A generic, hard transition to chaos

A hard-in-amplitude transition to chaos in a class of dissipative flows of broad applicability is presented. For positive values of a parameter F, no matter how small, a fully developed chaotic attractor exists within some domain of additional parameters, whereas no chaotic behavior exists for F < 0. As F is made positive, an unstable fixed point reaches an invariant plane to enter a phase half-space of physical solutions; the ghosts of a line of fixed points and a rich heteroclinic structure existing at F = 0 make the limits t --* +oc, F ~ +0 non-commuting, and allow an exact description of the chaotic flow. The formal structure of flows that exhibit the transition is determined. A subclass of such flows (coupled oscillators in near-resonance at any 2 : q frequency ratio, with F representing linear excitation of the first oscillator) is fully analysed

A derivation of thermodynamic principles

A detailed macroscopic description as in continuum mechanics, and just the concept of microstate,have been used to derive thermodynamics from mechanics. In opposition to statistical physics, the derivation lays emphasis on a definite prescription for macrostates (and non-equilibrium entropy), and uses basic features of the macrostate concept: complementary descriptions, involving either conservative and additive quantities or densities;scale-free character; reference to finite velocities and regions distant in space, thus introducing time indirectly. On the other hand, the derivation keeps the particle substratum (limit of number of particles N taken at fixed densities), and makes no ergodic-type considerations.

Alfvén wave far field from steady-current tethers

We analyzed he Alfvén waves ignaturele ft behindi n the ionospherbe y orbiting insulatedt etherso peratinga s thrusterso r generatorws ith steadyc urrentsU. sing a recentd escription of tetherr adiationt o determineth e far field, we showt hat, at their leadinge dges,t heA lfv6n wingsh avea n Airy functionc rosswises tructureT. he field amplitudef alls off weakly as the inversec uber oot of the distancea longt he wavef ront.T he fronti tself, whichc arriesa negligible fractiono f the powerr adiateda sA lfven waves,b roadensp roportionallyto the cuber oot of that distanceW. e showt hatc ollisionadl ecayb ecomesim portanat t about1 03k m alongt he front.F or tethersl ongert han about2 km, the top andb ottoms tructures("wings")a re fully disjoint.

The radiation impedance of orbiting conductors

The dispersion relation for waves in a cold, magnetized plasma is discussed using the potential for the longitudinal part of the electric field. This clarifies wave emission from a conductor in low Earth orbit and should be useful in considering the far field and both hot plasma and nonlinear, near-field effects. General formulas for radiation impedance are directly obtained. For tethers a fundamental dependence on contactor size is discussed. Spherical and ellipsoidal contactors and an (anodcless) bare tether are considered. Simple arguments on nonlinear contactor effects lead to a surprisingly simple result for impedances off the Alfven branch.

Artificial auroral effects from a bare conducting tether

An electrically floating metallic bare tether in a low Earth orbit would be highly negative with respect to the ambient plasma over most of its length, and would be bombarded by ambient ions.This would liberates secondary electrons which after acceleration through the same voltage, would form a magnetically guided two-sided planar e beam,and result in auroral effects(ionization and light emission)upon impacto on the atmospheric E layer, at about 120-140 km altitude.This papere examines in a preliminary way the feasibility of using this effecet as an uppeart atmospheric probe. Ionization rate can reach up to 10 3 cm 3 S -1 if a tape, instead of a wire, is used as tether. Contrary to standard e beams,the beam from the tether is free of spacecrafct charging and plasma interaction problems and its energy flux varies across the crosss ection,w hich is quite large;this would make possible continuous observation from the satellite, with high resolution both spectral and vertical, of the induced optical emissions. Ground observation might be possible at latitudes around 40ø , for night, magnetically quiet conditions.

Experimental evidence of a hard transition to chaos

A generic, sudden transition to chaos has been experimentally verified using electronic circuits. The particular system studied involves the near resonance of two coupled oscillators at 2:1 frequency ratio when the damping of the first oscillator becomes negative. We identified in the experiment all types of orbits described by theory. We also found that a theoretical, ID limit map fits closely a map of the experimental attractor which, however, could be strongly disturbed by noise. In particular, we found noisy periodic orbits, in good agreement with noise theory.

The orbital-motion-limited regime of cylindrical Langmuir probes

An asymptotic analysis of electron collection at high bias Fp serves to determine the domain of validity of the orbital-motion-limited regime of cylindrical Langmuir probes, which is basic for the workings of conductive bare tethers. The radius of a wire collecting OML current in an unmagnetized plasma at rest cannot exceed a value, Rmax , which is found to exhibit a minimum as a function of Fp ; atFp values of interest, Rmax is already increasing and is larger than the electron Debye length lDe . The breakdown of the regime relates to conditions far fromthe probe, at electron energies comparable to the ion thermal energy, kTi ; Rmax is found to increase with Ti . It is also found that ~1! the maximumwidth of a thin tape, if used instead of a wire, is 4Rmax ; ~2! the electron thermal gyroradius must be larger than both R and lDe for magnetic effects to be negligible; and ~3! conditions applying to the tether case are such that trapped-orbit effects are negligible.

