated with the upper atmosphere dynamo which is driven by neutral winds in the ionosphere. The diurnal component of the dynamo wind fields produces a dawn-dusk asymmetry in the decimetric radiation from the electrons in the belts, and the lack of obvious measured asymmetries in the decimetric radiation measurements provides estimates of upper limits for these Jovian ionospheric neutral winds.

Brice, N.↗
NASA NTRS1973

Diffusion of ring current particles by low-frequency long-wavelength electrostatic oscillations.

The diffusion of charged particles by randomly fluctuating low-frequency long-wavelength electrostatic oscillations in the magnetosphere is investigated as a possible mechanism for transporting ring current particles. The diffusion process is assumed to preserve the first adiabatic invariant. The magnetosphere is represented by a simple model with cylindrical geometry. In the model the ionospheres are assumed to be perfectly conducting and the ring current is assumed to have a Maxwellian distribution of velocities. The electrostatic oscillations are treated as natural modes of the magnetospheric cavity which are driven by variations in the electric potential on the magnetopause. It is concluded that diffusion of ring current protons by this process is not important in the magnetosphere.

Maggs, J. E.↗
NASA NTRS1974

The average motion of a charged particle in a dipole field

The numerical representation of the average motion of a charged particle trapped in a geomagnetic field is developed. An assumption is made of the conservation of the first two adiabatic invariants where integration is along a field line between mirror points. The averaged motion also involved the parameters defining the magnetic field line to which the particle is attached. Methods involved in obtaining the motion in the equatorial plane of model magnetospheres are based on Hamiltonian functions. The restrictions imposed by the special nature of the dipole field are defined.

Chen, A. J.↗
NASA NTRS1974

Transport of charged particles in the earth's magnetosphere

A review of recent data on and conceptions of processes in which high energy particles are transported across magnetic shells in the earth's magnetosphere is presented. The processes discussed include adiabatic processes (with conservation of all three adiabatic invariants of charged particle motion in the magnetic field), diffusion processes (with violation of only the third or third and second invariants), and the so-called fast nonadiabatic processes, which appear to result from the action of strong electric fields.

Shalimov, V. P.↗
NASA NTRS1972

Diffusion models for Jupiter's radiation belt

Solutions are given for the diffusion of trapped particles in a planetary magnetic field in which the first and second adiabatic invariants are preserved but the third is not, using as boundary conditions a fixed density at the outer boundary (the magnetopause) and a zero density at an inner boundary (the planetary surface). Losses to an orbiting natural satellite are included and an approximate evaluation is made of the effects of the synchrotron radiation on the energy of relativistic electrons. Choosing parameters appropriate to Jupiter, the electrons required to produce the observed synchrotron radiation are explained. If a speculative mechanism in which the diffusion is driven by ionospheric wind is the true explanation of the electrons producing the synchrotron emission it can be concluded that Jupiter's inner magnetosphere is occupied by an energetic proton flux that would be a serious hazard to spacecraft.

Jacques, S. A.↗