A pp-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices

Suppose that $M$ is an even lattice with dual $M^{*}$ and level $N$. Then the group $Mp_{2}(\mathbb{Z})$, which is the unique non-trivial double cover of $SL_{2}(\mathbb{Z})$, admits a representation $\rho_{M}$, called the Weil representation, on the space $\mathbb{C}[M^{*}/M]$. The main aim of this paper is to show how the formulae for the $\rho_{M}$-action of a general element of $Mp_{2}(\mathbb{Z})$ can be obtained by a direct evaluation which does not depend on ``external objects'' such as theta functions. We decompose the Weil representation $\rho_{M}$ into $p$-parts, in which each $p$-part can be seen as subspace of the Schwartz functions on the $p$-adic vector space $M_{\mathbb{Q}_{p}}$. Then we consider the Weil representation of $Mp_{2}(\mathbb{Q}_{p})$ on the space of Schwartz functions on $M_{\mathbb{Q}_{p}}$, and see that restricting to $Mp_{2}(\mathbb{Z})$ just gives the $p$-part of $\rho_{M}$ again. The operators attained by the Weil representation are not always those appearing in the formulae from 1964, but are rather their multiples by certain roots of unity. For this, one has to find which pair of elements, lying over a matrix in $SL_{2}(\mathbb{Q}_{p})$, belong to the metaplectic double cover. Some other properties are also investigated.Comment: 29 pages, shortened a lo

Measurement of the heaviest beta-delayed 2-neutron emitter : Sb-136

The beta-delayed neutron emission probability, P-n, of very exotic nuclei is crucial for the understanding of nuclear structure properties of many isotopes and astrophysical processes such as the rapid neutron capture process (r-process). In addition beta-delayed neutrons are important in a nuclear power reactor operated in a prompt sub-critical, delayed critical condition, as they contribute to the decay heat inducing fission reactions after a shut down. The study of neutron-rich isotopes and the measurement of beta-delayed one-neutron emitters (beta 1n) is possible thanks to the Rare Isotope Beam (RIB) facilities, where radioactive beams allow the production of exotic nuclei of interest, which can be studied and analyzed using specific detection systems. This contribution reports two recent measurements of beta-delayed neutron emitters which allowed the determination of half-lives and the neutron branching ratio of isotopes in the mass region above A = 200 and N > 126, and a second experiment which confirmed Sb-136 as the heaviest double neutron emitter (beta 2n) measured so far.The beta-delayed neutron emission probability, P-n, of very exotic nuclei is crucial for the understanding of nuclear structure properties of many isotopes and astrophysical processes such as the rapid neutron capture process (r-process). In addition beta-delayed neutrons are important in a nuclear power reactor operated in a prompt sub-critical, delayed critical condition, as they contribute to the decay heat inducing fission reactions after a shut down. The study of neutron-rich isotopes and the measurement of beta-delayed one-neutron emitters (beta 1n) is possible thanks to the Rare Isotope Beam (RIB) facilities, where radioactive beams allow the production of exotic nuclei of interest, which can be studied and analyzed using specific detection systems. This contribution reports two recent measurements of beta-delayed neutron emitters which allowed the determination of half-lives and the neutron branching ratio of isotopes in the mass region above A = 200 and N > 126, and a second experiment which confirmed Sb-136 as the heaviest double neutron emitter (beta 2n) measured so far.The beta-delayed neutron emission probability, P-n, of very exotic nuclei is crucial for the understanding of nuclear structure properties of many isotopes and astrophysical processes such as the rapid neutron capture process (r-process). In addition beta-delayed neutrons are important in a nuclear power reactor operated in a prompt sub-critical, delayed critical condition, as they contribute to the decay heat inducing fission reactions after a shut down. The study of neutron-rich isotopes and the measurement of beta-delayed one-neutron emitters (beta 1n) is possible thanks to the Rare Isotope Beam (RIB) facilities, where radioactive beams allow the production of exotic nuclei of interest, which can be studied and analyzed using specific detection systems. This contribution reports two recent measurements of beta-delayed neutron emitters which allowed the determination of half-lives and the neutron branching ratio of isotopes in the mass region above A = 200 and N > 126, and a second experiment which confirmed Sb-136 as the heaviest double neutron emitter (beta 2n) measured so far.Peer reviewe

First evidence of multiple beta-delayed neutron emission for isotopes with A > 100

The beta-delayed neutron emission probability, P-n, of very neutron-rich nuclei allows us to achieve a better understanding of the nuclear structure above the neutron separation energy, S-n. The emission of neutrons can become the dominant decay process in neutron-rich astrophysical phenomena such as the rapid neutron capture process (r-process). There are around 600 accessible isotopes for which beta-delayed one-neutron emission (beta 1n) is energetically allowed, but the branching ratio has only been determined for about one third of them. beta 1n decays have been experimentally measured up to the mass A similar to 1 5 0, plus a single measurement of Tl-210. Concerning two-neutron emitters (beta 2n), similar to 3 0 0 isotopes are accessible and only 24 have been measured so far up to the mass A = 100. In this contribution, we report recent experiments which allowed the measurement of beta 1n emitters for masses beyond A > 200 and N > 1 2 6 and identified the heaviest beta 2n emitter measured so far, Sb-136.Peer reviewe

