Confinement Time Research Articles

Pushing the limits of existing plasma focus towards 1016 fusion neutrons with Q = 0.01

Existing conventional megajoule plasma focus machines with 2–3 MA are producing fusion neutron yields of several times 1011 in deuterium operation, the fusion yields predominantly being the beam-gas target. Increasing the current to 10 MA and using 50%–50% D-T mixture will scale the neutron yield towards 1016 D-T fusion neutrons. In this work, we derive the Lawson criterion for plasma focus devices with a beam-target fusion neutron mechanism, so that we may glimpse what future technological advancements are needed for a break-even Q = 1 plasma focus. We perform numerical experiments with a present-day feasible 0.9 MV, 8.1 MJ, 11 MA machine operating in 100 Torr in 50%–50% D-T mixture. The Lee Code simulation gives a detailed description of the plasma focus dynamics through each phase, and provides plasma and yield parameters which show that out of 1.1 × 1019 fast beam ions produced in the plasma focus pinch, only 1.24 × 1014 ions take part in beam-target fusion reactions within the pinch, producing the same number of D-T neutrons. The remnant beam ions, numbering at least 1019, exit the focus pinch at 1.9 MeV, which is far above the 115 keV ion energy necessary for an optimum beam-target cross-section. We propose to regain the lost fusion rates by using a high-pressure D-T-filled drift-tube to attenuate the energy of the remnant beam ions until they reach the energy for the optimum fusion cross-section. Such a fusion enhancement tube would further harvest beam-target fusion reactions by increasing the interaction path length (1 m) at increased interaction density (6 atm). A gain factor of 300 is conservatively estimated, with a final yield of 3.7 × 1016 D-T neutrons carrying kinetic energy of 83.6 kJ, demonstrating Q = 0.01.

Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment.

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37MJ of fusion for 1.92MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion.

Design of an inertial fusion experiment exceeding the Lawson criterion for ignition.

We present the design of the first igniting fusion plasma in the laboratory by Lawson's criterion that produced 1.37MJ of fusion energy, Hybrid-E experiment N210808 (August 8, 2021) [Phys. Rev. Lett. 129, 075001 (2022)10.1103/PhysRevLett.129.075001]. This design uses the indirect drive inertial confinement fusion approach to heat and compress a central "hot spot" of deuterium-tritium (DT) fuel using a surrounding dense DT fuel piston. Ignition occurs when the heating from absorption of α particles created in the fusion process overcomes the loss mechanisms in the system for a duration of time. This letter describes key design changes which enabled a ∼3-6× increase in an ignition figureof merit (generalized Lawson criterion) [Phys. Plasmas 28, 022704 (2021)1070-664X10.1063/5.0035583, Phys. Plasmas 25, 122704 (2018)1070-664X10.1063/1.5049595]) and an eightfold increase in fusion energy output compared to predecessor experiments. We present simulations of the hot-spot conditions for experiment N210808 that show fundamentally different behavior compared to predecessor experiments and simulated metrics that are consistent with N210808 reaching for the first time in the laboratory "ignition."

Experimental achievement and signatures of ignition at the National Ignition Facility.

An inertial fusion implosion on the National Ignition Facility, conducted on August 8, 2021 (N210808), recently produced more than a megajoule of fusion yield and passed Lawson's criterion for ignition [Phys. Rev. Lett. 129, 075001 (2022)10.1103/PhysRevLett.129.075001]. We describe the experimental improvements that enabled N210808 and present the first experimental measurements from an igniting plasma in the laboratory. Ignition metrics like the product of hot-spot energy and pressure squared, in the absence of self-heating, increased by ∼35%, leading to record values and an enhancement from previous experiments in the hot-spot energy (∼3×), pressure (∼2×), and mass (∼2×). These results are consistent with self-heating dominating other power balance terms. The burn rate increases by an order of magnitude after peak compression, and the hot-spot conditions show clear evidence for burn propagation into the dense fuel surrounding the hot spot. These novel dynamics and thermodynamic properties have never been observed on prior inertial fusion experiments.

