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This paper examines discreteness effects in nearly collisionless N-body systems of charged particles interacting via an unscreened r^-2 force, allowing for bulk potentials admitting both regular and chaotic orbits. Both for ensembles and individual orbits, as N increases there is a smooth convergence towards a continuum limit. Discreteness effects are well modeled by Gaussian white noise with relaxation time t_R = const * (N/log L)t_D, with L the Coulomb logarithm and t_D the dynamical time scale. Discreteness effects accelerate emittance growth for initially localised clumps. However, even allowing for discreteness effects one can distinguish between orbits which, in the continuum limit, feel a regular potential, so that emittance grows as a power law in time, and chaotic orbits, where emittance grows exponentially. For sufficiently large N, one can distinguish two different `kinds of chaos. Short range microchaos, associated with close encounters between charges, is a generic feature, yielding large positive Lyapunov exponents X_N which do not decrease with increasing N even if the bulk potential is integrable. Alternatively, there is the possibility of larger scale macrochaos, characterised by smaller Lyapunov exponents X_S, which is present only if the bulk potential is chaotic. Conventional computations of Lyapunov exponents probe X_N, leading to the oxymoronic conclusion that N-body orbits which look nearly regular and have sharply peaked Fourier spectra are `very chaotic. However, the `range of the microchaos, set by the typical interparticle spacing, decreases as N increases, so that, for large N, this microchaos, albeit very strong, is largely irrelevant macroscopically. A more careful numerical analysis allows one to estimate both X_N and X_S.
This paper discusses three new issues that necessarily arise in realistic attempts to apply nonlinear dynamics to galaxy evolution, namely: (i) the meaning of chaos in many-body systems, (ii) the time-dependence of the bulk potential, which can trigg
The dynamics of wave-particle interactions in magnetized plasmas restricts the wave amplitude to moderate values for particle beam acceleration from rest energy. We analyze how a perturbing invariant robust barrier modifies the phase space of the sys
Electron evaporation plays an important role in the electron temperature evolution and thus expansion rate in low-density ultracold plasmas. In addition, evaporation is useful as a potential tool for obtaining colder electron temperatures and charact
This paper continues a numerical investigation of orbits evolved in `frozen, time-independent N-body realisations of smooth time-independent density distributions corresponding to both integrable and nonintegrable potentials, allowing for N as large
In this work, we analyze the creation of the discharge asymmetry and the concomitant formation of the DC self-bias voltage in capacitively coupled radio frequency plasmas driven by multi-frequency waveforms, as a function of the electrode surface cha