Bayesian modeling of microwave radiometer calibration on the example of the Wendelstein 7-X electron cyclotron emission diagnostic

Abstract

This paper reports about a novel approach to the absolute intensity calibration of an electron cyclotron emission (ECE) spectroscopy system. Typically, an ECE radiometer consists of tens of separated frequency channels corresponding to different plasma locations. An absolute calibration of the overall diagnostic including near plasma optics and transmission line is achieved with blackbody sources at LN 2 temperature and room temperature via a hot/cold calibration mirror unit. As the thermal emission of the calibration source is typically a few thousand times lower than the receiver noise temperature, coherent averaging over several hours is required to get a sufficient signal to noise ratio. A forward model suitable for any radiometer calibration using the hot/cold method and a periodic switch between them has been developed and used to extract the voltage difference between the hot and cold temperature source via Bayesian analysis. In contrast to the classical analysis which evaluates only the reference temperatures, the forward model takes into account intermediate effective temperatures caused by the finite beam width and thus uses all available data optimally. This allows the evaluation of weak channels where a classical analysis would not be feasible, is statistically rigorous and provides a measurement of the beam width. By using a variance scaling factor a model sensitive adaptation of the absolute uncertainties can be implemented, which will be used for the combined diagnostic Bayesian modelling analysis.

Demonstration of reduced neoclassical energy transport in Wendelstein 7-X

“…An optimized line-of-sight is realized across the 3D plasma shape by means of an in vessel Gauss telescope. The radiometer channels are calibrated relative to each other and absolute calibration is carried out using a second 'identical' Gauss telescope outside the torus that views a hot-cold light source 49 . For the results presented here, the absolute calibration has been scaled up (red) measurements are compared to the theoretical expectations from the ambipolarity constraint (black) for the plasma profiles of Fig.…”

Measurements of visible bremsstrahlung and automatic Bayesian inference of the effective plasma charge Zeff at W7-X

“…Since the Bayesian analysis is meant to be carried automatically after every plasma discharge, a fallback solution is provided for those cases in which Thomson scattering measurements are not available. The n e profile is assumed to be parabolic, and absolute values are scaled accordingly using interferometer measurements, as previously mentioned; the T e profile, on the other hand, is obtained from measurements by the electron cyclotron emission (ECE) diagnostic using the cold resonance approximation [10,11].…”

High-performance plasmas after pellet injections in Wendelstein 7-X

“…The principal plasma parameters of W7-X are well diagnosed [50]. The main systems used throughout the paper are: a dispersion interferometer for the line integrated density [51]; a Thomson scattering system for the electron density and electron temperature profiles [52,53]; an electron cyclotron emission (ECE) diagnostic with 32 channels for electron temperature profiles (calibrated with a cold source) [54,55]; a multi-line X-ray imaging crystal spectrometer (XICS) for profiles of ion temperature and radial electric field [56,57]; a charge exchange recombination spectroscopy (CXRS) diagnostic for profiles of ion temperature and radial electric field [58]; a compensated diamagnetic loop for the plasma energy [59]; and a gold foil multi-line bolometer system for total radiated power and plasma radiation power profiles [60]. In the first half of the campaign, the Thomson scattering diagnostic covered a half profile with 16 spatial points and ran with a repetition rate of 10 Hz.…”