An intuitive two-fluid picture of spontaneous 2D collisionless magnetic reconnection and whistler wave generation

An intuitive and physical two-fluid picture of spontaneous 2D collisionless magnetic reconnection and whistler wave generation is presented in the framework of 3D electron-magnetohydrodynamics. In this regime, canonical circulation (Q = m_e ∇ × u + q_e B) flux tubes can be defined in analogy to magnetic flux tubes in ideal magnetohydrodynamics. Following the 3D behavior of these Q flux tubes provides a new perspective on collisionless reconnection—a perspective that has been hard to perceive via examinations of 2D projections. This shows that even in a 2D geometry with an ignorable coordinate, a 3D examination is essential for a full comprehension of the process. Intuitive answers are given to three main questions in collisionless reconnection: why is reconnection spontaneous, why do particles accelerate extremely fast, and why are whistler waves generated? Possible extensions to other regimes are discussed

A generalized two-fluid picture of non-driven collisionless reconnection and its relation to whistler waves

A generalized, intuitive two-fluid picture of 2D non-driven collisionless magnetic reconnection is described using results from a full-3D numerical simulation. The relevant two-fluid equations simplify to the condition that the flux associated with canonical circulation Q=m_e ∇ × u_e + q_e B is perfectly frozen into the electron fluid. In the reconnection geometry, flux tubes defined by Q are convected with the central electron current, effectively stretching the tubes and increasing the magnitude of Q exponentially. This, coupled with the fact that Q is a sum of two quantities, explains how the magnetic fields in the reconnection region reconnect and give rise to strong electron acceleration. The Q motion provides an interpretation for other phenomena as well, such as spiked central electron current filaments. The simulated reconnection rate was found to agree with a previous analytical calculation having the same geometry. Energy analysis shows that the magnetic energy is converted and propagated mainly in the form of the Poynting flux, and helicity analysis shows that the canonical helicity ∫P·Q dV as a whole must be considered when analyzing reconnection. A mechanism for whistler wave generation and propagation is also described, with comparisons to recent spacecraft observations

Nondiffusive Pitch-Angle Scattering of a Distribution of Energetic Particles by Coherent Whistler Waves

Whether or not coherent magnetospheric whistler waves play important roles in the pitch‐angle scattering of energetic particles is a crucial question in magnetospheric physics. The interaction of a thermal distribution of energetic particles with coherent whistler waves is thus investigated. The distribution is prescribed by the Maxwell‐Jüttner distribution, which is a relativistic generalization of the Maxwell‐Boltzmann distribution. Coherent whistler waves are modeled by circularly polarized waves propagating parallel to the background magnetic field. It is shown that for parameters relevant to magnetospheric chorus, a significant fraction (1‐5%) of the energetic particle population undergoes drastic, non‐diffusive pitch‐angle scattering by coherent chorus. The scaling of this fraction with the wave amplitude may also explain the association of relativistic microbursts to large‐amplitude chorus. A much improved condition for large pitch‐angle scattering is presented that is related to, but may or may not include the exact resonance condition depending on the particle's initial conditions. The theory reveals a critical mechanism not contained in the widely‐used second‐order trapping theory

Nondiffusive Pitch-Angle Scattering of a Distribution of Energetic Particles by Coherent Whistler Waves

Whether or not coherent magnetospheric whistler waves play important roles in the pitch‐angle scattering of energetic particles is a crucial question in magnetospheric physics. The interaction of a thermal distribution of energetic particles with coherent whistler waves is thus investigated. The distribution is prescribed by the Maxwell‐Jüttner distribution, which is a relativistic generalization of the Maxwell‐Boltzmann distribution. Coherent whistler waves are modeled by circularly polarized waves propagating parallel to the background magnetic field. It is shown that for parameters relevant to magnetospheric chorus, a significant fraction (1‐5%) of the energetic particle population undergoes drastic, non‐diffusive pitch‐angle scattering by coherent chorus. The scaling of this fraction with the wave amplitude may also explain the association of relativistic microbursts to large‐amplitude chorus. A much improved condition for large pitch‐angle scattering is presented that is related to, but may or may not include the exact resonance condition depending on the particle's initial conditions. The theory reveals a critical mechanism not contained in the widely‐used second‐order trapping theory

Kinetic Verification of the Stochastic Ion Heating Mechanism in Collisionless Magnetic Reconnection

The origin of anomalous, non-classical ion heating during magnetic reconnection has been a longstanding problem. It is verified via fully kinetic analyses and particle-in-cell simulations that stochastic heating is the main ion heating mechanism in collisionless magnetic reconnection up to moderate guide fields. Strong in-plane Hall electric fields that form during reconnection render ion motions chaotic and de facto broaden the ion distribution function. The mechanism is consistent with numerous observed features of ion heating in reconnection, such as the preferential heating of ions with higher mass-to-charge ratios and the non-conservation of the ion magnetic moment

Probing the Progression, Properties, and Progenies of Magnetic Reconnection

Magnetic reconnection is a plasma phenomenon in which opposing magnetic fields annihilate and release their magnetic energy into other forms of energy. In this thesis, various aspects of collisionless magnetic reconnection are studied analytically and numerically, and an experimental diagnostic for magnetic fields in a plasma is described. The progression of magnetic reconnection is first illustrated through the formulation of a framework that revolves around canonical vorticity flux, which is ideally a conserved quantity. The reconnection instability, electron acceleration, and whistler wave generation are explained in an intuitive manner by analyzing the dynamics of canonical vorticity flux tubes. The validity of the framework is then extended down to first principles by the inclusion of the electron canonical battery effect. The importance of this effect during reconnection determines the overall structure and evolution of the process. A crucial property of magnetic reconnection is its accompaniment by anomalous ion heating much faster than conventional collisional heating. Stochastic heating is a mechanism in which, under a sufficiently strong electric field, particles undergo chaotic motion in phase space and heat up dramatically. Using the previously established canonical vorticity framework, it is demonstrated that the Hall electric fields that develop during reconnection satisfy the stochastic ion heating criterion and that the ions involved indeed undergo chaotic motion. This mechanism is then kinetically verified via exact analyses and particle simulations and is thus ultimately established as the main ion heating mechanism in magnetic reconnection. An important progeny of magnetic reconnection is whistler waves. These waves interact with energetic particles and scatter their pitch-angles, triggering losses of magnetic confinement. A previous study demonstrated via exact relativistic analyses that if a particle undergoes a "two-valley" motion, it undergoes drastic changes in its pitch-angle. This analysis is extended to a relativistic thermal distribution of particles. The condition for two-valley motion is first derived; it is then shown that a significant fraction of the particle distribution meets this condition and thus undergoes large pitch-angle scatterings. The scaling of this fraction with the wave amplitude suggests that relativistic microburst events may be explained by the two-valley mechanism. It is also found that the widely-used second-order trapping theory is an inaccurate approximation of the theory presented. A new method of probing the magnetic field in a plasma is described and developed to some extent. It utilizes the two-photon Doppler-free laser-induced fluorescence technique, where two counter-propagating laser beams effectively cancel out the Doppler effect and excite electron populations. The fluorescence resulting from the subsequent de-excitation is then measured, enabling the resolution of Zeeman splitting of the spectral lines from which the magnetic field information can be inferred. A high-power, repetitively-pulsed radio-frequency plasma source was developed as the subject of diagnosis, and preliminary results are presented.</p

Some inequalities on totally real submanifolds in locally conformal Kaehler space forms

In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension.Korea Research Foundation Gran