Search

The inclusion of drifts in plasma edge codes like SOLPS-ITER is required to match simulation data with experimental profiles. However, this remains numerically challenging. In this paper, the effect of some numerical factors on the final plasma solution is investigated. This study is performed on three EAST simulations in upper single null configuration: an attached purely deuterium case, an attached case with limited Ne-seeding and a detached Ne-seeded case. The effects of the anomalous conductivity and anomalous thermo-electric coefficient on the plasma potential are investigated. Next, the effect of the employed grids is shown. In order to investigate these effects, accurate drift simulations are needed. Therefore, the employed time step and used numerical parameters are discussed for the three studied simulations. For all presented simulations, it is verified that the restriction of the grid to the first flux surface tangent to the main chamber wall has only a small effect on the divertor solution. This means that the main power dissipation takes place inside the simulated domain and only a small fraction of the power is leaving the B2.5 grid trough the grid boundary closest to the first wall. Finally the effect of drifts on the asymmetry between the inner and outer target for EAST simulations is demonstrated.

We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates and of the present time. We describe how the model was motivated through an heuristic connection to a self-interacting, planar random walk which interacts with its own centre of mass via an excluded-volume mechanism, and is conjectured to be superdiffusive with a scale exponent $3/4$. The self-interacting process originated in discussions with Francis Comets., Comment: 26 pages, 4 figures; v2: minor revision

We explore the existence of a continuous marginal law with respect to the Lebesgue measure for each component $(X,Y,Z)$ of the solution to coupled quadratic forward-backward stochastic differential equations (QFBSDEs) {for which the drift coefficient of the forward component is either bounded and measurable or H\"older continuous. Our approach relies on a combination of the existence of a weak {\it decoupling field} (see \cite{Delarue2}), the integration with respect to space time local time (see \cite{Ein2006}), the analysis of the backward Kolmogorov equation associated to the forward component along with an It\^o-Tanaka trick (see \cite{FlanGubiPrio10})}. The framework of this paper is beyond all existing papers on density analysis for Markovian BSDEs and constitutes a major refinement of the existing results. We also derive a comonotonicity theorem for the control variable in this frame and thus extending the works \cite{ChenKulWei05}, \cite{DosDos13}. As applications of our results, we first analyse the regularity of densities of solution to coupled FBSDEs. In the second example, we consider a regime switching term structure interest rate models (see for e.g., \cite{ChenMaYin17}) for which the corresponding FBSDE has discontinuous drift. Our results enables us to: firstly study classical and Malliavin differentiability of the solutions for such models, secondly the existence of density of such solutions. Lastly we consider a pricing and hedging problem of contingent claims on non-tradable underlying, when the dynamic of the latter is given by a regime switching SDE (i.e., the drift coefficient is allowed to be discontinuous). We obtain a representation of the derivative hedge as the weak derivative of the indifference price function, thus extending the result in \cite{ArImDR10}., Comment: 46 pages, New Section with applications was added with a change of title

In this article we provide various analytical and numerical methods for calculating the average drift of magnetically trapped particles across field lines in complex geometries, and we compare these methods against each other. To evaluate bounce-integrals, we introduce a generalisation of the trapezoidal rule which is able to circumvent integrable singularities. We contrast this method with more standard quadrature methods in a parabolic magnetic well and find that the computational cost is significantly lower for the trapezoidal method, though at the cost of accuracy. With numerical routines in place, we next investigate conditions on particles which cross the computational boundary, and we find that important differences arise for particles affected by this boundary, which can depend on the specific implementation of the calculation. Finally, we investigate the bounce-averaged drifts in the optimized stellarator NCSX. From investigating the drifts, one can readily deduce important properties, such as what subset of particles can drive trapped-particle modes, and in what regions radial drifts are most deleterious to the stability of such modes., Comment: 12 pages, 6 figures

The High Field High Density Region (HFSFD) has been experimentally observed in both divertor and limiter tokamak devices. In order to numerically reproduced the HFSHD region in the limiter tokamak device J-TEXT, we first performed SOLPS-ITER simulations on the J-TEXT limiter tokamak with the activation of drifts, which is associated with the HFSHD region. The validated physical models, which is from ASDEX Upgrade (AUG) divertor modelling including full drifts and currents, were applied. Through a gas puffing rate scan, both attached and detached regimes were numerically obtained in the AUG divertor and J-TEXT limiter. The key plasma parameters in the J-TEXT limiter are evaluated with and without drifts that have a qualitative performance like AUG except the roll-overment of the total ion flux at the targets. The drift effects on the target profiles are investigated in which the maximum electron temperature at the outer targets is 15eV and 5eV respectively. When the outer targets are attached in the J-TEXT limiter and AUG divertor, the drifts result in the partial detachment of the inner targets. In the detached regimes, the drifts decrease the electron temperature on AUG divertor targets. However, for the J-TEXT limiter, the electron temperature only decreases at the far SOL region. The effect of drifts on the neutral density is also presented.

The transport properties of gapless edge modes at boundaries between topologically distinct domains are of fundamental and technological importance. Therefore, it is crucial to gain a better understanding of topological edge states and their response to interparticle interactions. Here, we experimentally study long-distance quantised Hall drifts in a harmonically confined topological pump of non-interacting and interacting ultracold fermionic atoms. We find that quantised drifts halt and reverse their direction when the atoms reach a critical slope of the confining potential, revealing the presence of a topological boundary. The drift reversal corresponds to a band transfer between a band with Chern number $C = +1$ and a band with $C = -1$ via a gapless edge mode, in agreement with the bulk-edge correspondence for non-interacting particles. We establish that a non-zero repulsive Hubbard interaction leads to the emergence of an additional edge in the system, relying on a purely interaction-induced mechanism, in which pairs of fermions are split.

The nonequilibrium Fokker-Planck dynamics with a non-conservative drift field, in dimension $N\geq 2$, can be related with the non-Hermitian quantum mechanics in a real scalar potential $V$ and in a purely imaginary vector potential -$iA$ of real amplitude $A$. Since Fokker-Planck probability density functions may be obtained by means of Feynman's path integrals, the previous observation points towards a general issue of "magnetically affine" propagators, possibly of quantum origin, in real and Euclidean time. In below we shall follow the $N=3$ "magnetic thread", within which one may keep under a computational control formally and conceptually different implementations of magnetism (or surrogate magnetism) in the dynamics of diffusion processes. We shall focus on interrelations (with due precaution to varied, not evidently compatible, notational conventions) of: (i) the pertinent non-conservatively drifted diffusions, (ii) the classic Brownian motion of charged particles in the (electro)magnetic field, (iii) diffusion processes arising within so-called Euclidean quantum mechanics (which from the outset employs non-Hermitian "magnetic" Hamiltonians), (iv) limitations of the usefulness of the Euclidean map $\exp(-itH_{quant}) \rightarrow \exp(-tH_{Eucl})$, regarding the probabilistic significance of inferred (path) integral kernels in the description of diffusion processes., Comment: 28 pp. Title and Abstract modified, sections VI and VII written anew