Predictive JET current ramp-up modelling using QuaLiKiz-neural-network

This work applies the coupled JINTRAC and QuaLiKiz-neural-network (QLKNN) model on the ohmic current ramp-up phase of a JET D discharge. The chosen scenario exhibits a hollow T-e profile attributed to core impurity accumulation, which is observed to worsen with the increasing fuel ion mass from D to T. A dynamic D simulation was validated, evolving j, n(e), T-e, T-i, n(Be), n(Ni), and n(W) for 7.25 s along with self-consistent equilibrium calculations, and was consequently extended to simulate a pure T plasma in a predict-first exercise. The light impurity (Be) accounted for Z(eff) while the heavy impurities (Ni, W) accounted for Prad. This study reveals the role of transport on the Te hollowing, which originates from the isotope effect on the electron-ion energy exchange affecting T-i. This exercise successfully affirmed isotopic trends from previous H experiments and provided engineering targets used to recreate the D q-profile in T experiments, demonstrating the potential of neural network surrogates for fast routine analysis and discharge design. However, discrepancies were found between the impurity transport behaviour of QuaLiKiz and QLKNN, which lead to notable T-e hollowing differences. Further investigation into the turbulent component of heavy impurity transport is recommended

Peripheral temperature gradient screening of high-Z impurities in optimised 'hybrid' scenario H-mode plasmas in JET-ILW

Screening of high-Z (W) impurities from the confined plasma by the temperature gradient at the plasma periphery of fusion-grade H-mode plasmas has been demonstrated in the JET-ILW (ITER-like wall) tokamak. Through careful optimisation of the hybrid-scenario, deuterium plasmas with sufficient heating power (greater than or similar to 32 MW), high enough ion temperature gradients at the H-mode pedestal top can be achieved for the collisional, neo-classical convection of the W impurities to be directed outwards, expelling them from the confined plasma. Measurements of the W impurity fluxes between and during edge-localised modes (ELMs) based on fast bolometry measurements show that in such plasmas there is a net efflux (loss) between ELMs but that ELMs often allow some W back into the confined plasma. Provided steady, high-power heating is maintained, this mechanism allows such plasmas to sustain high performance, with an average D-D neutron rate of similar to 3.2 x 10(16) s(-1) over a period of similar to 3 s, after an initial overshoot (equivalent to a D-T fusion power of similar to 9.4 MW), without an uncontrolled rise in W impurity radiation, giving added confidence that impurity screening by the pedestal may also occur in ITER, as has previously been predicted (Dux et al 2017 Nucl. Mater. Energy 12 28-35)

Overview of JET results for optimising ITER operation

The JET 2019–2020 scientific and technological programme exploited the results of years of concerted scientific and engineering work, including the ITER-like wall (ILW: Be wall and W divertor) installed in 2010, improved diagnostic capabilities now fully available, a major neutral beam injection upgrade providing record power in 2019–2020, and tested the technical and procedural preparation for safe operation with tritium. Research along three complementary axes yielded a wealth of new results. Firstly, the JET plasma programme delivered scenarios suitable for high fusion power and alpha particle (α) physics in the coming D–T campaign (DTE2), with record sustained neutron rates, as well as plasmas for clarifying the impact of isotope mass on plasma core, edge and plasma-wall interactions, and for ITER pre-fusion power operation. The efficacy of the newly installed shattered pellet injector for mitigating disruption forces and runaway electrons was demonstrated. Secondly, research on the consequences of long-term exposure to JET-ILW plasma was completed, with emphasis on wall damage and fuel retention, and with analyses of wall materials and dust particles that will help validate assumptions and codes for design and operation of ITER and DEMO. Thirdly, the nuclear technology programme aiming to deliver maximum technological return from operations in D, T and D–T benefited from the highest D–D neutron yield in years, securing results for validating radiation transport and activation codes, and nuclear data for ITER

Testing a prediction model for the H-mode density pedestal against JET-ILW pedestals

The neutral ionisation model proposed by Groebner et al (2002 Phys. Plasmas 9 2134) to determine the plasma density profile in the H-mode pedestal, is extended to include charge exchange processes in the pedestal stimulated by the ideas of Mahdavi et al (2003 Phys. Plasmas 10 3984). The model is then tested against JET H-mode pedestal data, both in a 'standalone' version using experimental temperature profiles and also by incorporating it in the Europed version of EPED. The model is able to predict the density pedestal over a wide range of conditions with good accuracy. It is also able to predict the experimentally observed isotope effect on the density pedestal that eludes simpler neutral ionization models

Overview of JET results for optimising ITER operation

The JET 2019–2020 scientific and technological programme exploited the results of years of concerted scientific and engineering work, including the ITER-like wall (ILW: Be wall and W divertor) installed in 2010, improved diagnostic capabilities now fully available, a major neutral beam injection upgrade providing record power in 2019–2020, and tested the technical and procedural preparation for safe operation with tritium. Research along three complementary axes yielded a wealth of new results. Firstly, the JET plasma programme delivered scenarios suitable for high fusion power and alpha particle (α) physics in the coming D–T campaign (DTE2), with record sustained neutron rates, as well as plasmas for clarifying the impact of isotope mass on plasma core, edge and plasma-wall interactions, and for ITER pre-fusion power operation. The efficacy of the newly installed shattered pellet injector for mitigating disruption forces and runaway electrons was demonstrated. Secondly, research on the consequences of long-term exposure to JET-ILW plasma was completed, with emphasis on wall damage and fuel retention, and with analyses of wall materials and dust particles that will help validate assumptions and codes for design and operation of ITER and DEMO. Thirdly, the nuclear technology programme aiming to deliver maximum technological return from operations in D, T and D–T benefited from the highest D–D neutron yield in years, securing results for validating radiation transport and activation codes, and nuclear data for ITER