Comparison of a radial fractional transport model with tokamak experiments

Abstract

A radial fractional transport model [Kullberg et al., Phys. Rev. E 87, 052115 (2013)], that correctly incorporates the geometric effects of the domain near the origin and removes the singular behavior at the outer boundary, is compared to results of off-axis heating experiments performed in the Rijnhuizen Tokamak Project (RTP), ASDEX Upgrade, JET, and DIII-D tokamak devices. This comparative study provides an initial assessment of the presence of fractional transport phenomena in magnetic confinement experiments. It is found that the nonlocal radial model is robust in describing the steady-state temperature profiles from RTP, but for the propagation of heat waves in ASDEX Upgrade, JET, and DIII-D the model is not clearly superior to predictions based on Fick's law. However, this comparative study does indicate that the order of the fractional derivative, a, is likely a function of radial position in the devices surveyed. V C 2014 AIP Publishing LLC.

Nonlocal transport in bounded two-dimensional systems: An iterative method

“…Another element for a successful modeling of a nonlocal transport experiment using Lévy pdfs is the capability to handle spatial variations in the parameters associated with the distributions. This situation may arise in physical systems because the internal dynamics switches character within various regions of the system, as has been found in some model comparisons [29]. Fractional diffusion in a composite medium has been addressed by Sickler and Schachinger using a finite-width boundary between layers of different fractional order [30].…”

Generalized Thermopiezoelectricity with Memory‐Dependent Derivative and Transient Thermoelectromechanical Responses Analysis

“…In the latest decades, the increasing applications of fractional derivatives and integrals can be found in various domains of electrical engineering, laser cooling, signal/image processing, control system, and so forth. Particularly, in the researches of heat conduction behavior, it is noteworthy that the introduction of fractional-order derivatives/integrals has been experimentally verified to be a more accurate approach than the classical one [28,29]. As a powerful mathematical tool, the methodology of fractional calculus has been widely employed in micro-/nanoscale heating problems [30][31][32][33].…”

Self-adjoint integral operator for bounded nonlocal transport

“…3 of Ref. [24]. To obtain the blue curve, the left-hand side of the system ( x < 0.5 ) is wall material with κ = 10 8 , and the right-hand side is a nonlocal system with α = 1.1 , γ = 1 .…”

“…Another element for a successful modeling of a nonlocal transport experiment using Lévy pdfs is the capability to handle spatial variations in the parameters associated with the distributions. This situation may arise in physical systems because the internal dynamics switches character within various regions of the system, as has been found in some model comparisons [24]. Fractional diffusion in a composite medium has been addressed by Sickler and Schachinger using a finite-width boundary between layers of different fractional order [25].…”