Investigation: Two-dimensional magnetic structures in space In space plasma envi

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Investigation: Two-dimensional magnetic structures in space In space plasma environment, the magnetic field often plays an important role, and the set of Maxwell's equations applies. In particular, under the assumption that the field is two-dimensional (partial differential/partial differential z = 0: see the above figure) and time independent, the 2D magnetic field can lie described by a scalar flux function A(x, y), or the magnetic vector potential. A = A(x, y)z, i.e., B_x = partial differential A/partial differential y. and B_y - partial differential A/partial differential x. See the figure above for the coordinate system and the simple geometry, where the dashed straight line represents an arbitrary spacecraft trajectory across the upper half plane. Now assume the magnetic field in the upper half plane is potential, i.e., current-free. (a) Show that the magnetic field in the upper half plane satisfies the following Laplace's equation (in terms of the scalar function): partial differential^2 A/partial differential x^2 + partial differential^2 A/partial differential y^2 = 0. (b) Show that on the spacecraft trajectory the field components are related by the following Hilbert transformation pair: B_x(zeta) = 1/pi integral^+ infinity_- infinity B_y(zeta') d zeta' B_y (zeta) = -1/pi integral^+ infinity_- infinity B_y(zeta')/zeta - zeta' d zeta'

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In the near-Earth space plasma environment such as the magnetospheric boundary and magnetosheath, Alfvénic solitary or coherent structures are commonly detected, which are often interpreted as nonlinear steepening of large-amplitude magnetosonic perturbation.11 Hasegawa and Chen found that plasma heating can be attained by mode conversion of Alfvén wave through the resonant surface in inhomogeneous plasmas.12,13 It is known that the electron acceleration has a close relationship with large amplitude solitary Alfvén wave. For instance, slow magnetosonic solitons observed in the magnetosphere by Cluster spacecraft may accelerate electrons up to several keV.14–17 Ofman and Davila employed 2.5D MHD simulation and SOHO UCVS signals to show that such a solitary wave may account for the solar wind acceleration and large velocity fluctuation.18 De Assis et al. showed that runaway electron production by DC field can be enhanced by kinetic Alfvén waves.19 Wu proposed an electron acceleration mechanism through shock-like structure of dissipative solitary kinetic Alfvén wave (DSKAW) where electron collision and ion acoustic turbulence effects play a key role.20,21

The above survey of the literature serves to illustrate the importance of Alfvénic waves of various forms in the particle acceleration and heating process, which may take place in various space plasma environments. The purpose of the present paper is to explore the physics of large amplitude solitary Alfvénic structure and the effects of trapped electrons. In the literature, the importance of trapped particles on large amplitude Alfvén waves has received attention. In Maxwell-Poisson plasma (that is, under electrostatic assumption), the Boltzmann relation breaks down even for infinitesimal wave amplitude as long as trapped electrons are present.22 In such a case, the parallel electric field along magnetic field is crucial for large amplitude solitary Alfvénic structures. We expect that trapped electrons will give non-trivial current contribution for Alfvén mode in Maxwell-Ampere plasma (that is, under more general electromagnetic formalism). It is the aim of the present paper to investigate the transverse Alfvénic solitary wave and the role of trapped electrons.

We present a method to analyze the wave and shock structures arising from Petschek-type magnetic reconnection. Based on a time-dependent analytical approach developed by Heyn and Semenov [Phys. Plasmas 3, 2725 (1996)] and Semenov et al. [Phys. Plasmas 11, 62 (2004)], we calculate the perturbations caused by a delta function-shaped reconnection electric field, which allows us to achieve a representation of the plasma variables in the form of Green’s functions. Different configurations for the initial conditions are considered. In the case of symmetric, antiparallel magnetic fields and symmetric plasma density, the well-known structure of an Alfvén discontinuity, a fast body wave, a slow shock, a slow wave, and a tube wave occurs. In the case of asymmetric, antiparallel magnetic fields, additionally surface waves are found. We also discuss the case of symmetric, antiparallel magnetic fields and asymmetric densities, which leads to a faster propagation in the lower half plane, causing side waves forming a Mach cone in the upper half plane. Complex effects like anisotropic propagation characteristics, intrinsic wave coupling, and the generation of different nonlinear and linear wave modes in a finite plasma are retained. The temporal evolution of these wave and shock structures is shown.

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