Interval nonlinear initial-valued problem using constraint intervals: Theory and an application to the Sars-Cov-2 outbreak.

This article discusses the theory of constraint interval solutions to interval nonlinear initial value problems and applies the notion of constraint interval solutions to analyze the asymptotic behavior of a susceptible-infected-recovered (SIR) epidemiological nonlinear differential equation model, specifically the covid pandemic, in the presence of interval uncertainty to illustrate the efficacy of this approach. Furthermore, constraint interval solutions are used to estimate the intervals for the parameters by fitting solutions to the Brazilian's Sars-Cov-2 pandemic official data. Simulations and graphical solutions incorporating constraint interval uncertainties are presented to help in the visualization of the pandemic's behavior.

The neutron camera upgrade for MAST Upgrade.

The Neutron Camera Upgrade (NCU) is a neutron flux monitor consisting of six lines of sight (LoSs) under installation on Mega Ampere Spherical Tokamak (MAST) Upgrade. The NCU is expected to contribute to the study of the confinement of fast ions and on the efficiency of non-inductive current drive in the presence of on-axis and off-axis neutral beam injection by measuring the neutron emissivity profile along the equatorial plane. This paper discusses the NCU main design criteria, the engineering and interfacing issues, and the solutions adopted. In addition, the results from the characterization and performance studies of the neutron detectors using standard γ-rays sources and a 252Cf source are discussed. The proposed design has a time resolution of 1 ms with a statistical uncertainty of less than 10% for all MAST Upgrade scenarios with a spatial resolution of 10 cm: higher spatial resolution is possible by moving the LoSs in-between plasma discharges. The energy resolution of the neutron detector is better than 10% for a light output of 0.8 MeVee, and the measured pulse shape discrimination is satisfactory.

Investigating fusion plasma instabilities in the Mega Amp Spherical Tokamak using mega electron volt proton emissions (invited).

The proton detector (PD) measures 3 MeV proton yield distributions from deuterium-deuterium fusion reactions within the Mega Amp Spherical Tokamak (MAST). The PD's compact four-channel system of collimated and individually oriented silicon detectors probes different regions of the plasma, detecting protons (with gyro radii large enough to be unconfined) leaving the plasma on curved trajectories during neutral beam injection. From first PD data obtained during plasma operation in 2013, proton production rates (up to several hundred kHz and 1 ms time resolution) during sawtooth events were compared to the corresponding MAST neutron camera data. Fitted proton emission profiles in the poloidal plane demonstrate the capabilities of this new system.

Determination of hydrogen/deuterium ratio with neutron measurements on MAST.

On MAST, compressional Alfvén eigenmodes can be destabilized by the presence of a sufficiently large population of energetic particles in the plasma. This dependence was studied in a series of very similar discharges in which increasing amounts of hydrogen were puffed into a deuterium plasma. A simple method to estimate the isotopic ratio nH/nD using neutron emission measurements is here described. The inferred isotopic ratio ranged from 0.0 to 0.6 and no experimental indication of changes in radial profile of nH/nD were observed. These findings are confirmed by TRANSP/NUBEAM simulations of the neutron emission.

Conceptual design of a neutron camera for MAST Upgrade.

This paper presents two different conceptual designs of neutron cameras for Mega Ampere Spherical Tokamak (MAST) Upgrade. The first one consists of two horizontal cameras, one equatorial and one vertically down-shifted by 65 cm. The second design, viewing the plasma in a poloidal section, also consists of two cameras, one radial and the other one with a diagonal view. Design parameters for the different cameras were selected on the basis of neutron transport calculations and on a set of target measurement requirements taking into account the predicted neutron emissivities in the different MAST Upgrade operating scenarios. Based on a comparison of the cameras' profile resolving power, the horizontal cameras are suggested as the best option.

Validation of neutron emission profiles in MAST with a collimated neutron monitor.

A neutron camera with liquid scintillator detectors is used in MAST to measure the neutron emissivity from D(d,n)(3)He reactions along collimated lines of sight. In this work, the measured recoil proton pulse height spectra generated in the detectors by the incident neutrons is modelled taking into account the energy spectrum of the generated neutrons, their spatial distribution and transport to the detectors as well as the detector's response function. The contribution of scattered neutrons to the pulse height spectrum is also modelled. Good agreement is found between the experimental data and the simulations. Examples are given showing the sensitivity of the recoil proton pulse height spectra to different observation angles with respect the neutral beam injection and the plasma rotation direction.

A neutron camera system for MAST.

A prototype neutron camera has been developed and installed at MAST as part of a feasibility study for a multichord neutron camera system with the aim to measure the spatial and time resolved 2.45 MeV neutron emissivity profile. Liquid scintillators coupled to a fast digitizer are used for neutron/gamma ray digital pulse shape discrimination. The preliminary results obtained clearly show the capability of this diagnostic to measure neutron emissivity profiles with sufficient time resolution to study the effect of fast ion loss and redistribution due to magnetohydrodynamic activity. A minimum time resolution of 2 ms has been achieved with a modest 1.5 MW of neutral beam injection heating with a measured neutron count rate of a few 100 kHz.

Neutron spectroscopy as a fuel ion ratio diagnostic: lessons from JET and prospects for ITER.

The determination of the fuel ion ratio n(t)/n(d) in ITER is required at a precision of 20%, time resolution of 100 ms, spatial resolution of a/10, and over a range of 0.016 keV and for n(T)/n(D)<0.6. A crucial issue is the signal-to-background situation in the measurement of the weak 2.5 MeV emission from DD reactions in the presence of a background of scattered 14 MeV DT neutrons. Important experimental input and corroboration for this assessment are presented from the time-of-flight neutron spectrometer at JET where the presence of a strong component of backscattered neutrons is observed. Neutron emission components on ITER due to beam-thermal and tritium-tritium reactions can further enhance the prospects for NES.

Neutron spectrometry of JET discharges with ICRH-acceleration of helium beam ions.

Recent experiments at JET aimed at producing 4He ions in the MeV range through third harmonic ion cyclotron resonance heating (ICRH) acceleration of 4He beams in a 4He dominated plasma. MeV range D was also present through parasitic ICRH absorption on residual D. In this contribution, we analyze TOFOR neutron spectrometer data from these experiments. A consistent description of the data is obtained with d(d,n)3He and 9Be(α,n)12C neutron components calculated using Stix distributions for the fast D and 4He, taking finite Larmor radius effects into account and with a ICRH power partition of P(D)(RF) = 0.01×P(4He)(RF), in agreement with TOMCAT simulations.

Feedback stabilization of multiple resistive wall modes.

Active feedback stabilization of multiple independent resistive wall modes is experimentally demonstrated in a reversed-field pinch plasma. A reproducible simultaneous suppression of several nonresonant resistive wall modes is achieved. Coupling of different modes due to the limited number of the feedback coils is observed in agreement with theory. The feedback stabilization of nonresonant RWMs also has an effect on tearing modes that are resonant in the central plasma, leading to a significant prolongation of the discharge pulse.