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In tokamak operation the control of dangerous MHD instabilities, possibly in real-time sce- narios, must rely on prompt and robust diagnostics of the state and stability of the system. The information on the current J profile details is generally considered undetectable from out- side the plasma boundary, but it can be conjectured that it is somehow mapped onto the sur- face providing a Shannon-Bekenstein information entropy [1], associated to the probability that some internal profile feature ("mode") exists.

This thesis concentrates on investigating the presence of 3D ideal MHD instabilities, particularly a saturated 1/1 ideal internal kink, on neoclassical phenomena such as the bootstrap current and heavy impurity transport. The MHD equilibria are generated using the ideal MHD equilibrium solver \texttt{VMEC} under free-boundary conditions and is used as a basis for the neoclassical calculations performed. The bootstrap current and the parallel flows are examined using the Shaing-Callen 3D neoclassical formulation\cite{ShaingReview}. The examination of equilibria with ideal response to 3D perturbations such as toroidal field ripple and resonant magnetic perturbations (RMPs) is performed. It is found that RMPs and toroidal ripple produce a weak 3D response leading to a bootstrap current profile indistinguishable from axisymmetry. Any additional effects are further obscured by the presence of numerical resonances on q-rational surfaces. It is found, however, that a non-resonant 1/1 ideal internal kink which avoids the q=1 resonance, is well-suited for computation of the bootstrap current density. The bootstrap current is observed to be strongly augmented in the helical core region of the 1/1 internal kink before returning to match the axisymmetric values in the near-axisymmetric region outside the helical core. Explanations for the augmentation of the bootstrap current are provided in an analytical derivation. A similar augmentation is observed for background ion flows as well, including the presence of a finite poloidal flow. Heavy impurities such as tungsten face friction because of the impurity particles colliding with the background ions, and therefore the magnitude of this flow becomes of paramount importance. The \texttt{VENUS-LEVIS} orbit-following code is used to follow the impurity particles with additional effects provided by the centrifugal and Coriolis forces while colliding them in the correct frame of the background ion distribution. This is successfully benchmarked with known results in neoclassical theory concerning impurity transport. Without flows in axisymmetry, an on-axis peaked impurity distribution is observed. With flows, an off-axis peaking of impurities is observed, following known neoclassical expressions. Furthermore, it is found that the impurity accumulation was strongly increased for the combined case of helical core with flows, leading again to a near-axis peaked density profile. The results are compared heuristically with a known peaking formula incorporating the presence of a finite poloidal flow with toroidal flows, and a reasonable agreement is observed.

A local magnetic equilibrium model is presented, with finite aspect ratio and up-down asymmetrically shaped cross section, that depends on eight free parameters. In contrast with other local equilibria, which provide simple magnetic-surface parametrizations at the cost of complex poloidal-field flux descriptions, the proposed model is intentionally built to afford analytically tractable magnetic-field components. Therefore, it is particularly suitable for analytical assessments of equilibrium-shaping effects on a variety of tokamak-plasma phenomena., 6 pages, 3 figures

A largely unsolved theoretical issue in controlled fusion research is the consistent \textit{kinetic} treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may include finite pressure anisotropies as well as strong toroidal and poloidal differential rotation, characteristic of Tokamak plasmas. Despite the fact that physical phenomena occurring in fusion plasmas depend fundamentally on the microscopic particle phase-space dynamics, their consistent kinetic treatment remains still essentially unchalleged to date. The goal of this paper is to address the problem within the framework of Vlasov-Maxwell description. The gyrokinetic treatment of charged particles dynamics is adopted for the construction of asymptotic solutions for the quasi-stationary species kinetic distribution functions. These are expressed in terms of the particle exact and adiabatic invariants. The theory relies on a perturbative approach, which permits to construct asymptotic analytical solutions of the Vlasov-Maxwell system. In this way, both diamagnetic and energy corrections are included consistently into the theory. In particular, by imposing suitable kinetic constraints, the existence of generalized bi-Maxwellian asymptotic kinetic equilibria is pointed out. The theory applies for toroidal rotation velocity of the order of the ion thermal speed. These solutions satisfy identically also the constraints imposed by the Maxwell equations, i.e. quasi-neutrality and Ampere's law. As a result, it is shown that, in the presence of non-uniform fluid and EM fields, these kinetic equilibria can sustain simultaneously toroidal differential rotation, quasi-stationary finite poloidal flows and temperature anisotropy., Accepted for publication in Physics of Plasmas

Context. Magnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic three-dimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy. Aims. We extend the results of a previous paper on three-dimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudo-potential U, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the co-rotating frame of reference, a particular form for the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a non-aligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae.

Context. Magnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic three-dimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy. Aims. We extend the results of a previous paper on three-dimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudo-potential U, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the co-rotating frame of reference, a particular form for the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a non-aligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae. Postprint

This paper shows a constructive proof of the existence of a path of solutions to a nonlinear eigenvalue problem expressed by -Δu=λu^+ in Ω, and u=-1 on ∂Ω, where Ω is a two-dimensional domain with a boundary ∂Ω. this problem arises from the ideal MHD equilibria in tori. The existence proof is based on the principle of contraction mappings, which is widely employed in nonlinear problems such as those associated with bifurcation phenomena. Some comments are also given on the application of the present iteration techniques to numerical methods., 資料番号: SA2401360000