Pitch angle

About: Pitch angle is a research topic. Over the lifetime, 4859 publications have been published within this topic receiving 94460 citations.

Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field

Abstract: The quasi‐linear velocity space diffusion is considered for waves of any oscillation branch propagating at an arbitrary angle to a uniform magnetic field in a spatially uniform plasma. The space‐averaged distribution function is assumed to change slowly compared to a gyroperiod and characteristic times of the wave motion. Nonlinear mode coupling is neglected. An H‐like theorem shows that both resonant and nonresonant quasi‐linear diffusion force the particle distributions towards marginal stablity. Creation of the marginally stable state in the presence of a sufficiently broad wave spectrum in general involves diffusing particles to infinite energies, and so the marginally stable plateau is not accessible physically, except in special cases. Resonant particles with velocities much larger than typical phase velocities in the excited spectrum are scattered primarily in pitch angle about the magnetic field. Only particles with velocities the order of the wave phase velocities or less are scattered in energy at a rate comparable with their pitch angle scattering rate.

Relativistic theory of wave‐particle resonant diffusion with application to electron acceleration in the magnetosphere

Abstract: Resonant diffusion curves for electron cyclotron resonance with field-aligned electromagnetic R mode and L mode electromagnetic ion cyclotron (EMIC) waves are constructed using a fully relativistic treatment. Analytical solutions are derived for the case of a single-ion plasma, and a numerical scheme is developed for the more realistic case of a multi-ion plasma. Diffusion curves are presented, for plasma parameters representative of the Earth's magnetosphere at locations both inside and outside the plasmapause. The results obtained indicate minimal electron energy change along the diffusion curves for resonant interaction with L mode waves. Intense storm time EMIC waves are therefore ineffective for electron stochastic acceleration, although these waves could induce rapid pitch angle scattering for ≳ 1 MeV electrons near the duskside plasmapause. In contrast, significant energy change can occur along the diffusion curves for interaction between resonant electrons and whistler (R mode) waves. The energy change is most pronounced in regions of low plasma density. This suggests that whistler mode waves could provide a viable mechanism for electron acceleration from energies near 100 keV to above 1 MeV in the region outside the plasmapause during the recovery phase of geomagnetic storms. A model is proposed to account for the observed variations in the flux and pitch angle distribution of relativistic electrons during geomagnetic storms by combining pitch angle scattering by intense EMIC waves and energy diffusion during cyclotron resonant interaction with whistler mode chorus outside the plasmasphere.

Regular and chaotic charged particle motion in magnetotaillike field reversals: 1. Basic theory of trapped motion

Abstract: We give a systematic theoretical analysis of trapped nonadiabatic charged particle motion in two-dimensional taillike magnetic field reversals. Particle dynamics is shown to be controlled by the curvature parameter κ, i.e., the ratio κ² = Rmin/ρmax between the minimum radius of curvature of the magnetic field and the maximum Larmor radius in it for a particle of given energy. κ≫1 corresponds to the usual adiabatic case with the magnetic moment μ as a first-order invariant of motion. As κ decreases toward unity, the particle motion becomes stochastic due to deterministic chaos, caused by the overlapping of nonlinear resonances between the bounce- and the gyro-motion. We determine the threshold of deterministic chaos and derive the related pitch angle diffusion coefficient which describes statistically the particle behavior in the limit κ → 1. Such behavior, which for κ ≅ 1 becomes strongly chaotic, applies, e.g., to thermal electrons in Earth's magnetotail and makes its collisionless tearing mode instability possible. We also show that in sharply curved field reversals, i.e., for κ 1. Both types of trapped particle motion in sharply curved magnetic field reversals κ<1 are closely connected with fast oscillations perpendicular to the reversal plane. However, the trajectories are adiabatic only in the case that they permanently remain crossing the reversal plane. The adiabatic are of a ring type, i.e., they resemble rings in phase space and also in real physical space. For ring-type orbits the action integral over the fast oscillations is an adiabatic invariant in the usual sense. On the other hand, the most common particle trajectories in a sharply curved field reversal with κ<1 are essentially of a cucumberlike quasi-adiabatic type. For quasi-adiabatic cucumberlike orbits the action integral over the fast oscillations is an adiabatic invariant only in a piecemeal way between successive traversals in the phase space of the fast motion of a separatrix between orbits which do and those, which do not cross the reversal plane. Due to the effect of separatrix traversals the slow motion shifts between different cucumber orbits with a conservation of the action integral on average but with its chaotic phase space diffusion even for very small perturbation parameters κ. The case κ<1 is applicable, e.g., to thermal ions and high-energy electrons in Earth's magnetotail. Our findings lead to a systematic interpretation of particle observations in Earth's magnetotail and of numerous numerical calculations, carried out in the past. They also explain rather well, e.g., the pitch angle diffusion of plasma sheet particles, the isotropization of the plasma sheet electron distribution immediately before a substorm and provide with the transition to chaos a mechanism for the onset of a large-scale tail instability and the explosion of isolated substorms. Further implications for magnetotail physics, such as acceleration processes and the influence of the particle escape from the field reversal will be discussed in a second related paper.

Evidence for the presence of quasi‐two‐dimensional nearly incompressible fluctuations in the solar wind

Abstract: Assuming that the slab and isotropic models of solar wind turbulence need modification (largely due to the observed anisotropy of the interplanetary fluctuations and the results of laboratory plasma experiments), this paper proposes a model of the solar wind. The solar wind is seen as a fluid which contains both classical transverse Alfvenic fluctuations and a population of quasi-transverse fluctuations. In quasi-two-dimensional turbulence, the pitch angle scattering by resonant wave-particle interactions is suppressed, and the direction of minimum variance of interplanetary fluctuations is parallel to the mean magnetic field. The assumed incompressibility is consistent with the fact that the density fluctuations are small and anticorrelated, and that the total pressure at small scales is nearly constant.

Timescale for radiation belt electron acceleration by whistler mode chorus waves

Abstract: [1] Electron acceleration inside the Earth's magnetosphere is required to explain increases in the ∼MeV radiation belt electron flux during magnetically disturbed periods. Recent studies show that electron acceleration by whistler mode chorus waves becomes most efficient just outside the plasmapause, near L = 4.5, where peaks in the electron phase space density are observed. We present CRRES data on the spatial distribution of chorus emissions during active conditions. The wave data are used to calculate the pitch angle and energy diffusion rates in three magnetic local time (MLT) sectors and to obtain a timescale for acceleration. We show that chorus emissions in the prenoon sector accelerate electrons most efficiently at latitudes above 15° for equatorial pitch angles between 20° and 60°. As electrons drift around the Earth, they are scattered to large pitch angles and further accelerated by chorus on the nightside in the equatorial region. The timescale to accelerate electrons by whistler mode chorus and increase the flux at 1 MeV by an order of magnitude is approximately 1 day, in agreement with satellite observations during the recovery phase of storms. During wave acceleration the electrons undergo many drift orbits and the resulting pitch angle distributions are energy-dependent. Chorus scattering should produce pitch angle distributions that are either flat-topped or butterfly-shaped. The results provide strong support for the wave acceleration theory.