520 research outputs found
Nonquasilinear evolution of particle velocity in incoherent waves with random amplitudes
The one-dimensional motion of particles in the field of many incoherent
waves is revisited numerically. When the wave complex amplitudes are
independent, with a gaussian distribution, the quasilinear approximation is
found to always overestimate transport and to become accurate in the limit of
infinite resonance overlap.Comment: 8 pages Elsevier style. Communications in Nonlinear Science and
Numerical Simulation accepted (2008) in pres
Diffusion limit for many particles in a periodic stochastic acceleration field
The one-dimensional motion of any number \cN of particles in the field of
many independent waves (with strong spatial correlation) is formulated as a
second-order system of stochastic differential equations, driven by two Wiener
processes. In the limit of vanishing particle mass , or
equivalently of large noise intensity, we show that the momenta of all
particles converge weakly to independent Brownian motions, and this
convergence holds even if the noise is periodic. This justifies the usual
application of the diffusion equation to a family of particles in a unique
stochastic force field. The proof rests on the ergodic properties of the
relative velocity of two particles in the scaling limit.Comment: 20 page
Kinetic limit of N-body description of wave-particle self- consistent interaction
A system of N particles eN=(x1,v1,...,xN,vN) interacting self-consistently
with M waves Zn=An*exp(iTn) is considered. Hamiltonian dynamics transports
initial data (eN(0),Zn(0)) to (eN(t),Zn(t)). In the limit of an infinite number
of particles, a Vlasov-like kinetic equation is generated for the distribution
function f(x,v,t), coupled to envelope equations for the M waves. Any initial
data (f(0),Z(0)) with finite energy is transported to a unique (f(t),Z(t)).
Moreover, for any time T>0, given a sequence of initial data with N particles
distributed so that the particle distribution fN(0)-->f(O) weakly and with
Zn(0)-->Z(O) as N tends to infinity, the states generated by the Hamiltonian
dynamics at all time 0<t<T are such that (eN(t),Zn(t)) converges weakly to
(f(t),Z(t)). Comments: Kinetic theory, Plasma physics.Comment: 18 pages, LaTe
Ornstein-Uhlenbeck limit for the velocity process of an -particle system interacting stochastically
An -particle system with stochastic interactions is considered.
Interactions are driven by a Brownian noise term and total energy conservation
is imposed. The evolution of the system, in velocity space, is a diffusion on a
-dimensional sphere with radius fixed by the total energy. In the
limit, a finite number of velocity components are shown to
evolve independently and according to an Ornstein-Uhlenbeck process.Comment: 19 pages ; streamlined notations ; new section on many particles with
momentum conservation ; new appendix on Kac syste
A symplectic, symmetric algorithm for spatial evolution of particles in a time-dependent field
A symplectic, symmetric, second-order scheme is constructed for particle
evolution in a time-dependent field with a fixed spatial step. The scheme is
implemented in one space dimension and tested, showing excellent adequacy to
experiment analysis.Comment: version 2; 16 p
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