Self-organized magnetic equilibria in tokamak plasmas with very low edge safety factor

Tokamak plasmas often exhibit self-organizing behavior in which internal modes shape the toroidal current density profile, a common example being the sawtooth instability. However, such behavior has not been studied in detail for edge safety factor below 2 due to disruptive kink instabilities that typically prevent operation in this regime. Now, steady tokamak plasmas with an edge safety factor down to 0.8 have been created in the Madison Symmetric Torus, where disruptions are prevented due to a thick, conductive wall and a feedback power supply that sustains the plasma current. Internal measurements and nonlinear magnetohydrodynamic modeling reveal a family of safety factor profiles with a central value clamped near unity as the edge safety factor decreases, indicating current profile broadening through a relaxation process. As the safety factor decreases, the magnetic fluctuations become irregular, and the electron energy confinement time decreases.

Women's Access to Sexual and Reproductive Health Services during Confinement Due to the COVID-19 Pandemic in Spain.

(1) Background: The COVID-19 pandemic has created a challenge for women’s sexual and reproductive health care. The objective of this research was to analyse access to sexual and reproductive health services during confinement in Spain. (2) Methods: A descriptive and cross-sectional study was conducted with a random sample that was stratified by age in July and August 2020. (3) Results: A total of 1800 women were invited to participate, obtaining a response rate of 98.72%. The frequency of sexual relationships reduced during confinement. Counselling was offered both in person (30.7%) and telematically (39%), although there were also women who experienced access problems (30%). Of those women who required some LARC, only half had access to it, mainly due to the contact difficulties as a result of the limited number of consultations with their prescribing physicians. The use of emergency oral contraception and the use of services for the voluntary interruption of pregnancy were considerably reduced. The women who stated having been victims of gender-based violence were those that lived with their aggressors during confinement and had children. (4) Conclusions: It is necessary to ensure sexual and reproductive rights in confinement times and, for such a purpose, telemedicine can be a good tool that helps to avoid unmet contraceptive needs and unplanned pregnancies.

Development of the pellet injection system on the J-TEXT tokamak

Pellet injection is an attractive technology for core-fueling and magnetohydrodynamic study in magnetic-confinement fusion devices like tokamaks and stellarators. It can inject solid hydrogen/deuterium pellets into the plasma with deeper density deposition compared with other fueling methods, such as gas puffing. A three-barrel H2 pellet injection system was installed on the J-TEXT tokamak and experiments were carried out. The pellets are formed in three barrels cooled by a cryocooler and compressor system at around 9 K, and are 0.8 mm/1 mm diameter and 0.8 mm length. The pellet is launched by helium propellant gas and injected from the low-field side of the plasma. The normal range of pellet speed is 210–310 m s−1 for different propellant gas pressures. Due to the three-barrel structure, the number of injected pellets can be adjusted between one and three. Pellets can be launched sequentially with arbitrary time intervals, which enables flexible applications. The results of the experiments show that pellet fueling efficiency can reach 50%. The energy confinement time increased by about 7.5‒10 ms after pellet injection.

Progress toward fusion energy breakeven and gain as measured against the Lawson criterion

The Lawson criterion is a key concept in the pursuit of fusion energy, relating the fuel density n, pulse duration τ or energy confinement time τE, and fuel temperature T to the energy gain Q of a fusion plasma. The purpose of this paper is to explain and review the Lawson criterion and to provide a compilation of achieved parameters for a broad range of historical and contemporary fusion experiments. Although this paper focuses on the Lawson criterion, it is only one of many equally important factors in assessing the progress and ultimate likelihood of any fusion concept becoming a commercially viable fusion-energy system. Only experimentally measured or inferred values of n, τ or τE, and T that have been published in the peer-reviewed literature are included in this paper, unless noted otherwise. For extracting these parameters, we discuss methodologies that are necessarily specific to different fusion approaches (including magnetic, inertial, and magneto-inertial fusion). This paper is intended to serve as a reference for fusion researchers and a tutorial for all others interested in fusion energy.

Hydroscaling indirect-drive implosions on the National Ignition Facility

A goal of the laser-based National Ignition Facility (NIF) is to increase the liberated fusion energy “yield” in inertial confinement fusion experiments well past the ignition threshold and the input laser energy. One method of increasing the yield, hydrodynamic scaling of current experiments, does not rely on improving compression or implosion velocity, but rather increases the scale of the implosion to increase hotspot areal density and confinement time. Indirect-drive (Hohlraum driven) implosions carried out at two target sizes, 12.5% apart, have validated hydroscaling expectations. Moreover, extending comparisons to the best-performing implosions at five different capsule sizes shows that their performance also agrees well with hydroscaling expectations even though not direct hydroscales of one another. In the future, by switching to a reduced loss Hohlraum geometry, simulations indicate that we can drive 20% larger-scale implosions within the current power and energy limitations on the NIF. At the demonstrated compression and velocity of these smaller-scale implosions, these 1.2× hydroscaled implosions should put us well past the ignition threshold.

