G. Sánchez-Arriaga

Damping models in the truncated derivative nonlinear Schrödinger equation

Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schrodinger equation, has been analyzed; wave 1 is linearly unstable with growth rate Γ, and waves 2 and 3 are stable with damping γ2 and γ3, respectively. The dependence of gross dynamical features on the damping model (as characterized by the relation between damping and wave-vector ratios, γ2∕γ3, k2∕k3), and the polarization of the waves, is discussed; two damping models, Landau (γ∝k) and resistive (γ∝k2), are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist for Γ<2(γ2+γ3)∕3, as against flow contraction ju...

Impact of Nonideal Effects on Bare Electrodynamic Tether Performance

The paper deals with three nonideal effects, often neglected in the literature, which affect the current and potential profiles along a bare electrodynamic tether. The first appears when the size of the tether cross-section width is large enough to have potential barriers for the probe radius in the radial effective potential energy of the plasma electrons. The tether is not able to capture the orbital-motion-limited current law and is said to operate beyond the orbital-motion-limited regime. It is shown that this effect can be accurately modeled by just scaling the tether characteristic length according to a dimensionless factor depending on tether and plasma properties. The high-bias approximation in the orbital-motion-limited current collection law, normally assumed in past work, is discussed. The third effect becomes relevant when the cathodic plasma contactor potential drop is nonnegligible compared with the product of the tether length and the motional electric field. Numerical simulations performed...

The truncation model of the derivative nonlinear Schrödinger equation

The derivative nonlinear Schrodinger (DNLS) equation is explored using a truncation model with three resonant traveling waves. In the conservative case, the system derives from a time-independent Hamiltonian function with only one degree of freedom and the solutions can be written using elliptic functions. In spite of its low dimensional order, the truncation model preserves some features from the DNLS equation. In particular, the modulational instability criterion fits with the existence of two hyperbolic fixed points joined by a heteroclinic orbit that forces the exchange of energy between the three waves. On the other hand, numerical integrations of the DNLS equation show that the truncation model fails when wave energy is increased or left-hand polarized modulational unstable modes are present. When dissipative and growth terms are added the system exhibits a very complex dynamics including appearance of several attractors, period doubling bifurcations leading to chaos as well as other nonlinear pheno...

Direct Vlasov simulations of electron-attracting cylindrical Langmuir probes in flowing plasmas

Current collection by positively polarized cylindrical Langmuir probes immersed in flowing plasmas is analyzed using a non-stationary direct Vlasov-Poisson code. A detailed description of plasma density spatial structure as a function of the probe-to-plasma relative velocity U is presented. Within the considered parametric domain, the well-known electron density maximum close to the probe is weakly affected by U. However, in the probe wake side, the electron density minimum becomes deeper as U increases and a rarified plasma region appears. Sheath radius is larger at the wake than at the front side. Electron and ion distribution functions show specific features that are the signature of probe motion. In particular, the ion distribution function at the probe front side exhibits a filament with positive radial velocity. It corresponds to a population of rammed ions that were reflected by the electric field close to the positively biased probe. Numerical simulations reveal that two populations of trapped electrons exist: one orbiting around the probe and the other with trajectories confined at the probe front side. The latter helps to neutralize the reflected ions, thus explaining a paradox in past probe theory.

Relativistic breather-type solitary waves with linear polarization in cold plasmas

Linearly polarized solitary waves, arising from the interaction of an intense laser pulse with a plasma, are investigated. Localized structures, in the form of exact numerical nonlinear solutions of the one-dimensional Maxwell-fluid model for a cold plasma with fixed ions, are presented. Unlike stationary circularly polarized solitary waves, the linear polarization gives rise to a breather-type behavior and a periodic exchange of electromagnetic energy and electron kinetic energy at twice the frequency of the wave. A numerical method based on a finite-differences scheme allows us to compute a branch of solutions within the frequency range Ωmin<Ω<ωpe, where ωpe and Ωmin are the electron plasma frequency and the frequency value for which the plasma density vanishes locally, respectively. A detailed description of the spatiotemporal structure of the waves and their main properties as a function of Ω is presented. Small-amplitude oscillations appearing in the tail of the solitary waves, a consequence of the linear polarization and harmonic excitation, are explained with the aid of the Akhiezer-Polovin system. Direct numerical simulations of the Maxwell-fluid model show that these solitary waves propagate without change for a long time.

