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

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At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Emergent Properties from Three-Dimensional Assemblies of (Nano)particles in Confined Spaces

The assembly of (nano)particles into compact hierarchical structures yields emergent properties not found in the individual constituents. The formation of these structures relies on a profound knowledge of the nanoscale interactions between (nano)particles, which are often designed by researchers aided by computational studies. These interactions have an effect when the (nano)particles are brought into close proximity, yet relying only on diffusion to reach these closer distances may be inefficient. Recently, physical confinement has emerged as an efficient methodology to increase the volume fraction of (nano)particles, rapidly accelerating the time scale of assembly. Specifically, the high surface area of droplets of one immiscible fluid into another facilitates the controlled removal of the dispersed phase, resulting in spherical, often ordered, (nano)particle assemblies. In this review, we discuss the design strategies, computational approaches, and assembly methods for (nano)particles in confined spaces and the emergent properties therein, such as trigger-directed assembly, lasing behavior, and structural photonic color. Finally, we provide a brief outlook on the current challenges, both experimental and computational, and farther afield application possibilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Observational studies of the clearing phase in proto-planetary disk systems

Progress in this study is summarized for its second year. An extensive program of high dispersion UV spectral studies using the IUE (International Ultraviolet Explorer) has resulted in acquisition of 40 Herbig Ae/Be star and related object spectra. We find that accreting, circumstellar gas is detected with velocities consistent with material in free-fall toward the stars in approximately 38% of the sample. With acquisition of optical measurements of the projected stellar rotational velocities, we find that the systems with accreting gas exhibit systematically higher projected rotational velocities than the systems showing signatures of outflowing material only. When combined with polarimetric and photometric data, the IUE spectra for these stars indicate that accretion in intermediate-mass pre-main sequence stars is confined to the plane of the circumstellar dust disk. This is in contrast to lower-mass PMS stars where accretion, persumably along magnetic field lines, is seen at polar latitudes. Our data also support significant clearing of the central regions of these circumstellar disks, as originally suggested. The model which most closely matches the observational data is accretion from a disk envelope, as developed by Calvet et al. (1994).

Grady, Carol A.↗
NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. VIII - Overstability in a magnetic field in a downdraft

The dynamical properties of convective overstability in a vertical magnetic field with a downdraft are considered. A variety of effects is illustrated. The overstability produces Alfven waves propagating both upward or downward along the magnetic field. The favored direction of emission may be upward or downward depending upon the magnitude of the heat transport coefficient. The largest asymmetry is produced by a difference in reflectivity between the upper and lower boundaries. It is shown that a very modest reflection coefficient of the upper boundary, with no reflection at the lower boundary, causes most of the waves to be emitted downward, and vice versa. Applying these results to the flux tubes extending up through the convective zone of the Sun, it follows that those flux tubes are dynamically active beneath the surface, as suggested earlier by ourselves and others, but there is no reason to expect any significant wave flux to appear in the field above the surface. The waves propagate downward into the Sun and are presumably dispersed there by the nonlinear interaction with the turbulent convection, etc.

Parker, E. N.↗
NASA NTRS2012

Properties of Ground Level Enhancement Events and the Associated Solar Eruptions During Solar Cycle 23