Development and validation of the numerical model of Electron Cyclotron Resonance Ion Sources

Processes of the secondary electron emission (SEE) from the walls are included into the Numerical Advanced Model of Electron Cyclotron Resonance Ion Sources (NAM-ECRIS). It is found that SEE strongly influences electron confinement time and ion production. With the modified model, we observe reactions of the source to changes in a gas flow into the source and in an injected microwave power. The source performance with scaling the hexapole magnetic field is investigated. The calculated tendencies are close to the experimental observations.

Core‐SOL simulations of high‐power JET‐ILW pulses fuelled with gas and/or with pellets

AbstractExperimental analysis of two couples of pulses in the range of input power of 26–32 MW, shows that addition of pellet throughput to high gas dosing pulses does not modify the plasma energy, but leads to better conditions as far as the tungsten concentration and core radiation are concerned. Significantly decreasing the gas dosing with addition of high pellet throughput causes the increase of plasma energy, but the W concentration increases from 5.2 × 10−5 to 6.9 × 10−5 and the core radiation from 7.5 to 11 MW. From the numerical results of the self‐consistent core‐SOL COREDIV code two mechanisms appear to be responsible for the observed different W concentrations: the core residence time of W, which is related to the energy and particle confinement time, and the divertor impurity screening efficiency, dependent on the electron density and on the perpendicular transport coefficient in the SOL.

Start of experiments in the design configuration of the GOL-NB multiple-mirror trap

A multiple-mirror confinement is an alternative concept in fusion energy development that improves the particle and energy confinement times in open traps (linear magnetic systems). The paper discusses the development progress of the GOL-NB multiple-mirror experiment that was recently commissioned at BINP. The reference description of the GOL-NB hardware is presented. Properties of a low-temperature start plasma are discussed. The first results from test experiments with injection of one 25 keV neutral beam are shown. Methods of plasma stabilization in the non-min-B configuration are discussed. In general, the ongoing commissioning progress and results of the preliminary experiments are modestly optimistic for the expected device performance.

Estimation of stagnation performance metrics in magnetized liner inertial fusion experiments using Bayesian data assimilation

We present a new analysis methodology that allows for the self-consistent integration of multiple diagnostics including nuclear measurements, x-ray imaging, and x-ray power detectors to determine the primary stagnation parameters, such as temperature, pressure, stagnation volume, and mix fraction in magnetized liner inertial fusion (MagLIF) experiments. The analysis uses a simplified model of the stagnation plasma in conjunction with a Bayesian inference framework to determine the most probable configuration that describes the experimental observations while simultaneously revealing the principal uncertainties in the analysis. We validate the approach by using a range of tests including analytic and three-dimensional MHD models. An ensemble of MagLIF experiments is analyzed, and the generalized Lawson criterion χ is estimated for all experiments.

Design Of An Electrostatic Ion Trap And Time-of-Flight Tube Using SIMION Software

Electrostatic traps are a class of ion traps that rely on electric fields to confine charged particles in a region of space. It uses an electric field to trap the incoming ions from an ion source, confine them for a certain period of time, and then release them either as a continuous or pulsed ion beam. Ions once released from the trap are made to fly through a Time of Flight (ToF) tube for segregation based on their energies and mass. The time taken to travel the length of the ToF tube is equated to the mass of the ion, which can further be used to calculate the energy and mass of the ions. SIMION software simulates the trajectories of charged particles through electric and magnetic fields of different geometries. In this proposed paper, we will be presenting simulations of an (a) electrostatic ion trap and (b) Time of Flight tube using SIMION software. Experimental data of confinement time of ions in the trap and the time of flight of the ions in a 1m and 2m long ToF tube are simulated and tabled. The results from the simulations reported in this paper can be used as a template to design and develop custom electrostatic traps in conjunction with ToF tubes for specific instruments like spectrometers, medical devices, etc.

