158 research outputs found
Energy Conserving Non-relativistic Guiding Center Mechanics and the Galilean Principle of Relativity
Simultaneous Petri Net Synthesis
Petri net synthesis deals with the problem whether, given a labelled transition system TS, one can find a Petri net N with an initial marking M0 such that the reachability graph of (N. M0) is isomorphic to TS. This may be preceded by a pre-synthesis phase that will quickly reject ill-formed transition systems (and give structural reasons for the failure) and otherwise build data structures needed by the proper synthesis. The last phase proceeds by solving systems of linear inequalities, and may still fail but for less transparent reasons. In this paper, we consider an extended problem. A finite set of transition systems {TS1, ...,TSm} shall be called simultaneously Petri net solvable if there is a single Petri net N with several initial markings {M01,...,M0m}, such that for every i = 1,...,m, the reachability graph of (N, M0i) is isomorphic to TSi. The focus will be on choice-free nets, that is, nets without structural choices, and we explore how previously published efficient algorithms for the pre-synthesis and proper synthesis of bounded and choice-free Petri nets can be generalised for the simultaneous pre-synthesis and synthesis of such multi-marked nets. At the same time, the choice-free pre-synthesis of a single transition system shall be strengthened by introducing new structural checks
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 , a new
regime appears, not present in plane equilibria, in which negative-energy
perturbations exist for {\em any} value of . 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 (), 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 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 ( is the
electrostatic potential) and ( is
the total plasma pressure), a case which is of operational interest in magnetic
confinement systems, the existence of perpendicular NEPs depends on ,
where is the charge of the particle species . 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
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