Diamagnetic measurements and plasma energy in toroidal systems

Abstract

Sensitivity of the diamagnetic signal to several operational and geometrical factors is analysed. Among them are the flux conservation in the plasma, eddy currents induced in the outer structures at fast processes, toroidal shift and deformation of the plasma boundary due to its energy change, and inhomogeneity of the confining magnetic field. It is shown that in each case, under proper experimental circumstances, the contribution, unaccounted in the traditional theory of diamagnetic measurements, can reach a level compared to β (ratio of the volumeaveraged plasma pressure to the magnetic field pressure). The approach is fully analytical with all relevant dependencies shown explicitly, allowing easy estimates and suggesting a resolution of the problem in order to restore the accuracy of finding β from diamagnetic measurements. This essentially extends the analysis [1] of possible measures to improve separation of the useful fraction of the measured diamagnetic signal. The approach is aimed to explanation of the discrepancies between model estimates and experimental results, unification of a knowledge obtained in separate numerical studies, extending a theoretical basis of magnetic diagnostics and uncovering potential dangers in interpretations. This is also an essential step from traditional cylindrical theory to analytical derivations in the toroidal geometry. The results are equally applicable to tokamaks and stellarators.Interpretation of diamagnetic measurements in tokamaks and stellarators is based on a simple formuladerived for a circular plasma cylinder more than 50 years ago, or its modifications. HereΦ is the flux of the magnetic field through the diamagnetic loop and ΔΦ is the difference between the current state and initial state when, B is the magnetic field, v B is the vacuum magnetic field (assumed unchanged in this case),

Nonlocal effects in energy balance in an equilibrium plasma during its fast heating/cooling in tokamaks and stellarators

“…The energy exchange between the plasma and magnetic field is governed by the equilibrium constraints. It is sensitive to subtle changes in the plasma shape and position [56,57,65,66] and, therefore, can be affected by the equilibrium control system. This transforms into a strong dependence of the result on the boundary conditions.…”

“…One integral restriction is that, because of the strong toroidal field, the displacement v ⊥ dt cannot be large in a flux-conserving plasma in tokamaks and stellarators [64]. Precisely, a relative change in the plasma volume, δV pl /V pl , must be on the level of δβ/2 [57,64,65], where β is the ratio of the plasma pressure to the magnetic field pressure and δ means increment. In the cases of interest, this can be of the order of 10 −3 , which can be hardly detected in experiments, especially when the plasma is not absolutely quiescent.…”

Magnetic well scan and confinement in the TJ-II stellarator

“…The present results take into account tens of plasma discharges, with more than five reproducible plasmas obtained in all the magnetic configurations described in section 2. A set of diamagnetic loops allows us to measure the stored diamagnetic energy for all the cases [17]. Taking into account that the plasma volume decreases drastically as we move from the most Mercier-stable to the most unstable configurations, we study the evolution of the stored energy divided by the plasma volume (density of plasma stored energy) instead of the plasma energy itself.…”

Note: Internal diamagnetic flux measurements on ASDEX Upgrade

“…The observed toroidal symmetry of the poloidal magnetic probe and divertor tile current signals makes the toroidal asymmetry of the internal diamagnetic flux di cult to explain, as it would require toroidal symmetry of the plasma at the separatrix and toroidal asymmetry of the plasma pressure collapse. It is also feasible that outward movement of the plasma to a region of smaller toroidal magnetic field or a change of plasma volume could produce changes in the diamagnetic flux [14]. Nevertheless, the observation of toroidal asymmetry of fast changes in diamagnetic flux indicates that caution is warranted when using these changes to calculate power losses to plasma facing components.…”