Solar cycle 23 witnessed the most complete set of observations of coronal mass ejections (CMEs) associated with the Ground Level Enhancement (GLE) events. We present an overview of the observed properties of the GLEs and those of the two associated phenomena, viz., flares and CMEs, both being potential sources of particle acceleration. Although we do not find a striking correlation between the GLE intensity and the parameters of flares and CMEs, the solar eruptions are very intense involving X-class flares and extreme CME speeds (average approx. 2000 km/s). An M7.1 flare and a 1200 km/s CME are the weakest events in the list of 16 GLE events. Most (80 %) of the CMEs are full halos with the three non-halos having widths in the range 167 to 212 degrees. The active regions in which the GLE events originate are generally large: 1290 msh (median 1010 msh) compared to 934 msh (median: 790 msh) for SEP-producing active regions. For accurate estimation of the CME height at the time of metric type II onset and GLE particle release, we estimated the initial acceleration of the CMEs using flare and CME observations. The initial acceleration of GLE-associated CMEs is much larger (by a factor of 2) than that of ordinary CMEs (2.3 km/sq s vs. 1 km/sq s). We confirmed the initial acceleration for two events for which CME measurements are available in the inner corona. The GLE particle release is delayed with respect to the onset of all electromagnetic signatures of the eruptions: type II bursts, low frequency type III bursts, soft X-ray flares and CMEs. The presence of metric type II radio bursts some 17 min (median: 16 min; range: 3 to 48 min) before the GLE onset indicates shock formation well before the particle release. The release of GLE particles occurs when the CMEs reach an average height of approx 3.09 R(sub s) (median: 3.18 R (sub s) ; range: 1.71 to 4.01 R (sub s) ) for well-connected events (source longitude in the range W20–W90). For poorly connected events, the average CME height at GLE particle release is ∼66 % larger (mean: 5.18 R (sub s) ; median: 4.61 R (sub s) ; range: 2.75–8.49 R (sub s) ). The longitudinal dependence is consistent with shock accelerations because the shocks from poorly connected events need to expand more to cross the field lines connecting to an Earth observer. On the other hand, the CME height at metric type II burst onset has no longitudinal dependence because electromagnetic signals do not require magnetic connectivity to the observer. For several events, the GLE particle release is very close to the time of first appearance of the CME in the coronagraphic field of view, so we independently confirmed the CME height at particle release. The CME height at metric type II burst onset is in the narrow range 1.29 to 1.8 R(sub s), with mean and median values of 1.53 and 1.47 R(sub s). The CME heights at metric type II burst onset and GLE particle release correspond to the minimum and maximum in the Alfven speed profile. The increase in CME speed between these two heights suggests an increase in Alfvenic Mach number from 2 to 3. The CME heights at GLE particle release are in good agreement with those obtained from the velocity dispersion analysis, including the source longitude dependence. We also discuss the implications of the delay of GLE particle release with respect to complex type III bursts by approx 18 min (median: 16 in; range: 2 to 44 min) for the flare acceleration mechanism. A similar analysis is also performed on the delay of particle release relative to the hard X-ray emission.

Geomagnetic Storms↗
DOE OSTI2026

Stability and Characteristics of Lower-hybrid Drift Waves: Dependence on Electron Beta and Cross-field Relative Drift

Lower-hybrid drift waves (LHDWs) are frequently observed microinstabilities in both space and laboratory plasmas. Despite decades of study, the relationship between electrostatic (ES-LHDW) and electromagnetic (EM-LHDW) variants and the plasma parameters controlling their stability remains unclear. Here, we systematically examine LHDW behavior by solving the local linear dispersion relation over a wide range of plasma and field conditions. Our results demonstrate that ES-LHDWs and EM-LHDWs are not distinct modes but rather two different regimes of the same drift wave whose character evolves smoothly with electron beta (β e ) and the cross-field electron drift velocity relative to ions, normalized to the ion sound speed (u 0x /C s ). The nature of the waves changes from electrostatic to electromagnetic when β e increases. Growth rates increase with u 0x /C s but decrease with β e , while the most unstable wavelength remains nearly universal, with kρ e ∼ 0.8 (k is the magnitude of the wave vector and ρ e is the electron gyroradius). We further present quasi-linear estimates of nonlinear saturation properties, including energy partition among electric fields, magnetic fields, and particle kinetic responses. We show that ES-LHDWs reach higher electric-field saturation amplitudes, whereas EM-LHDWs generate strong magnetic perturbations and parallel electric fields that may enable efficient particle heating. Comparisons with the classical model reveal that retaining electromagnetic effects is essential for accurate predictions of frequency, growth rate, and the propagation angle. These findings provide a unified framework for understanding LHDWs across diverse collisionless plasma environments, including current sheets of magnetic reconnection, shear layers, collisionless shocks, and boundary regions.

Solar coronal waves↗
NASA NTRS1971

Magnetic stress anisotropy field in plated cylindrical Permalloy films.