Electron current to a probe in a magnetized, collisional plasma

Collisional analysis of electron collection by a probe in a strongly magnetized, fully ionized plasma is carried out. A solution to the complete set of macroscopic equations with classical transport coefficients that is wholly consistent in the domain is determined; R and le are probe radius and electron gyroradius, respectively. If R2/le 2 is large compared with mi/3me probe large compared with ion gyroradius, ion–electron energy exchange—rather than electron heat diffusion—keeps electrons isothermal. For smaller probes at negative bias, however, electron cooling occurs in the plasma beyond the sheath, with a potential overshoot lying well away from it. The probe characteristic in the electron-retarding range may then mimic the characteristic for a two electron-temperature plasma and lead to an overestimate of electron temperature; the validity of these results for other transport models is discussed

Cylindrical Langmuir probes beyond the orbital-motion-limited regime

The current I to a cylindrical probe at rest in an unmagnetized plasma, with probe bias highly positive, is determined. The way I lags behind the orbital-motion-limited OMLcurrent, 1 OML R, as the radius R exceeds the maximum radius for the OML regime to hold, is of interest for space-tether applications. The ratio I/I OML is roughly a decreasing function of R/lD R max /lDe , which is independent of bias, with lDe the electron Debye length and Rmax /l De roughly an increasing function of the temperature ratio, Ti /Te. The dependence of current on ion energy is used to discuss the effect of probe motion through the plasma, a case applying to tethers in low orbit.

A new basic effect in retarding potential analyzers

The Retarding Potential Analyzer (RPA) is the standard instrument for in situ measurement of ion temperature and other ionospheric parameters. The fraction of incoming ions rejected by a RPA produces perturbations that reach well ahead of a thin Debye sheath, a feature common to all collisionless, hypersonic flows past ion-rejecting bodies. This phenomenon is here found to result in a correction to Whipple’s classical law for the current characteristic of an ideal RPA sheath thin; inverse ram ion Mach number M-1, and ram angle of RPA aperture u, small or moderately small.

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 Schrödinger equation, has been analyzed; wave 1 is linearly unstable with growth rate , and waves 2 and 3 are stable with damping 2 and 3, respectively. The dependence of gross dynamical features on the damping model as characterized by the relation between damping and wave-vector ratios, 2 /3, k2 /k3, and the polarization of the waves, is discussed; two damping models, Landau k and resistive 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 as against flow contraction just requiring.In the case of right-hand RH polarization, point P may exist for all models other than Landau damping; for the resistive model, P may exist for RH polarization only if 2+3/2.

Bare-tether cathodic contact through thermoionic emission by low work-function materials

A new material, C12A7 : electride, which might present a work function as low as 0.6 eV and moderately high temperature stability, was recently proposed as coating for floating bare tethers. Arising from heating under space operation, current is emitted by thermionic emission along a thus coated cathodic segment. A preliminary study on the space-charge-limited (SCL) double layer in front of the cathodic segment is presented using Langmuir’s SCL electron current between cylindrical electrodes and orbital-motion-limited ion-collection sheath. A detailed calculation of current and bias profiles along the entire tether length is carried out with ohmic effects and the transition from SCL to full Richardson-Dushman emission included. Analysis shows that in the simplest drag mode, under typical orbital and tether conditions, thermionic emission leads to a short cathodic section and may eliminate the need for an active cathodic device and its corresponding gas feed requirements and power subsystem, which results in a truly “propellant-less” tether system for such basic applications as de-orbiting low earth orbit satellites.

E-beam propagation and interaction with atmosphere

This study purports to investigate whether a conductive tether left uninsulated and electrically floating in LEO could serve as an effective e-beam source to produce artificial auroras. An electrically floating tether comes out biased highly negative over most of its length. Ambient ions impacting it with KeV energies liberate secondary electrons, which are locally accelerated through the 2D tether voltage-bias, race down magnetic lines, and result in peak auroral emissions at about 120-160 km altitude. Since no current flows at either tether end, a bare-tether e-beam is fully free of spacecraft charging problems. Beam propagation and beam-atmosphere interactions need be modelled in a simple but quantitative way so as to allow a satisfactory discussion of observational options and their feasibility. The evolution in the energy spectrum of secondary electrons, their pitch distribution, and beam broadening due to collisions with neutrals, which would result in a broader but weaker tether footprint in the E-layer, need be modelled. Relations between particle/energy flux values, and ionization and accompanying emission rates, are considered.

Reduced three-wave model to study the hard transition to chaotic dynamics in Alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves