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This paper deals with a third‐order three‐point boundary value problem. By using Leray Schauder nonlinear alternative, we establish the existence of a nontrivial solution, then we give some examples to illustrate our results.

The upgraded 3.7 GHz Lower Hybrid Current Drive (LHCD) system for the Tore Supra (TS) tokamak is in the process of installation [1]. When complete, it will permit long pulse injection (1000s) at coupled power level up to 6, 5 MW. Steady state operation of high power RF sources and components is challenging and requires careful validation before the system can be commissioned on the tokamak.Results on the validation of CW klystrons, improvements on the RF components forming part of the power generation circuit and the development of an RF water load to sustain CW pulses under 700 kW RF power are presented.

Arc detection systems are developed for ICRH on ITER to prevent arcs from damaging the RF components. One of the detectors, the Sub‐Harmonic Arc Detector (SHAD) is based on the detection of the frequencies emitted in the MHz range by arcs [R1]. To ensure the high level of reliability required for this safety system, it is necessary to demonstrate that these frequencies present a signal with a Signal to Noise Ratio high enough to be detected under the wide range of operational conditions (frequency, power, configuration) and for the different types of arcs that can appear in the feeding lines and on the antennas (vacuum arc, glow discharge, multipactor‐induced discharge). For each type of arc, we analyze the evolution of the frequency spectrum relative to the evolution of other electrical parameters (reflected power, voltage).

A voltage breakdown in an Ion Cyclotron Resonance Heating (ICRH) system is usually detected as an abrupt change in the module of the reflection coefficient |Γin| at the power source output. The same effect can be due to a large load variation. This study is carried out by constructing a electrical model for a Tore Supra ITER‐like antenna (TS ILA) [1], and to analyse how a voltage breakdown, localized in any part of the system, modifies several electrical parameters of the circuit (with respect to perfect match conditions), as detected at the location of the monitoring points. The phase difference between the reflections coefficients measured at the output of tuning network when an arc strikes in one of two Resonant double loop (RDL) sections of the ICRH TS ILA appears to be the most promising parameter to detect the arc and identify its position. It is also significantly insensitive to a load variation so an arc and edge localized modes (ELMs) can be distinguished.

Forming simulation technologies continues to develop at a rapid pace, to address formability, tolerance control, and product performance issues in an increasing range of processes, and in ever more detail. Springback prediction and compensation continue to evolve, with new concepts for improving the accuracy of the springback prediction for example by the incorporation of geometric drawbeads, and further refinement in compensation techniques. The paper highlights how the integration of simulation and geometry plays an ever more important role, in improving accuracy and reducing time.Other techniques which can help speed‐up and improve simulation results for hydroforming, and tube bending are ‘classical’ and more recently ‘in‐process’ optimization techniques. The paper will show the advantages on an industrial case, and the potential for the future.The paper will discuss how the PAM‐STAMP 2G™ and PAM‐TUBE 2G™ integrated solutions are successfully implemented to deliver a positive business impact, by provid...

The last few years have seen the use of stamping simulation evolve to the extent that it is now a mainstream activity; a core part of the press tool engineering process. Now, new requirements for the use of challenging materials like Dual phase / Complex phase steel, VHSS, and aluminum, together with more stringent quality expectations, and shorter development cycles, there is a need to assess the panel quality in a wider context, before committing to tool manufacture.The integrated approach from ESI Group allows early up‐front feasibility assessment, geometry and process optimization, and detailed process validation all within one system. Rapid die design and quick forming simulation modules play an essential role in the early stages of the process. A seamless connection between simulation and geometry is a vital characteristic, with the accurate simulation being used to validate and fine tune the process in order to assess final component quality in unprecedented detail, utilizing some of the most accur...