An analysis is made of the magnetic stress anisotropy field (Hks) arising from internal and external stress sources in plated-wire memory elements. The analysis takes into consideration circumferential composition variation and cylindrical geometry of the Permalloy film. Expressions are derived relating Hks to uniaxial film stress, average composition, and amplitude of composition variation. A result of particular importance is that even for average zeromagnetostrictive composition (ZMC) films, Hks may still make an appreciable contribution to the total anisotropy field if the composition is not uniform. Calculated Hks characteristics are shown to correlate with anisotropy field changes observed in annealing experiments. Examples are given to show the importance of composition uniformity in determining the stability of the anisotropy field. The utility of the analysis is extended by the inclusion of data expressing the inverse relation between anisotropy field and easy-axis dispersion in the film.

Lutes, O. S.↗
NASA NTRS1990

A mathematical model of the structure and evolution of small scale discrete auroral arcs

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

Seyler, C. E.↗
DOE OSTI2024

Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, Q N , connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from Q N is given by χ − 1 ∝ | Δ q | . Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ − 1 ∝ | Δ q | 2 dependence yields a robust finite- T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the ( t − t ′ ) Hubbard model and found that at large U / t > 5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ − 1 ∝ | Δ q | 2 . Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

Structure of a slow mode shock observed in the plasma sheet boundary layer

A detailed study of the plasma parameters and magnetic field measured using instrumentation aboard ISEE 2 during the recovery phase of a substorm on Apr. 24, 1979, is presented. The purpose of this study was to determine the nature and structure of the lobe-plasma sheet boundary layer. The analysis shows that the lobeward edge of the boundary is consistent with a freestanding slow mode shock. This shock is followed by a slow compression wave containing a trailing ion cyclotron wave which also stands in the flow. Measurement of the cross-tail current in the shock and the current system within the wave gives a shock thickness and wavelength comparable to but larger than both the upstream ion inertial length and the downstream proton gyroradius. Equality of the shock thickness with the standing ion cyclotron wavelength suggests that the steepness of the front is limited by dispersion rather than current-driven anomalous resistivity.

Feldman, W. C.↗
DOE OSTI2025

Synergistic effects of Pd single atoms and nanoclusters boosting SnO 2 gas sensing performance

Tin(IV) oxide-supported Pd is a promising heterogenous catalyst for CO oxidation relevant for environmental cleanup reactions. In this study, an atomically dispersed Pd catalyst on SnO 2 (ADC Pd/SnO 2 ) hybrid material is successfully synthesized via a straightforward wet chemistry method and is found to exhibit superior performance toward CO sensing. Ex situ EXAFS analysis confirms the formation of single Pd atoms and small Pd nanoclusters stabilized on the SnO 2 (110) surface. Further, the material exhibits high efficiency in generating adsorbed O 2 - as well as high activity in catalyzing CO oxidation at low temperatures, resulting in exceptional sensitivity and selectivity toward CO in comparison to pure SnO 2 and Pd nanoparticles loaded on SnO 2 respectively. In situ FTIR measurements unravel CO adsorption kinetics on ADC Pd/SnO 2 under reaction conditions, and a possible sensing mechanism is put forth in which CO is transformed into CO 2 by reaction with active oxygen species; and concurrently, carbon-related species (bicarbonates and carbonates) are formed and decomposed into CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1978

Pitch angle dispersion of drifting energetic protons at synchronous orbit

The time of arrival at ATS 6 of substorm-associated energetic proton flux enhancements has been examined as a function of both energy and pitch angle by using electron-proton spectrometer data. The protons exhibit energy dispersion with the particles with the highest energy arriving first. This has generally been interpreted as evidence that these particles have gradient- and curvature-drifted to the spacecraft from an acceleration region on the nightside. In the evening quadrant, proton enhancements at 90 deg pitch angle arrived at the spacecraft prior to those at small pitch angles. However, on the dayside the increase occurs first at the smallest pitch angle (about 30 degrees). The difference between the arrival times of the 30 deg and 90 deg protons increases for more westward local times. For the highest energy range observed, drifting protons are rarely seen at large pitch angles. These observations place severe restrictions on the simple drift models. Since the pitch angle dependence of the particle drift velocity is a field geometric quantity, the observations require the modification of present magnetospheric magnetic field models. In particular, the models need to reproduce better the enhanced field observed on the dayside near synchronous orbit.

