Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSolitary and Periodic Waves in Collisionless Plasmas: The Adlam-Allen Model Revisited
86
0
0.0
(
0
)
Added by
Vassilis Koukouloyannis
Publication date
2020
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider the Adlam-Allen (AA) system of partial differential equations which, arguably, is the first model that was introduced to describe solitary waves in the context of propagation of hydrodynamic disturbances in collisionless plasmas. Here, we identify the solitary waves of the model by implementing a dynamical systems approach. The latter suggests that the model also possesses periodic wave solutions --which reduce to the solitary wave in the limiting case of infinite period-- as well as rational solutions which are obtained herein. In addition, employing a long-wave approximation via a relevant multiscale expansion method, we establish the asymptotic reduction of the AA system to the Korteweg-de Vries equation. Such a reduction, is not only another justification for the above solitary wave dynamics, but also may offer additional insights for the emergence of other possible plasma waves. Direct numerical simulations are performed for the study of multiple solitary waves and their pairwise interactions. The stability of solitary waves is discussed in terms of potentially relevant criteria, while the robustness of spatially periodic wave solutions is touched upon by our numerical experiments.
rate research
Read More
We study the interactions of two or more solitons in the Adlam-Allen model describing the evolution of a (cold) plasma of positive and negative charges, in the presence of electric and transverse magnetic fields. In order to show that the interactions feature an exponentially repulsive nature, we elaborate two distinct approaches: (a) using energetic considerations and the Hamiltonian structure of the model; (b) using the so-called Manton method. We compare these findings with results of direct simulations, and identify adjustments necessary to achieve a quantitative match between them. Additional connections are made, such as with solitons of the Korteweg--de Vries equation. Future challenges are also mentioned in connection to this model and its solitary waves.
We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the classic variational method for proving orbital stability of solitary waves fails dramatically due to the fact that the second variation of the energy-momentum functional is infinitely indefinite. We establish nonlinear stability in energy norm under the spectral stability hypothesis that the linearization admits no non-zero eigenvalues of non-negative real part. We also verify this hypothesis for waves of small energy.
A model of global magnetic reconnection rate in relativistic collisionless plasmas is developed and validated by the fully kinetic simulation. Through considering the force balance at the upstream and downstream of the diffusion region, we show that the global rate is bounded by a value $sim 0.3$ even when the local rate goes up to $sim O(1)$ and the local inflow speed approaches the speed of light in strongly magnetized plasmas. The derived model is general and can be applied to magnetic reconnection under widely different circumstances.
Using fully kinetic simulations, we study the scaling of the inflow speed of collisionless magnetic reconnection from the non-relativistic to ultra-relativistic limit. In the anti-parallel configuration, the inflow speed increases with the upstream magnetization parameter $sigma$ and approaches the light speed when $sigma > O(100)$, leading to an enhanced reconnection rate. In all regimes, the divergence of pressure tensor is the dominant term responsible for breaking the frozen-in condition at the x-line. The observed scaling agrees well with a simple model that accounts for the Lorentz contraction of the plasma passing through the diffusion region. The results demonstrate that the aspect ratio of the diffusion region remains $sim 0.1$ in both the non-relativistic and relativistic limits.
A higher-order dispersive equation is introduced as a candidate for the governing equation of a field theory. A new class of solutions of the three-dimensional field equation are considered, which are not localized functions in the sense of the integrability of the square of the profile over an infinite domain. For this new class of solutions, the gradient and/or the Hessian/Laplacian are square integrable. In the linear limiting case, an analytical expression for the pseudolocalized solution is found and the method of variational approximation is applied to find the dynamics of the centers of the quasi-particles (QPs) corresponding to these solutions. A discrete Lagrangian can be derived due to the localization of the gradient and the Laplacian of the profile. The equations of motion of the QPs are derived from the discrete Lagrangian. The pseudomass (wave mass) of a QP is defined as well as the potential of interaction. The most important trait of the new QPs is that at large distances, the force of attraction is proportional to the inverse square of the distance between the QPs. This can be considered analogous to the gravitational force in classical mechanics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
