Negative-Energy Perturbations in Circularly Cylindrical Equilibria within the Framework of Maxwell-Drift Kinetic Theory

The conditions for the existence of negative-energy perturbations (which could be nonlinearly unstable and cause anomalous transport) are investigated in the framework of linearized collisionless Maxwell-drift kinetic theory for the case of equilibria of magnetically confined, circularly cylindrical plasmas and vanishing initial field perturbations. For wave vectors with a non-vanishing component parallel to the magnetic field, the plane equilibrium conditions (derived by Throumoulopoulos and Pfirsch [Phys Rev. E {\bf 49}, 3290 (1994)]) are shown to remain valid, while the condition for perpendicular perturbations (which are found to be the most important modes) is modified. Consequently, besides the tokamak equilibrium regime in which the existence of negative-energy perturbations is related to the threshold value of 2/3 of the quantity $\eta_\nu = \frac {\partial \ln T_\nu} {\partial \ln N_\nu}$, a new regime appears, not present in plane equilibria, in which negative-energy perturbations exist for {\em any} value of $\eta_\nu$. For various analytic cold-ion tokamak equilibria a substantial fraction of thermal electrons are associated with negative-energy perturbations (active particles). In particular, for linearly stable equilibria of a paramagnetic plasma with flat electron temperature profile ($\eta_e=0$), the entire velocity space is occupied by active electrons. The part of the velocity space occupied by active particles increases from the center to the plasma edge and is larger in a paramagnetic plasma than in a diamagnetic plasma with the same pressure profile. It is also shown that, unlike in plane equilibria, negative-energy perturbations exist in force-free reversed-field pinch equilibria with a substantial fraction of active particles.Comment: 31 pages, late

Negative-energy perturbations in cylindrical equilibria with a radial electric field

The impact of an equilibrium radial electric field $E$ on negative-energy perturbations (NEPs) (which are potentially dangerous because they can lead to either linear or nonlinear explosive instabilities) in cylindrical equilibria of magnetically confined plasmas is investigated within the framework of Maxwell-drift kinetic theory. It turns out that for wave vectors with a non-vanishing component parallel to the magnetic field the conditions for the existence of NEPs in equilibria with E=0 [G. N. Throumoulopoulos and D. Pfirsch, Phys. Rev. E 53, 2767 (1996)] remain valid, while the condition for the existence of perpendicular NEPs, which are found to be the most important perturbations, is modified. For $|e_i\phi|\approx T_i$ ($\phi$ is the electrostatic potential) and $T_i/T_e > \beta_c\approx P/(B^2/8\pi)$ ($P$ is the total plasma pressure), a case which is of operational interest in magnetic confinement systems, the existence of perpendicular NEPs depends on $e_\nu E$, where $e_\nu$ is the charge of the particle species $\nu$. In this case the electric field can reduce the NEPs activity in the edge region of tokamaklike and stellaratorlike equilibria with identical parabolic pressure profiles, the reduction of electron NEPs being more pronounced than that of ion NEPs.Comment: 30 pages, late

Entre circulations individuelles et immobilité familiale : les élites napolitaines face au déclin

Les travaux sur les nouvelles mobilités des classes supérieures dans le contexte de la mondialisation se sont multipliés ces dernières années. Étudiant les circulations des cadres des firmes multinationales, certains ont formulé l’idée d’une distension des liens entre bourgeoisie et territoire national (Duclos, 2002), voire d’une émergence d’une nouvelle « élite transnationale » (Beaverstock, 2001). D’autres ont au contraire souligné les décalages entre discours et pratiques dans ce milieu des élites de la mondialisation, entre un « imaginaire globalitaire » relevant largement de la posture et des pratiques sociales et patrimoniales encore fortement enracinées localement (Wagner, 1998, 2003 ; Pierre, 2005)

Szegő-type trace asymptotics for operators with translational symmetry

The classical Szegő limit theorem describes the asymptotic behaviour of Toeplitz determinants as the size of the Toeplitz matrix grows. The continuous analogue are trace asymptotics for Wiener--Hopf operators on intervals of growing length. We study two problems related to these scaling asymptotics. The first problem concerns the higher-dimensional version of the trace asymptotics. Namely, consider a translation-invariant bounded linear operator in dimension two whose integral kernel exhibits super-polynomial off-diagonal decay. Then we study the spectral asymptotics of its spatial restriction to the interior of a scaled polygon, as the scaling parameter tends to infinity. To this end, we provide complete trace asymptotics for analytic functions of the truncated operator. These consist of three terms, which reflect the geometry of the polygon. If the polygon is substituted by a domain with smooth boundary, then the corresponding asymptotics are well-known. However, we show that the constant order term in the expansion for the polygon cannot be recovered from a formal approximation by smooth domains. This fact is reminiscent of the heat trace anomaly for the Dirichlet Laplacian. A prominent application of trace asymptotics for Wiener--Hopf operators lies in quantum information theory: they can be used to compute the bipartite entanglement entropy for the ground state of a free Fermi gas in the absence of an external field. At zero temperature, this requires studying Wiener--Hopf operators with a discontinuous symbol, which causes notable difficulties. In the second part of the thesis, based on joint work with Alexander V. Sobolev, we prove a two-term asymptotic trace formula for the periodic Schrödinger operator in dimension one. This formula can be applied to compute the aforementioned entanglement entropy when the fermions are exposed to a periodic electric field. Moreover, the subleading order of the asymptotics identifies the spectrum of the periodic Schrödinger operator