Walker, R. J.↗
NASA NTRS1994

Observation of anomalous slow-mode shock and reconnection layer in the dayside magnetospause

Plasma and magnetic field data from the International Sun-Earth Explorer ISEE 2 spacecraft recorded during an outbound crossing of the dayside, northern hemisphere magnetopause in October 29, 1979, provide evidence for a slow shock (SS) in the observed reconnection layer. This layer is found to be bounded on the magnetosheath side by the SS; near the magnetospheric side of the layer, a second current sheet is found that may have been rotational discontinuity (RD). The direction of the accelerated plasma flow, the earthward sense of the normal magnetic filed across the SS and RD, and the relative orientation of the SS and the RD all indicate that the reconection site was located south of the spacecraft. Quantitative tests show that, allowing for experiemental uncertanties, data taken upstream and downstream of the SS are consistent with coplanarity and other Rankine-Hugoniot (RH) conditions. Examiniations of the flow parameters indicates two anomalous properties of the SS: the upstream flow, viewed in the deHoffmann-Teller frame, is superalfvenic and the downstream plasma is firehose unstable. In comparison to the long-wavelength slow-mode phase speed, however, the flow in the upstream region is super slow, while in the downstream region it is subslow, as requeired for a slow-mode shock. Further properties of the shock include a large decrease in total enthalpy across it, indicating the escape of a sizable heat flux from the shock structure, and the occurrence of a polarization reversal of the tangential magnetic field within the shock layer, a feature that is predicted by linear double-polytropic Hall-MHD and results from a large increase in pressure anistropy from the upstream region, where p(sub parallel) approximately equal to p(sub perp), to the downstream region, where p(sub parrallel) greater than p(sub perp). Quantitative tests of the RD-like discontinuity show that it satisfies the necessary RH conditions within experimental uncertainties and indicate that the flow across it is earthward, that is, it is the same as for the SS. Thus the RD is propagating behind the SS in the direction away from the Earth. The reversal in the order of the discontinuities is attributed to the reversal of the slow and intermediate phase speeds produced by the pressure anistropy in the region between the RD and the SS. The linear dispersion relation and polarization properties of dispersive MHD waves in an anisotropic plasma are examined in the appendix.

Walthour, D. W↗
DOE OSTI2024

Type-II superconductivity at 9K in Pb–Bi alloy

In the present work, we report the synthesis of Pb–Bi alloy with enhanced Tc of up to 9K, which is higher than that of Pb. The alloy is synthesized via a solid-state reaction route in the vacuum-encapsulated quartz tube at 700°C in an automated furnace. The synthesized sample is characterized by X-ray Diffraction(XRD) and Energy dispersive X-ray analysis(EDAX) for its phase purity and elemental composition. Rietveld refinement of XRD reveals that the end product is a majority hexagonal Pb 7 Bi 3 , with minor rhombohedral Bi. The electronic transport measurement shows metallic behavior with the Debye temperature of 108K and a superconductivity transition temperature (T c ) below 9K, which is the maximum to date for any reported Pb–Bi alloy, Pb or Bi at ambient pressure. Partial substitution of Bi at the Pb site may modify the free density of electronic states within the BCS model to attain the optimum T c , which is higher by around 2K from the reported T c of Pb. The superconductor phase diagram derived from magneto-transport measurements reveals that the synthesized alloy is a conventional superconductor with an upper critical field (H c2 ) of 3.9 T, which lies well within the Pauli paramagnetic limit. The magnetization measurements carried out following ZFC(Zero Field Cool) protocols infer that the synthesized alloy is a bulk superconductor below 9K. The isothermal M-H(Magnetization vs. Field) measurements performed below T c establish it as a type-II superconductor. Furthermore, the specific heat capacity measurements show that the Pb–Bi alloy is a strongly coupled bulk superconductor below around 9K with possibly two superconducting gaps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

Numerical methods for analyzing electromagnetic scattering

Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.