Remotely triggered door and real‐time monitoring for bear cage traps

AbstractWe modified the bear cage trap with a low‐cost remotely triggered trap door and fitted the trap with a motion activated camera that relayed bear captures to researchers in real time. We built 4 modified bear cage traps and used them to capture free‐ranging American black bears (Ursus americanus) during summer 2020 on MPG Ranch in western Montana, USA. Lacking data on bear confinement time in traps from previous studies, we compared the amount of time that bears were confined in our modified traps with estimated confinement time had the same bears in our study been captured in traditional traps that were physically checked once daily at 0900, once daily at 1200, or twice daily at 0900 and 1600. We captured bears 30 times during 195 trap nights. The camera system relayed photos of all captures in real time and the remotely triggered door release was 100% successful. When we evaluated all bear captures and recaptures (n = 30), mean bear confinement time in our modified traps (4.92 hrs) was significantly lower than estimated mean confinement time had the same bears been captured in traditional traps that were checked once daily at 0900 (14.95 hrs), once daily at 1200 (10.73 hrs), or twice daily at 0900 and 1600 (7.01 hrs). For bears that were recaptured during regular trap monitoring hours (0700–1800) and remotely released without immobilization (n = 12), mean confinement time in our modified traps was <1 hr. By remotely monitoring traps, we saved an estimated US $6,580 or $13,624 in gas and staff hours during 3 months of trapping, had we physically checked traps once or twice daily, respectively. Our modified traps minimized animal confinement time, eliminated unnecessary animal immobilizations, and helped us maximize time and resource efficiencies. Our findings are relevant to bear research and management, and the technology we used can be adapted for trapping other wildlife species.

An Unsupervised Spectrogram Cross-Correlation Method to Assess ELM Triggering Efficiency by Pellets

The high confinement mode (H-mode) is considered the optimal regime for the production of energy through nuclear fusion for industrial purposes since it allows to increase the energy confinement time of the plasma roughly by a factor of two. Consequently, it has been selected at the moment as the standard scenario for the next generation of devices, such as ITER. However, pressure-driven edge instabilities, known as edge localized modes (ELMs), are a distinct feature of this plasma regime. Their extrapolated thermal and particle peak loads on the plasma-facing components (PFC) of the next generation of devices are expected to be so high as to damage such structures, compromising the normal operations of the reactors themselves. Consequently, the induced loads have to be controlled; this can be achieved by mitigating ELMs. A possibility then lays in increasing the ELMs frequency to lower the loads on the PFCs. As already demonstrated at JET, the pellet pacing of ELMs is considered one of the most promising techniques for such scope, and its optimization is therefore of great interest for present and future operations of nuclear fusion facilities. In this work, we suggest a method to access primary pieces of information to perform statistics, assess and characterize the pacing efficiency. The method, tested on JET data, is based on the clustering (k-means) of convoluted signals, using so-called spectrogram cross-correlation, between the measured pellets and ELMs time traces. Results have also been obtained by taking advantage of a new type of diagnostic for measuring the ELMs dynamic, based on synthetic diamond sensors, faster than the standard spectroscopic cameras used at JET.

Non-linear MHD modelling of edge localized modes suppression by resonant magnetic perturbations in ITER

Edge localized modes (ELMs) suppression by resonant magnetic perturbations (RMPs) was studied with the non-linear magneto-hydro-dynamic (MHD) code JOREK for the ITER H-mode scenarios at 15 MA, 12.5 MA, 10 MA/5.3 T. The main aim of this work was to demonstrate that ELMs can be suppressed by RMPs while the divertor 3D footprints of heat and particle fluxes remain within divertor material limits. The unstable peeling–ballooning modes responsible for ELMs without RMPs were modelled first for each scenario using numerically accessible parameters for ITER. Then the stabilization of ELMs by RMPs was modelled with the same parameters. RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N = 2, N = 3, N = 4 have been used as boundary conditions of the computational domain of JOREK, including realistic RMP coils, main plasma, scrape off layer (SOL) divertor and realistic first wall. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. With RMPs, the main toroidal harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing saturated modes and a continuous MHD turbulent transport thereby avoiding ELM crashes in all scenarios considered here. The threshold for ELM suppression was found at a maximum RMP coils current of 45 kAt–60 kAt compared to the coils maximum capability of 90 kAt. In the high beta poloidal steady-state 10 MA/5.3 T scenario, a rotating QH-mode without ELMs was observed even without RMPs. In this scenario with RMPs N = 3, N = 4 at 20 kAt maximum current in RMP coils, similar QH-mode behaviour was observed however with dominant edge harmonic corresponding to the main toroidal number of RMPs. The present MHD modelling was limited in time by few tens of ms after RMPs were switched on until the magnetic energy of the modes saturates. As a consequence the thermal energy was still evolving on this time scale, far from the ITER confinement time scale and hence only the form of 3D footprints on the divertor targets can be indicated within this set-up. Also note, that the divertor physics was missing in this model, so realistic values of fluxes are out of reach in this modelling. However the stationary 3D divertor and particle fluxes could be simply extrapolated from these results to the stationary situation considering that a large power fraction should be radiated in the core and SOL and only about 50 MW power is going to the divertor, which is an arbitrary, but reasonable number used here. The 3D footprints with RMPs show the characteristic splitting with the main RMP toroidal symmetry. The maximum radial extension of the footprints typically was ∼20 cm in inner divertor and ∼40 cm in outer divertor with stationary heat fluxes decreasing further out from the initial strike point from ∼5 MW m−2 to ∼1 MW m−2 assuming a total power in the divertor and walls is 50 MW. The heat fluxes remain within the divertor target and baffle areas, however with rather small margin in the outer divertor which could be an issue for the first wall especially in transient regimes when part of the plasma thermal energy is released due to switching on the RMP coils. This fact should be considered when RMPs are applied with a more favorable application before or soon after the L–H transition, although optimization is required to avoid increasing the L–H power threshold with RMPs.

