The relationship between the dynamical response to perturbations of the soft X-ray emissivity (δE), the electron temperature (δTe), the electron density (δne) and the impurity concentration (δni) for a Maxwellian plasma is analysed in detail. In particular, the so-called 'impurity function' F(Zeff) is also strongly dependent on Te via the direct radiative recombination (DRR) contribution to the X-ray emission, which significantly affects the relation between the perturbed quantities as derived from the popular expression E ∝ F(Zeff)ne2Tealpha even if the impurity content (or Zeff) remains constant. In order to overcome this difficulty, a simple analytical approximation is derived for F(Zeff,Te) that can be used as a formula to relate the perturbed quantities δE, δTe, δne and δF with ease and accuracy. This simple approximation is illustrated by studying saw-toothing discharges on the Tokamak de Varennes (TdeV) with Te, ne and E measured by the Thomson scattering, the FIR interferometer and the X-ray camera diagnostics, and its accuracy is tested against the predictions of a full X-ray modelling code
Impact of plasma response on plasma displacements in DIII-D during application of external 3D perturbations