Lee, S. W.↗
NASA NTRS2001

Traveling-Wave Tube Amplifier Model to Predict High-Order Modulation Intersymbol Interference

Demands for increased data rates in satellite communications necessitate higher order modulation schemes, larger system bandwidth, and minimum distortion of the modulated signal as it is passed through the traveling wave tube amplifier (TWTA). One type of distortion that the TWTA contributes to is intersymbol interference (ISI), and this becomes particularly disruptive with wide-band, complex modulation schemes. It is suspected that in addition to the dispersion of the TWT, frequency dependent reflections due to mismatches within the TWT are a significant contributor to ISI. To experimentally investigate the effect of these mismatches within the physical TWT on ISI would be prohibitively expensive, as it would require manufacturing numerous amplifiers in addition to the acquisition of the required digital hardware. In an attempt to develop a more accurate model to correlate IS1 with the TWTA and the operational signal, a fully three-dimensional (3D), time-dependent, TWT interaction model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA (solution of Maxwell's equations by the Finite-Integration-Algorithm). The model includes a user defined slow-wave circuit with a spatially tapered region of loss to implement a sever, and spatially varied geometry (such as helical pitch) to implement a phase velocity taper. The model also includes user defined input/output coupling and an electron beam contained by solenoidal, electrostatic, or periodic permanent magnet (PPM) focusing allowing standard or novel TWTs to be investigated. This model comprehensively takes into account the effects of frequency dependent nonlinear distortions (MAM and AMPM); gain ripple due to frequency dependent reflections at the input/output coupling, severs, and mismatches from dynamic pitch variations; drive induced oscillations; harmonic generation; intermodulation products; and backward waves.

Kory, Carol L.↗
DOE OSTI2025

Large Kohn Anomaly and Phonon Collapse Induced by Charge Density Wave in UPt 2⁢ Si 2

Using high-energy-resolution inelastic x-ray scattering, we observe anomalous softening and damping of the transverse acoustic phonon in UPt 2 ⁢Si 2 as the system is cooled toward the charge density wave (CDW) transition temperature 𝑇 CDW . The phonon exhibits a marked Kohn-type anomaly around the CDW wave vector 𝑄 CDW and becomes overdamped within a finite momentum range already well above 𝑇 CDW . The dispersion anomaly is consistent with potential Fermi surface nesting, which together with the extended phonon collapse indicates strong electron-phonon coupling. The transition temperature estimated from the phonon softening is markedly lower than 𝑇 CDW , consistent with a primarily electronic instability rather than a phonon-driven transition. In conclusion, our results establish UPt 2⁢ Si 2 as a prime example of a strongly correlated electron CDW system with exceptionally strong electron-phonon coupling driving phonon softening and collapse.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Dependence of ion-cyclotron range of frequencies instabilities on species mix and fast-ion distribution: I. Stability

Ion cyclotron emission (ICE) driven by fast ions has the potential to be a reactor relevant diagnostic of confined and escaping fast ions; moreover, controlled experiments in magnetic fusion devices can shed light on similar magnetospheric instabilities below and above the ion cyclotron frequency f ci . Dedicated DIII-D experiments studied instabilities below f ci and at cyclotron harmonics l f ci by injecting thirteen different neutral beam populations into plasmas with different thermal compositions of H, D, and 3He at five different values of toroidal field. High-frequency magnetic loops diagnose mode properties. Each beam type is individually injected for an approximate slowing-down time (~100 ms), resulting in a database of 2529 conditions that are analyzed in frequency bands corresponding to ICE harmonics and < f ci global Alfvén eigenmodes. The sub-cyclotron modes are more unstable at low field and in plasmas with large H concentration. For D injection, first harmonic ICE at f cD is more unstable in hydrogen plasmas but, for H injection, the converse is true (ICE at f cH is more unstable in D), suggesting that thermal same-species ions damp fundamental ICE. ICE stability also depends upon the pitch-angle anisotropy gradient and upon the ‘bump-on-tail’ gradient ∂f/∂v. Although the frequency of unstable ICE in these plasmas always occurs near the central cyclotron frequency, the precise value also depends on the Alfvén speed and beam direction, consistent with the idea that instability occurs for modes that simultaneously satisfy ω ≃ 2πlf ci , the magnetosonic dispersion relation, and the Doppler-shifted resonance condition.

electromagnetic ion cyclotron instabilities↗