Kinetic approach to the collective dynamics of the rock-paper-scissors binary game

This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness

Lessons learned after three years of SPIDER operation and the first MITICA integrated tests

ITER envisages the use of two heating neutral beam injectors plus an optional one as part of the auxiliary heating and current drive system, to reach the desired performances during its various phases of operation. The 16.5 MW expected neutral beam power per injector is several notches higher than worldwide existing facilities. In order to enable such development, a Neutral Beam Test Facility (NBTF) was established at Consorzio RFX, exploiting the synergy of two test beds, called SPIDER and MITICA. SPIDER is dedicated developing and characterizing large efficient negative ion sources at relevant parameters in ITER-like conditions: source and accelerator located in the same vacuum where the beam propagates, immunity to electromagnetic interferences of multiple radio-frequency (RF) antennas, avoidance of RF-induced discharges on the outside of the source. Three years of experiments on SPIDER have addressed to the necessary design modifications to enable full performances. The source is presently under a long shut-down phase to incorporate learnings from the experimental campaign, in particular events/issues occurred during operation, which led to the identification of improvement opportunities/necessities (e.g. RF discharges, local burns, water leaks, other damages, configuration/design upgrades to maximize chances/margin to quest target parameters). Parallelly, developments on MITICA, the full-scale prototype of the ITER Neutral Beam Injector (NBI) featuring a 1 MV accelerator and ion neutralization, are underway including manufacturing of the beam source, accelerator and the beam line components, while power supplies and auxiliary plants, already installed, are under final testing and commissioning. Integration, commissioning and tests of the 1 MV power supplies are essential for this first-of-kind system, unparalleled both in research and industry field. 1.2 MV dc insulating tests of high voltage components were successfully completed. The integrated test to confirm 1 MV output by combining invertor systems, DC generators and transmission lines extracted errors/accidents in some components. To realize a concrete system for ITER, said events have been addressed and solutions for the repair and the improvement of the system were developed. Hence, NBTF is emerging as a necessary facility, due to the large gap with existing injectors, effectively dedicated to identify issues and find solutions to enable successful ITER NBI operations in a time bound fashion. The lessons learned during the implementation on NBTF and future perspectives are here discussed

Lessons learned after three years of SPIDER operation and the first MITICA integrated tests

ITER envisages the use of two heating neutral beam injectors plus an optional one as part of the auxiliary heating and current drive system, to reach the desired performances during its various phases of operation. The 16.5 MW expected neutral beam power per injector is several notches higher than worldwide existing facilities. In order to enable such development, a Neutral Beam Test Facility (NBTF) was established at Consorzio RFX, exploiting the synergy of two test beds, called SPIDER and MITICA. SPIDER is dedicated developing and char- acterizing large efficient negative ion sources at relevant parameters in ITER-like conditions: source and accel- erator located in the same vacuum where the beam propagates, immunity to electromagnetic interferences of multiple radio-frequency (RF) antennas, avoidance of RF-induced discharges on the outside of the source. Three years of experiments on SPIDER have addressed to the necessary design modifications to enable full perfor- mances. The source is presently under a long shut-down phase to incorporate learnings from the experimental campaign, in particular events/issues occurred during operation, which led to the identification of improvement opportunities/necessities (e.g. RF discharges, local burns, water leaks, other damages, configuration/design upgrades to maximize chances/margin to quest target parameters). Parallelly, developments on MITICA, the full-scale prototype of the ITER Neutral Beam Injector (NBI) featuring a 1 MV accelerator and ion neutralization, are underway including manufacturing of the beam source, accel- erator and the beam line components, while power supplies and auxiliary plants, already installed, are under final testing and commissioning. Integration, commissioning and tests of the 1 MV power supplies are essential for this first-of-kind system, unparalleled both in research and industry field. 1.2 MV dc insulating tests of high voltage components were successfully completed. The integrated test to confirm 1 MV output by combining invertor systems, DC gener- ators and transmission lines extracted errors/accidents in some components. To realize a concrete system for ITER, said events have been addressed and solutions for the repair and the improvement of the system were developed. Hence, NBTF is emerging as a necessary facility, due to the large gap with existing injectors, effectively dedicated to identify issues and find solutions to enable successful ITER NBI operations in a time bound fashion. The lessons learned during the implementation on NBTF and future perspectives are here discussed

On the road to ITER NBIs: SPIDER improvement after first operation and MITICA construction progress

To reach fusion conditions and control the plasma configuration in ITER, the next step in tokamak fusion research, two neutral beam injectors (NBIs) will supply 16.5 MW each, by neutralizing accelerated negative hydrogen or deuterium ions. The requirements of ITER NBIs (40A/1 MeV D- ions for 641 h, 46A/870 keV H- ions for 641000 s) have never been simultaneously attained. So in the Neutral Beam Test Facility (NBTF, Consorzio RFX, Italy) the operation of the full-scale ITER NBI prototype (MITICA) will be tested and optimised up to full performances, focussing on accelerator (including voltage holding), beam optics, neutralisation, residual ion removal. The NBTF includes also the full-scale prototype of the ITER NBI source with 100 keV particle energy (SPIDER), for early investigation of: negative ion production and extraction, source uniformity, negative ion current density and beam optics. This paper will describe the main results of the first two years of SPIDER operation, devoted to characterizing plasma and beam parameters, including investigation of RF-plasma coupling efficiency and magnetic filter field effectiveness in reducing co-extracted electrons. SPIDER is progressing towards the first caesium injection, which aims at increasing the negative ion density. A major shutdown, planned for 2021, to solve the issues identified during the operation and to carry out programmed modifications, will be outlined. The installation of each MITICA power supply and auxiliary system is completed; in-vessel mechanical components are under procurement by Fusion for Energy (F4E). Integration, commissioning and test of the power supplies, procured by F4E and QST, as the Japanese Domestic Agency (JADA), will be presented. In particular, 1.0MV insulating tests were carried out step-by-step and successfully completed. In 2020 integrated tests of the power supplies on the accelerator dummy load started, including the assessment of their resilience to accelerator grid breakdowns using a short-circuit device located in vacuum. The aggressive programme, to validate the NBI design at NBTF and to meet ITER schedule (requiring NBIs in operation in 2032), will be outlined. Unfortunately, in 2020 the coronavirus disease infection affected the NBTF activities. A solution to proceed with integrated power tests despite the coronavirus is presented