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12 pages, 951 KiB

Open AccessArticle

Cross-Analysis of Magnetic and Current Density Field Topologies in a Quiescent High Confinement Mode Tokamak Discharge

by Marie-Christine Firpo

Foundations 2025, 5(2), 22; https://doi.org/10.3390/foundations5020022 - 17 Jun 2025

Viewed by 263

In axisymmetric fusion devices like tokamaks, the winding of the magnetic field is characterized by its safety profile

q = q_{B}

. Similarly, the winding of the current density field is characterized by

q_{J}

. Currently, the relationship between

q_{B}

[...] Read more.

In axisymmetric fusion devices like tokamaks, the winding of the magnetic field is characterized by its safety profile

q = q_{B}

. Similarly, the winding of the current density field is characterized by

q_{J}

. Currently, the relationship between

q_{B}

and

q_{J}

profiles and their effect on tokamak plasma confinement properties remains unexplored, as the

q_{J}

profile is neither computed nor considered. This study presents a reconstruction of the current density winding profile from experimental data in the quiescent H-mode. The topology analysis derived from

(q_{B}, q_{J})

was carried out using Hamada coordinates. It shows a large central plasma region unaffected by current filamentation-driven resonant magnetic perturbations, while the outer region harbors a spectrum of magnetic resonant modes, induced by current filaments located within the core plasma, which degrade peripheral confinement. These results suggest a QH-mode signature pattern needing further validation with additional data. Implementing

(q_{B}, q_{J})

real-time monitoring could provide insights into tokamak confinement regimes with significant implications. Full article

(This article belongs to the Section Physical Sciences)

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12 pages, 1780 KiB

Open AccessArticle

The Grad–Shafranov Equation in Cap-Cyclide Coordinates: The Heun Function Solution

by Flavio Crisanti, Clemente Cesarano and Artur Ishkhanyan

Mathematics 2023, 11(9), 2087; https://doi.org/10.3390/math11092087 - 27 Apr 2023

Cited by 1 | Viewed by 2094

Abstract

The Grad–Shafranov plasma equilibrium equation was originally solved analytically in toroidal geometry, which fitted the geometric shape of the first Tokamaks. The poloidal surface of the Tokamak has evolved over the years from a circular to a D-shaped ellipse. The natural geometry that describes such a shape is the prolate elliptical one, i.e., the cap-cyclide coordinate system. When written in this geometry, the Grad–Shafranov equation can be solved in terms of the general Heun function. In this paper, we obtain the complete analytical solution of the Grad–Shafranov equation in terms of the general Heun functions and compare the result with the limiting case of the standard toroidal geometry written in terms of the Fock functions. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

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22 pages, 584 KiB

Open AccessArticle

The Interplay between Coronal Holes and Solar Active Regions from Magnetohydrostatic Models

by Jaume Terradas

Physics 2023, 5(1), 276-297; https://doi.org/10.3390/physics5010021 - 28 Feb 2023

Cited by 2 | Viewed by 2012

Abstract

Coronal holes (CHs) and active regions (ARs) are typical magnetic structures found in the solar corona. The interaction of these two structures was investigated mainly from the observational point of view, but a basic theoretical understanding of how they are connected is missing. To address this problem, in this paper, magnetohydrostatic models are constructed by numerically solving a Grad–Shafranov equation in two dimensions. A common functional form for the pressure and temperature in the CH and in the AR are assumed throught the study. Keeping the parameters of the CH constant and modifying the parameters of the nearby bipolar AR, one finds essentially three types of solutions depending on the magnitude and sign of the magnetic field at the closest foot of the AR to the CH. Two of the three solutions match well with the observation, but the third solution predicts the existence of closed magnetic field lines with quite low density and temperature with opposite characteristics to those in typical ARs. Simple analytical expressions are obtained for the pressure, temperature and density at the core of the AR and their dependence upon several major physical parameters are studied. The results obtained in this paper need to be contrasted with observations. Full article

(This article belongs to the Special Issue A Themed Issue in Honor of Professor Marcel Goossens on the Occasion of His 75th Birthday)

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16 pages, 4548 KiB

Open AccessArticle

Magnetic Force-Free Theory: Nonlinear Case

by Brunello Tirozzi and Paolo Buratti

Physics 2022, 4(1), 21-36; https://doi.org/10.3390/physics4010003 - 10 Jan 2022

Viewed by 2806

Abstract

In this paper, a theory of force-free magnetic field useful for explaining the formation of convex closed sets, bounded by a magnetic separatrix in the plasma, is developed. This question is not new and has been addressed by many authors. Force-free magnetic fields [...] Read more.

\nabla \times B = Λ B

with some field conditions

B_{\partial Ω}

on the boundary

\partial Ω

of the plasma region. In many physical situations, it has been noticed that

Λ

is not constant but may vary in the domain

Ω

giving rise to many different interesting physical situations. We set

Λ = Λ (ψ)

with

ψ

being the poloidal magnetic flux function. Then, an analytic method, based on a first-order expansion of

ψ

with respect to a small parameter

α

, is developed. The Grad–Shafranov equation for

ψ

is solved by expanding the solution in the eigenfunctions of the zero-order operator. An analytic expression for the solution is obtained deriving results on the transition through resonances, the amplification with respect to the gun inflow. Thus, the formation of spheromaks or protosphera structure of the plasma is determined in the case of nonconstant

Λ

. Full article

(This article belongs to the Section Statistical Physics and Nonlinear Phenomena)

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