Correcting for non-periodic behaviour in perturbative experiments: application to heat pulse propagation and modulated gas-puff experiments

Abstract

This paper introduces a recent innovation in dealing with nonperiodic behavior often referred to as transients in perturbative experiments. These transients can be the result from unforced response due to the initial condition and other slow trends in the measurement data and are a source of error when performing and interpreting Fourier spectra. Fourier analysis is particularly relevant in system identification used to build feedback controllers and the analysis of various pulsed experiments such as heat pulse propagation studies. The basic idea behind the methodology is that transients are continuous complex-valued smooth functions in the Fourier domain which can be estimated from the Fourier data. Then, these smooth functions can be subtracted from the data such that only periodic components are retained. The merit of the approach is shown in two experimental examples, i.e., heat pulse propagation (core transport analysis) and radiation front movement due to gas puffing in the divertor. The examples show that the quality of the data is significantly improved such that it allows for new interpretation of the results even for non-ideal measurements.

Real-time feedback control of the impurity emission front in tokamak divertor plasmas

“…A comparison between experiments in terms of the DFT leads to the observation that nonlinear contributions of ELMs to the system dynamics result in significantly higher responses at non-excited frequencies 42 compared with the ELM-free L-mode case. These responses are clearly above the indicated noise floor, but well below the response at excited frequencies.…”

“…Both effects need to be accounted for in subsequent data processing to obtain the FRF. Here, we apply the Local Polynomial Method (LPM) to estimate the transient and drift effects in the data 42 . Then, the FRF is obtained by taking the ratio of the DFT of L pol ( f ) and Γ puff ( f ) with the estimated transient and drift effects removed.…”

“…The phase characteristic of all FRFs is reminiscent of an irrational transfer function model 44 . 2 σ -Error bars are calculated from the LPM 42 . …”

“… Magnitude (plot a ) and phase (plot b ) of the FRFs of all perturbation studies as obtained with the LPM 42 : Unbaffled L-mode # 63163 baffled L-mode # 65305, and baffled H-mode # 65309. The gain of the H-mode experiment is lower and close to the unbaffled L-mode case.…”

“…Common nonlinear system dynamics lead to clear contributions in measured system response at non-excited frequencies, particularly at integer multitudes (harmonics) of the excited frequencies 35 , 42 . To disentangle and quantify such effects in the measurement, some harmonics are removed in the perturbation 40 .…”