Relativistic solitary waves modulating long laser pulses in plasmas

This paper discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From a mathematical point of view they are exact solutions of the one-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of travelling wave solutions with velocity V and vector potential frequency ω, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. Using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a large variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values and classify them according to (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric V–ω plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particle-in-cell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.

Flight Dynamics and Stability of Kites in Steady and Unsteady Wind Conditions

The flight dynamics and stability of a kite with a single main line flying in steady and unsteady wind conditions are discussed. A simple dynamic model with five degrees of freedom is derived with the aid of Lagrangian formulation, which explicitly avoids any constraint force in the equations of motion. The longitudinal and lateral–directional modes and stability of the steady flight under constant wind conditions are analyzed by using both numerical and analytical methods. Taking advantage of the appearance of small dimensionless parameters in the model, useful analytical formulas for stable-designed kites are found. Under nonsteady wind-velocity conditions, the equilibrium state disappears and periodic orbits occur. The kite stability and an interesting resonance phenomenon are explored with the aid of a numerical method based on Floquet theory.

Efficient Computation of Current Collection in Bare Electrodynamic Tethers in and beyond OML Regime

AbstractOne key issue in the simulation of bare electrodynamic tethers (EDTs) is the accurate and fast computation of the collected current, an ambient dependent operation necessary to determine the Lorentz force for each time step. This paper introduces a novel semianalytical solution that allows researchers to compute the current distribution along the tether efficient and effectively under orbital-motion-limited (OML) and beyond OML conditions, i.e.,xa0if tether radius is greater than a certain ambient dependent threshold. The method reduces the original boundary value problem to a couple of nonlinear equations. If certain dimensionless variables are used, the beyond OML effect just makes the tether characteristic length L* larger and it is decoupled from the current determination problem. A validation of the results and a comparison of the performance in terms of the time consumed is provided, with respect to a previous ad hoc solution and a conventional shooting method.

Truncation model in the triple-degenerate derivative nonlinear Schrödinger equation

The triple-degenerate derivative nonlinear Schrodinger (TDNLS) system modified with resistive wave damping and growth is truncated to study the coherent coupling of four waves, three Alfven and one acoustic, near resonance. In the conservative case, the truncation equations derive from a time independent Hamiltonian function with two degrees of freedom. Using a Poincare map analysis, two parameters regimes are explored. In the first regime we check how the modulational instability of the TDNLS system affects to the dynamics of the truncation model, while in the second one the exact triple degenerated case is discussed. In the dissipative case, the truncation model gives rise to a six dimensional flow with five free parameters. Computing some bifurcation diagrams the dependence with the sound to Alfven velocity ratio as well as the Alfven modes involved in the truncation is analyzed. The system exhibits a wealth of dynamics including chaotic attractor, several kinds of bifurcations, and crises. The truncat...

Orbital motion theory and operational regimes for cylindrical emissive probes

A full-kinetic model based on the orbital-motion theory for cylindrical emissive probes (EPs) is presented. The conservation of the distribution function, the energy, and the angular momentum for cylindrical probes immersed in collisionless and stationary plasmas is used to write the Vlasov-Poisson system as a single integro-differential equation. It describes self-consistently the electrostatic potential profile and, consequently, the current-voltage (I-V) probe characteristics. Its numerical solutions are used to identify different EP operational regimes, including orbital-motion-limited (OML)/non-OML current collection and monotonic/non-monotonic potential, in the parametric domain of probe bias and emission level. The most important features of the potential and density profiles are presented and compared with common approximations in the literature. Conventional methods to measure plasma potential with EPs are briefly revisited. A direct application of the model is to estimate plasma parameters by fi...