• Energy Research

Wendelstein 7-X, the world largest superconducting advanced stellarator, aims to demonstrate high-performance steady-state experiments lasting up to 30 min. To this purpose, high heat flux (HHF) divertors capable of withstanding steady-state heat fluxes up to 10 MW/m2 are being installed on the machine, in preparation for the next experimental campaign (OP2.1). The real-time heat flux estimation is pivotal for controlling the divertor heat loads during the experiments. Currently, the THEODOR (Thermal Energy Onto DivertOR) code computes the heat flux offline by numerically solving the heat equation, but the computation time does not allow the application of this approach to the real-time operation of the device. In this work, a new approach based on Physics Informed Neural Networks (PINNs) is proposed for solving the heat equation and estimating the heat fluxes on the divertor tiles in real time. PINN models are Neural Networks that learn Partial Differential Equations (PDEs) by minimizing the PDE loss. The inputs of a PINN are the independent variables of the PDE, e.g., spatiotemporal coordinates, while the loss of the model is designed to make the neural network satisfy the PDE and related initial and boundary conditions. Hence, the model can be trained without any experimental data. Only the initial and boundary conditions of the PDE are necessary for constructing the model. First intermediate results are discussed considering a normalized tile and starting from a constant thermal diffusivity.

Nowadays, the demand for communication multi-carriers’ channels, where the sub-channels are made mutually independent by using orthogonal frequency division multiplexing (OFDM), is widespread both for wireless and wired communication systems. Even if OFDM is a spectrally efficient modulation scheme, due to the allowed number of subcarriers, high data rate, and good coverage, the transmitted signal can present high peak values in the time domain, due to inverse fast Fourier transform operations. This gives rise to high peak-to-average power ratio (PAPR) with respect to single carrier systems. These peaks can saturate the transmitting amplifiers, modifying the shape of the OFDM symbol and affecting its information content, and they give rise to electromagnetic compatibility issues for the surrounding electric devices. In this paper, a closed form PAPR reduction algorithm is proposed, which belongs to selected mapping (SLM) methods. These methods consist in shifting the phases of the components to minimize the amplitude of the peaks. The determination of the optimal set of phase shifts is a very complex problem; therefore, the SLM approaches proposed in literature all resort to iterative algorithms. Moreover, as this calculation must be performed online, both the computational cost and the effect on the bit rate (BR) cannot be established a priori. The proposed analytic algorithm finds the optimal phase shifts of an approximated formulation of the PAPR. Simulation results outperform unprocessed conventional OFDM transmission by several dBs. Moreover, the complementary cumulative distribution function (CCDF) shows that, in most of the packets, the proposed algorithm reduces the PAPR if compared with randomly selected phase shifts. For example, with a number of shifted phases U=8, the CCFD curves corresponding to the analytical and random methods intersect at a probability value equal to 10−2, which means that in 99% of cases the former method reduces the PAPR more than the latter one. This is also confirmed by the value of the gain, which, at the same number of shifted phases and at the probability value equal to 10−1, changes from 2.09 dB for the analytical to 1.68 dB for the random SLM.

Integrating the plasma core performance with an edge and scrape-off layer (SOL) that leads to tolerable heat and particle loads on the wall is a major challenge. The new European medium size tokamak task force (EU-MST) coordinates research on ASDEX Upgrade (AUG), MAST and TCV. This multi-machine approach within EU-MST, covering a wide parameter range, is instrumental to progress in the field, as ITER and DEMO core/pedestal and SOL parameters are not achievable simultaneously in present day devices. A two prong approach is adopted. On the one hand, scenarios with tolerable transient heat and particle loads, including active edge localised mode (ELM) control are developed. On the other hand, divertor solutions including advanced magnetic configurations are studied. Considerable progress has been made on both approaches, in particular in the fields of: ELM control with resonant magnetic perturbations (RMP), small ELM regimes, detachment onset and control, as well as filamentary scrape-off-layer transport. For example full ELM suppression has now been achieved on AUG at low collisionality with n = 2 RMP maintaining good confinement HH(98, y2) 0.95. Advances have been made with respect to detachment onset and control. Studies in advanced divertor configurations (Snowflake, Super-X and X-point target divertor) shed new light on SOL physics. Cross field filamentary transport has been characterised in a wide parameter regime on AUG, MAST and TCV progressing the theoretical and experimental understanding crucial for predicting first wall loads in ITER and DEMO. Conditions in the SOL also play a crucial role for ELM stability and access to small ELM regimes.