The use of Bayesian inversion to resolve plasma equilibrium

Abstract

Recently, bayesian probability theory has been used at a number of experiments to fold uncertainties and interdependencies in the diagnostic data and forward models, together with prior knowledge of the state of the plasma, to increase accuracy of inferred physics variables. A new probabilistic framework, MINERVA, based on bayesian graphical models, has been used at JET and W7-AS to yield predictions of internal magnetic structure. A feature of the framework is the bayesian inversion for poloidal magnetic flux without the need for an explicit equilibrium assumption. Building on this, we discuss results from a new project to develop bayesian inversion tools that aim to (1) distinguish between competing equilibrium theories, which capture different physics, using the MAST spherical tokamak, and (2) test the predictions of MHD theory, particularly mode structure, using the H-1 Heliac. Specifically, we report on correction of the motional Stark effect, pickup coils, flux-loop constrained bayesian inferred equilibrium for varying toroidal flux.

Integrated data analysis at TJ-II: The density profile

“…Examples of such issues arise from parametric entanglements, e.g., one of the diagnostic units could depend on the input from another measurement. Another example, although not of primary concern for the case discussed here, is the dependence of the aforementioned coordinate transformation on the plasma pressure -while the latter is an object of the measurement itself 3 . Moreover, beyond physical interdependencies, systematic effects affecting individual diagnostics, or a priori inaccessible parameters such as offsets, further complicate the situation.…”

Identification of edge-localized moments of the current density profile in a tokamak equilibrium from external magnetic measurements

“…The algorithm was speeded up considerably by the interleaving of force balance convergence and a linear regression to determine optimum values of the free parameters at each cycle, resulting in the computationally efficient EFIT equilibrium reconstruction code [2,3], now the most widely used worldwide. More recently, Bayesian methods have been applied to equilibrium reconstruction from multiple diagnostics on stellarators [4] and tokamaks [5,6]. Starting with Lackner's fast equilibrium solver based on the Buneman algorithm [7], the CLISTE interpretive equilibrium code [12,13], which is used here, was developed for equilibrium reconstruction from multiple diagnostics on the ASDEX Upgrade tokamak.…”

Bayesian modelling of a thermal helium beam for measurement of electron density and temperature in the W7-X divertor plasma

“…Other examples for the application of Bayesian methods in plasma physics can be found in [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23]. The textbooks [24], [25] give comprehensive introductions of the used approach.…”