Experimental confirmation of efficient island divertor operation and successful neoclassical transport optimization in Wendelstein 7-X

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.

Measurement of ionization, charge exchange and ion confinement times in charge breeder ECR ion sources with short pulse 1+ injection of metal ions

The Consecutive Transients (CT) method is used for estimating the characteristic times of ionization, charge exchange and confinement within the plasma of a Charge Breeder Electron Cyclotron Resonance Ion Source (CB-ECRIS). The method reveals differences in the characteristic times between different source configurations, with K9+ charge breeding efficiencies of 8.9 % and 20.4 %, and allows qualitative explanation of the improved breeding efficiency. The increase in K9+ efficiency is accompanied by a decrease in ionization time for low charge states, a decrease of charge exchange time for high charge states, and an overall decrease of the ion confinement time, which increases non-linearly with the charge state. The charge exchange time exhibits a minimum near charge state K8+, indicating low neutral density near the plasma core. The CT-method yields a distribution of possible ne and (Ee) corresponding to the spatial distribution of different charge state ions. The results hint at a non-uniform plasma electron density and energy distribution as well as a nested-layer distribution for the ion populations — hot and dense plasma with high charge state ions near the plasma core.

Transport hysteresis in electromagnetic microturbulence caused by mesoscale zonal flow pattern-induced mitigation of high β turbulence runaways

Electromagnetic microturbulence at finite normalized plasma pressure β=n0T0/(B02/2μ0) (n0 is the equilibrium density, T0 the equilibrium temperature, B0 the equilibrium magnetic field, and μ0 the permeability of free space) is investigated within a local gradient-driven gyrokinetic framework. The focus lies on the well-known high β turbulence runaways [R. E. Waltz, Phys. Plasmas 17, 072501 (2010)] that have been proposed to set a nonlinear upper threshold βc, also known as the nonzonal transition [M. J. Pueschel, Phys. Rev. Lett. 110, 155005 (2013)]. In this paper, it is shown that persistent mesoscale zonal flow patterns, developing self-consistently on long time scales, mitigate high β turbulence runaways. The application of such mesoscale zonal flow states as initial conditions allows for the access of an improved β-regime, that is, β>βc, in which no turbulence runaway occurs. Various aspects of those mesoscale zonal flow-dominated improved states are investigated, such as (i) the stability constraints with respect to the mesoscale zonal flow level for the triggering of turbulence runaways, (ii) the influence of mesoscale zonal flows on magnetic stochasticity [W. M. Nevins, Phys. Rev. Lett. 106, 065003 (2010)], and (iii) the transfer processes connected to the drive and damping of mesoscale zonal flows. This work implies that βc does not set the upper limit in the normalized plasma pressure for stationary operation, provided persistent mesoscale zonal flow patterns can develop. Since variations of β occur on the energy confinement time, which is large compared to the time required for mesoscale zonal flows to develop, the reported mesoscale zonal flow-dominated improved β-regime is expected to be the experimentally relevant branch. Furthermore, this work highlights the need for sufficiently long simulation time traces of at least a few ∼103 R0/vth,i (R0 is the major radius, and vth,i is the ion thermal velocity), also within kinetic electron frameworks, to capture non-negligible long-term dynamics.