The optimal pitch angle which maximizes the penetration distance, along the magnetic field, of relativistic charged particles injected from the midplane of an axisymmetric field is investigated analytically and numerically. Higher-order terms of the magnetic moment invariant are necessary to correctly determine the mirror point of trapped energetic particles, and therefore the loss cone. The modified loss cone resulting from the inclusion of higher-order terms is no longer entirely defined by the pitch angle but also by the phase angle of the particle at the point of injection. The optimal orientation of the injection has a nonzero component perpendicular to the magnetic field line, and is in the plane tangential to the flux surface. Numerical integration of particle orbits were carried out for a relativistic electron in a dipole field, showing agreement with analytic expressions. The results are relevant to experiments, which are concerned with injection of relativistic beams into the atmosphere from aboard a spacecraft in the magnetosphere.

The compressional component of magnetic perturbation dB k can play an important role in drift-Alfvenic instabilities in tokamaks, especially as the plasma b increases (b is the ratio of kinetic pressure to magnetic pressure). In this work, we have formulated a gyrokinetic particle simulation model incorporating dB k , and verified the model in kinetic Alfven wave simulations using the Gyrokinetic Toroidal Code in slab geometry. Simulations of drift-Alfvenic instabilities in tokamak geometry shows that the kinetic ballooning mode (KBM) growth rate decreases more than 20% when dB k is neglected for b e ¼ 0:02, and that dB k has stabilizing effects on the ion temperature gradient instability, but negligible effects on the collisionless trapped electron mode. The KBM growth rate decreases about 15% when equilibrium current is neglected.

A method for gyrokinetic simulation of low frequency (lower than the cyclotron frequency) magnetic compressional modes in general geometry is presented. The gyrokinetic-Maxwell system of equations is expressed fully in terms of the compressional component of the magnetic perturbation, δB∥, with finite Larmor radius effects. This introduces a “gyro-surface” averaging of δB∥ in the gyrocenter equations of motion, and similarly in the perpendicular Ampere’s law, which takes the form of the perpendicular force balance equation. The resulting system can be numerically implemented by representing the gyro-surface averaging by a discrete sum in the configuration space. For the typical wavelength of interest (on the order of the gyroradius), the gyro-surface averaging can be reduced to averaging along an effective gyro-orbit. The phase space integration in the force balance equation can be approximated by summing over carefully chosen samples in the magnetic moment coordinate, allowing for an efficient numerical implementation.

Tracing magnetic field-lines of the Earth's magnetosphere using beams of relativistic electrons will open up new insights into space weather and magnetospheric physics. Analytic models and a single-particle-motion code were used to explore the dynamics of an electron beam emitted from an orbiting satellite and propagating until impact with the Earth. The impact location of the beam on the upper atmosphere is strongly influenced by magnetospheric conditions, shifting up to several degrees in latitude between different phases of a simulated storm. The beam density cross-section evolves due to cyclotron motion of the beam centroid and oscillations of the beam envelope. The impact density profile is ring shaped, with major radius ∼ 22 m, given by the final cyclotron radius of the beam centroid, and ring thickness ∼ 2 m given by the final beam envelope. Motion of the satellite may also act to spread the beam, however it will remain sufficiently focused for detection by ground-based optical and radio detectors. An array of such ground stations will be able to detect shifts in impact location of the beam, and thereby infer information regarding magnetospheric conditions.

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Gyrokinetic particle simulation of low frequency compressional modes has been developed using flux coordinates in the global magnetic dipole geometry. The compressional component is formulated in a scalar form of the parallel magnetic perturbation, and the gyro-averaging is performed explicitly in the configuration space. A reduced gyrokinetic model, in which the compressional perturbations are decoupled from the shear Alfvén and electrostatic perturbations, has been implemented. Linear simulation results have been verified using a numerical Nyquist analysis of the dispersion relation in the slab limit. Global simulations of unstable drift-compressional modes in the dipole geometry with kinetic ions find that finite Larmor radius (FLR) effects reduce the linear growth rate significantly but change little the real frequency. Global eigenmode structures show that the modes are even along the equilibrium magnetic field and broadened by the FLR effects in the radial direction. Radial propagation away from the region of excitation is observed.

A hybrid gyrofluid‐kinetic electron model is adapted and used to simulate poloidal standing modes for different electron temperatures and azimuthal mode numbers. As in previous studies of toroidal standing modes, mirror force effects lead to increased parallel potential drops, monoenergetic electron energization, and wave energy dissipation as the ambient electron temperature is increased. A similar trend is also observed when the electron temperature is held fixed and the azimuthal mode number increased—owing to the narrowing of the azimuthal flux tube width, which necessitates more electron energization to carry the increased parallel current density. In both cases, the increase in electron energization eventually leads to more rapid decreases in the parallel current with time because of the dissipation of wave energy.

[1] A gyrokinetic simulation model for nonlinear studies of the mirror instability is described. The model is set in a uniform, periodic slab with anisotropic ions and cold electrons. Particle-in-cell simulations with a noise reducing ıf algorithm show agreement with the linear theory of the mirror instability. Results of nonlinear simulations near marginal stability are presented. Single-mode simulations show saturation due to trapping. Simulations with a spectrum of unstable modes show that the negative magnetic perturbations saturate at a lower amplitude and earlier than the positive magnetic perturbations, which results in the development of peaked saturated structures. The saturation amplitude of negative magnetic perturbations is in agreement with the trapped particle theory, while the saturation amplitude of the positive magnetic perturbations is determined by the local change in theˇ? (ratio of perpendicular plasma pressure to magnetic pressure) parameter.