360 research outputs found
N-body description of Debye shielding and Landau damping
This paper brings further insight into the recently published N-body
description of Debye shielding and Landau damping [Escande D F, Elskens Y and
Doveil F 2014 Plasma Phys. Control. Fusion 57 025017]. Its fundamental equation
for the electrostatic potential is derived in a simpler and more rigorous way.
Various physical consequences of the new approach are discussed, and this
approach is compared with the seminal one by Pines and Bohm [Pines D and Bohm D
1952 Phys. Rev. 85 338--353].Comment: invited talk to 42nd EPS conference on plasma physics (Lisbon, 2015),
submitted to Plasma Physics and Controlled Fusio
Perturbative approach to the nonlinear saturation of the tearing mode for any current gradient
Within the traditional frame of reduced MHD, a new rigorous perturbation
expansion provides the equation ruling the nonlinear growth and saturation of
the tearing mode for any current gradient. The small parameter is the magnetic
island width w. For the first time, the final equation displays at once terms
of order w ln(1/w) and w which have the same magnitude for practical purposes;
two new O(w) terms involve the current gradient. The technique is applicable to
the case of an external forcing. The solution for a static forcing is computed
explicitly and it exhibits three physical regimes.Comment: 4 pages, submitted to Physical Review Letter
Vlasov equation and -body dynamics - How central is particle dynamics to our understanding of plasmas?
Difficulties in founding microscopically the Vlasov equation for
Coulomb-interacting particles are recalled for both the statistical approach
(BBGKY hierarchy and Liouville equation on phase space) and the dynamical
approach (single empirical measure on one-particle
-space). The role of particle trajectories
(characteristics) in the analysis of the partial differential Vlasov--Poisson
system is stressed. Starting from many-body dynamics, a direct derivation of
both Debye shielding and collective behaviour is sketched.Comment: revTeX, 15 p
Calculation of transport coefficient profiles in modulation experiments as an inverse problem
The calculation of transport profiles from experimental measurements belongs
in the category of inverse problems which are known to come with issues of
ill-conditioning or singularity. A reformulation of the calculation, the
matricial approach, is proposed for periodically modulated experiments, within
the context of the standard advection-diffusion model where these issues are
related to the vanishing of the determinant of a 2x2 matrix. This sheds light
on the accuracy of calculations with transport codes, and provides a path for a
more precise assessment of the profiles and of the related uncertainty.Comment: V2: two typos correcte
Estimate of convection-diffusion coefficients from modulated perturbative experiments as an inverse problem
The estimate of coefficients of the Convection-Diffusion Equation (CDE) from
experimental measurements belongs in the category of inverse problems, which
are known to come with issues of ill-conditioning or singularity. Here we
concentrate on a particular class that can be reduced to a linear algebraic
problem, with explicit solution. Ill-conditioning of the problem corresponds to
the vanishing of one eigenvalue of the matrix to be inverted. The comparison
with algorithms based upon matching experimental data against numerical
integration of the CDE sheds light on the accuracy of the parameter estimation
procedures, and suggests a path for a more precise assessment of the profiles
and of the related uncertainty. Several instances of the implementation of the
algorithm to real data are presented.Comment: Extended version of an invited talk presented at the 2012 EPS
Conference. To appear in Plasma Physics and Controlled Fusio
Direct path from microscopic mechanics to Debye shielding, Landau damping, and wave-particle interaction
The derivation of Debye shielding and Landau damping from the -body
description of plasmas is performed directly by using Newton's second law for
the -body system. This is done in a few steps with elementary calculations
using standard tools of calculus, and no probabilistic setting. Unexpectedly,
Debye shielding is encountered together with Landau damping. This approach is
shown to be justified in the one-dimensional case when the number of particles
in a Debye sphere becomes large. The theory is extended to accommodate a
correct description of trapping and chaos due to Langmuir waves. Shielding and
collisional transport are found to be two related aspects of the repulsive
deflections of electrons, in such a way that each particle is shielded by all
other ones while keeping in uninterrupted motion.Comment: arXiv admin note: substantial text overlap with arXiv:1310.3096,
arXiv:1210.154
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