354 research outputs found
The Kinetic and Hydrodynamic Bohm Criterions for Plasma Sheath Formation
The purpose of this paper is to mathematically investigate the formation of a
plasma sheath, and to analyze the Bohm criterions which are required for the
formation. Bohm derived originally the (hydrodynamic) Bohm criterion from the
Euler--Poisson system. Boyd and Thompson proposed the (kinetic) Bohm criterion
from kinetic point of view, and then Riemann derived it from the
Vlasov--Poisson system. In this paper, we prove the solvability of boundary
value problems of the Vlasov--Poisson system. On the process, we see that the
kinetic Bohm criterion is a necessary condition for the solvability. The
argument gives a simpler derivation of the criterion. Furthermore, the
hydrodynamic criterion can be derived from the kinetic criterion. It is of
great interest to find the relation between the solutions of the
Vlasov--Poisson and Euler--Poisson systems. To clarify the relation, we also
study the hydrodynamic limit of solutions of the Vlasov--Poisson system.Comment: 24 pages, 2 figure
Traveling Waves of the Vlasov--Poisson System
We consider the Vlasov--Poisson system describing a two-species plasma with
spatial dimension and the velocity variable in . We find the
necessary and sufficient conditions for the existence of solitary waves, shock
waves, and wave trains of the system, respectively. To this end, we need to
investigate the distribution of ions trapped by the electrostatic potential.
Furthermore, we classify completely in all possible cases whether or not the
traveling wave is unique. The uniqueness varies according to each traveling
wave when we exclude the variant caused by translation. For the solitary wave,
there are both cases that it is unique and nonunique. The shock wave is always
unique. No wave train is unique.Comment: 56 pages, 9 figure
A priori estimates of solutions to the motion of an inextensible hanging string
We consider the initial boundary value problem to the motion of an
inextensible hanging string of finite length under the action of the gravity.
In this problem, the tension of the string is also an unknown quantity. It is
determined as a unique solution to a two-point boundary value problem, which is
derived from the inextensibility of the string together with the equation of
motion, and degenerates linearly at the free end. We derive a priori estimates
of solutions to the initial boundary value problem in weighted Sobolev spaces
under a natural stability condition. The necessity for the weights results from
the degeneracy of the tension. Uniqueness of solution is also proved.Comment: 40 pages, 3 figure
Nonlinear Stability and Instability of Plasma Boundary Layers
We investigate the formation of a plasma boundary layer (sheath) by
considering the Vlasov--Poisson system on a half-line with the completely
absorbing boundary condition. In an earlier paper by the first two authors, the
solvability of the stationary problem is studied. In this paper, we study the
nonlinear stability and instability of these stationary solutions of the
Vlasov--Poisson system
Gravitino Dark Matter without R-parity
Cosmological issues are examined when gravitino is the lightest superparticle
(LSP) and R-parity is broken. Decays of the next lightest superparticles occur
rapidly via R-parity violating interaction, and thus they do not upset the
big-bang nucleosynthesis, unlike the R-parity conserving case. The gravitino
LSP becomes unstable, but its lifetime is typically much longer than the age of
the Universe. It turns out that observations of diffuse photon background
coming from radiative decays of the gravitino do not severely constrain the
gravitino abundance, and thus the gravitino weighing less than around 1 GeV can
be dark matter of the Universe when bilinear R-parity violation generates a
neutrino mass which accounts for the atmospheric neutrino anomaly.Comment: 11 pages, 1 figur
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