Nonlinear Gaussian process tomography with imposed non-negativity constraints on physical quantities for plasma diagnostics

Abstract

We propose a novel tomographic method, nonlinear Gaussian process tomography (nonlinear GPT) that employs the Laplace approximation to ensure the non-negative physical quantity, such as the emissivity of plasma optical diagnostics. This new method implements a logarithmic Gaussian process (log-GP) to model plasma distribution more naturally, thereby expanding the limitations of standard GPT, which are restricted to linear problems and may yield non-physical negative values. The effectiveness of the proposed log-GP tomography is demonstrated through a case study using the Ring Trap 1 (RT-1) device, where log-GPT outperforms existing methods, standard GPT, and the Minimum Fisher Information (MFI) methods in terms of reconstruction accuracy. The result highlights the effectiveness of nonlinear GPT for imposing physical constraints in applications to an inverse problem.

Figures (7)

• Figure 1: Relation between the local quantity $f$ in the plasma volume $\Omega_{f}$ and the projected observed quantity $g$ in a sensor plane $\Omega_{g}$.
• Figure 2: The magnetospheric plasma device RT-1 and camera system. The camera is set to view a poloidal cross-section of RT-1 torus plasmas and to diagnose an emission from helium ionsK_Ueda_2021. The emissivity profile from the plasma is overlaid on the magnetic field lines.
• Figure 3: The referenced length scale distribution $\ell'(\vec{r})$ on the cross-section of RT-1, corresponds to in Eq. \ref{['eq: def of hyperparam']}
• Figure 4: The distribution of inducing points $\vec{r}^\mathrm{\,idc}$ (the blue points), boundary points $\vec{r}^\mathrm{\,bd}$ (the orange points), and rays for the LOS (the red lines) that start from the camera. These rays are projected onto the poloidal cross-section of the RT-1 device. The number of inducing points is 2041, and the number of boundary points is 229 in the setup. The number of rays is reduced for simplicity.
• Figure 5: The phantom distributions and their projected images. (a) is labeled the 'hollow' distribution, and (c) is the projected results with (a) using the geometry matrix $H$, and (d) includes 33% added noise (for example) from (c). Similarly, (b) is labeled 'double peaked', (e) shows its projected results, and (f) shows the same data with added noise.