The Moment Approach to Solve the Drift-Kinetic Equation for Impurity Ions in the Plasma Edge Region

1992 ◽  
Vol 32 (3-4) ◽  
pp. 290-296 ◽  
Author(s):  
H. A. Claaßen ◽  
H. Gerhauser
Keyword(s):  
Kinetic Equation ◽  
Plasma Edge ◽  
Edge Region ◽  
Impurity Ions ◽  
Moment Approach ◽  
The Moment

SDP vs. LP Relaxations for the Moment Approach in Some Performance Evaluation Problems

2004 ◽  
Vol 20 (4) ◽  
pp. 439-456 ◽  
Author(s):  
Jean-Bernard Lasserre ◽  
Tomás Prieto-Rumeau
Keyword(s):  
Performance Evaluation ◽  
Moment Approach ◽  
The Moment

Neutral Transport Analysis in Plasma Edge Region of the GAMMA-10 Central-Cell

2009 ◽  
Vol 55 (2T) ◽  
pp. 185-190
Author(s):  
Y. Higashizono ◽  
Y. Nakashima ◽  
M. Shoji ◽  
N. Nishino ◽  
S. Kobayashi ◽  
...  
Keyword(s):  
Central Cell ◽  
Plasma Edge ◽  
Edge Region ◽  
Transport Analysis

Balmer- Intensity and Particle Flux in Plasma Edge Region of LHD

2002 ◽  
Vol 42 (6-7) ◽  
pp. 616-621 ◽  
Author(s):  
M. Goto ◽  
S. Morita ◽  
LHD experiment group
Keyword(s):  
Particle Flux ◽  
Plasma Edge ◽  
Edge Region

THE LANGEVIN OR KRAMERS APPROACH TO BIOLOGICAL MODELING

2004 ◽  
Vol 14 (10) ◽  
pp. 1561-1583 ◽  
Author(s):  
KARL P. HADELER ◽  
THOMAS HILLEN ◽  
FRITHJOF LUTSCHER
Keyword(s):  
Wave Equations ◽  
Space Variable ◽  
Linear Partial Differential Equation ◽  
Reaction Diffusion ◽  
Nonlinear Problems ◽  
Kramers Equation ◽  
Moment Approach ◽  
The Moment ◽  
Nonlinear Damped Wave Equations ◽  
And Diffusion

In the Langevin or Ornstein–Uhlenbeck approach to diffusion, stochastic increments are applied to the velocity rather than to the space variable. The density of this process satisfies a linear partial differential equation of the general form of a transport equation which is hyperbolic with respect to the space variable but parabolic with respect to the velocity variable, the Klein–Kramers or simply Kramers equation. This modeling approach allows for a more detailed description of individual movement and orientation dependent interaction than the frequently used reaction diffusion framework.For the Kramers equation, moments are computed, the infinite system of moment equations is closed at several levels, and telegraph and diffusion equations are derived as approximations. Then nonlinearities are introduced such that the semi-linear reaction Kramers equation describes particles which move and interact on the same time-scale. Also for these nonlinear problems a moment approach is feasible and yields nonlinear damped wave equations as limiting cases.We apply the moment method to the Kramers equation for chemotactic movement and obtain the classical Patlak–Keller–Segel model. We discuss similarities between chemotactic movement of bacteria and gravitational movement of physical particles.

Stochastic magnetic and ambipolar electric fields in the plasma edge region of RFX

1996 ◽  
Vol 36 (4) ◽  
pp. 435-442 ◽  
Author(s):  
V Antoni ◽  
E Martines ◽  
M Bagatin ◽  
D Desideri ◽  
G Serianni
Keyword(s):  
Electric Fields ◽  
Plasma Edge ◽  
Edge Region

scholarly journals Impurity temperature screening in stellarators close to quasisymmetry

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
Mike F. Martin ◽  
Matt Landreman
Keyword(s):  
Magnetic Field ◽  
Kinetic Equation ◽  
Particle Flux ◽  
Radial Electric Field ◽  
Impurity Particle ◽  
The Core ◽  
Impurity Transport ◽  
Radial Flux ◽  
Impurity Ions ◽  
The Magnetic Field

Impurity temperature screening is a favourable neoclassical phenomenon involving an outward radial flux of impurity ions from the core of fusion devices. Quasisymmetric magnetic fields lead to intrinsically ambipolar neoclassical fluxes that give rise to temperature screening for low enough $\unicode[STIX]{x1D702}^{-1}\equiv d\ln n/d\ln T$ . In contrast, neoclassical fluxes in generic stellarators will depend on the radial electric field, which is predicted to be inward for ion-root plasmas, potentially leading to impurity accumulation. Here, we examine the impurity particle flux in a number of approximately quasisymmetric stellarator configurations and parameter regimes while varying the amount of symmetry breaking in the magnetic field. For the majority of this work, neoclassical fluxes have been obtained using the SFINCS drift-kinetic equation solver with electrostatic potential $\unicode[STIX]{x1D6F7}=\unicode[STIX]{x1D6F7}(r)$ , where $r$ is a flux-surface label. Results indicate that achieving temperature screening is possible, but unlikely, at low-collisionality reactor-relevant conditions in the core. Thus, the small departures from symmetry in nominally quasisymmetric stellarators are large enough to significantly alter the neoclassical impurity transport. A further look at the magnitude of these fluxes when compared to a gyro-Bohm turbulence estimate suggests that neoclassical fluxes are small in configurations optimized for quasisymmetry when compared to turbulent fluxes.

scholarly journals Improving the moment approach for astrometric binaries: possible application to Cygnus X-1

2014 ◽  
Vol 66 (5) ◽  
Author(s):  
Kei Yamada ◽  
Masaki S. Yamaguchi ◽  
Hideki Asada ◽  
Naoteru Gouda
Keyword(s):  
Moment Approach ◽  
The Moment ◽  
Astrometric Binaries
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