Generation of harmonic Langmuir modes during beam–plasma interaction is studied by means of nonlinear theoretical calculations and computer simulations. The present Vlasov simulation of multiple harmonic Langmuir modes (up to 12th harmonics), generalizes the previously available simulations which were restricted to the second harmonic only. The frequency-wave-number spectrum obtained by taking the Fourier transformation of simulated electric field both in time and space shows an excellent agreement with the theoretical nonlinear dispersion relations for harmonic Langmuir waves. The saturated wave amplitude features a quasi-power-law spectrum which reveals that the harmonic generation process may be an integral part of the Langmuir turbulence.

The Langmuir wave turbulence generated by a beam–plasma interaction has been studied since the early days of plasma physics research. In particular, mechanisms which lead to the quasi-power-law spectrum for Langmuir waves have been investigated, since such a spectrum defines the turbulence characteristics. Meanwhile, the generation of harmonic Langmuir modes during the beam–plasma interaction has been known for quite some time, and yet has not been satisfactorily accounted for thus far. In paper I of this series, nonlinear dispersion relations for these harmonics have been derived. In this paper (paper II), generalized weak turbulence theory which includes multiharmonic Langmuir modes is formulated and the self-consistent particle and wave kinetic equations are solved. The result shows that harmonic Langmuir mode spectra can indeed exhibit a quasi-power-law feature, implying multiscale structure in both frequency and wave number space spanning several orders of magnitude.

Generation of electrostatic multiple harmonic Langmuir modes during beam–plasma interaction process has been observed in laboratory and spaceborne active experiments, as well as in computer simulation experiments. Despite earlier efforts, such a phenomenon has not been completely characterized both theoretically and in terms of numerical simulations. This paper is a first in a series of three papers in which analytic expressions for harmonic Langmuir mode dispersion relations are derived and compared against the numerical simulation result.

Hume's project concerning the conflict between liberty and necessity is "reconciliatory". But what is the nature of Hume's project? Does he solve a problem in metaphysics only? And when Hume says that the dispute between the doctrines of liberty and necessity is merely verbal, does he mean that there is no genuine metaphysical dispute between the doctrines? In the present essay I argue for: (1) there is room for liberty in Hume's philosophy, and not only because the position is pro forma compatibilist, even though this has importance for the recognition that Hume's main concern when discussing the matter is with practice; (2) the position does not involve a "subjectivization" of every form of necessity: it is not compatibilist because it creates a space for the claim that the operations of the will are non-problematically necessary through a weakning of the notion of necessity as it applies to external objects; (3) Hume holds that the ordinary phenomena of mental causation do not preempt the atribuition of moral responsibility, which combines perfectly with his identification of the object of moral evaluation: the whole of the character of a person, in relation to which there is, nonetheless, liberty. I intend to support my assertions by a close reading of what Hume states in section 8 of the first Enquiry.