Tripled yield in direct-drive laser fusion through statistical modelling.

Focusing laser light onto a very small target can produce the conditions for laboratory-scale nuclear fusion of hydrogen isotopes. The lack of accurate predictive models, which are essential for the design of high-performance laser-fusion experiments, is a major obstacle to achieving thermonuclear ignition. Here we report a statistical approach that was used to design and quantitatively predict the results of implosions of solid deuterium-tritium targets carried out with the 30-kilojoule OMEGA laser system, leading to tripling of the fusion yield to its highest value so far for direct-drive laser fusion. When scaled to the laser energies of the National Ignition Facility (1.9 megajoules), these targets are predicted to produce a fusion energy output of about 500 kilojoules-several times larger than the fusion yields currently achieved at that facility. This approach could guide the exploration of the vast parameter space of thermonuclear ignition conditions and enhance our understanding of laser-fusion physics.

Persistent Hot-Spot Mix in Cryogenic Direct-Drive Fusion Experiments.

We show that an x-ray emission signature associated with acceleration phase mass injection [R. C. Shah et al., Phys. Rev. E 103, 023201 (2021)PRESCM2470-004510.1103/PhysRevE.103.023201] correlates with poor experimental hot-spot convergence and a reduced neutron production relative to expectations. It is shown that with increased target mass as well as with higher-design adiabats, this signature is reduced, whereas with increased debris on the target, the signature is increased. We estimate that the vapor region in typical best designs may have up to 2× the assumed hydrogen mass at the start of deceleration.

Effects of Laser Bandwidth in Direct-Drive High-Performance DT-Layered Implosions on the OMEGA Laser.

In direct-drive inertial confinement fusion, the laser bandwidth reduces the laser imprinting seed of hydrodynamic instabilities. The impact of varying bandwidth on the performance of direct-drive DT-layered implosions was studied in targets with different hydrodynamic stability properties. The stability was controlled by changing the shell adiabat from (α_{F}≃5) (more stable) to (α_{F}≃3.5) (less stable). These experiments show that the performance of lower adiabat implosions improves considerably as the bandwidth is raised indicating that further bandwidth increases, beyond the current capabilities of OMEGA, would be greatly beneficial. These results suggest that the future generation of ultra-broadband lasers could enable achieving high convergence and possibly high gains in direct drive ICF.

3D Simulations Capture the Persistent Low-Mode Asymmetries Evident in Laser-Direct-Drive Implosions on OMEGA.

Spherical implosions in inertial confinement fusion are inherently sensitive to perturbations that may arise from experimental constraints and errors. Control and mitigation of low-mode (long wavelength) perturbations is a key milestone to improving implosion performances. We present the first 3D radiation-hydrodynamic simulations of directly driven inertial confinement fusion implosions with an inline package for polarized crossed-beam energy transfer. Simulations match bang times, yields (separately accounting for laser-induced high modes and fuel age), hot spot flow velocities and direction, for which polarized crossed-beam energy transfer contributes to the systematic flow orientation evident in the OMEGA implosion database. Current levels of beam mispointing, imbalance, target offset, and asymmetry from polarized crossed-beam energy transfer degrade yields by more than 40%. The effectiveness of two mitigation strategies for low modes is explored.

Experimentally Inferred Fusion Yield Dependencies of OMEGA Inertial Confinement Fusion Implosions.

Statistical modeling of experimental and simulation databases has enabled the development of an accurate predictive capability for deuterium-tritium layered cryogenic implosions at the OMEGA laser [V. Gopalaswamy et al.,Nature 565, 581 (2019)10.1038/s41586-019-0877-0]. In this letter, a physics-based statistical mapping framework is described and used to uncover the dependencies of the fusion yield. This model is used to identify and quantify the degradation mechanisms of the fusion yield in direct-drive implosions on OMEGA. The yield is found to be reduced by the ratio of laser beam to target radius, the asymmetry in inferred ion temperatures from the ℓ=1 mode, the time span over which tritium fuel has decayed, and parameters related to the implosion hydrodynamic stability. When adjusted for tritium decay and ℓ=1 mode, the highest yield in OMEGA cryogenic implosions is predicted to exceed 2×10^{14} fusion reactions.

Experimental Evidence of a Variant Neutron Spectrum from the T(t,2n)α Reaction at Center-of-Mass Energies in the Range of 16-50 keV.

Full calculations of six-nucleon reactions with a three-body final state have been elusive and a long-standing issue. We present neutron spectra from the T(t,2n)α (TT) reaction measured in inertial confinement fusion experiments at the OMEGA laser facility at ion temperatures from 4 to 18 keV, corresponding to center-of-mass energies (E_{c.m.}) from 16 to 50 keV. A clear difference in the shape of the TT-neutron spectrum is observed between the two E_{c.m.}, with the ^{5}He ground state resonant peak at 8.6 MeV being significantly stronger at the higher than at the lower energy. The data provide the first conclusive evidence of a variant TT-neutron spectrum in this E_{c.m.} range. In contrast to earlier available data, this indicates a reaction mechanism that must involve resonances and/or higher angular momenta than L=0. This finding provides an important experimental constraint on theoretical efforts that explore this and complementary six-nucleon systems, such as the solar ^{3}He(^{3}He,2p)α reaction.

Using Inertial Fusion Implosions to Measure the T+

Light nuclei were created during big-bang nucleosynthesis (BBN). Standard BBN theory, using rates inferred from accelerator-beam data, cannot explain high levels of ^{6}Li in low-metallicity stars. Using high-energy-density plasmas we measure the T(^{3}He,γ)^{6}Li reaction rate, a candidate for anomalously high ^{6}Li production; we find that the rate is too low to explain the observations, and different than values used in common BBN models. This is the first data directly relevant to BBN, and also the first use of laboratory plasmas, at comparable conditions to astrophysical systems, to address a problem in nuclear astrophysics.

Publisher's Note: Demonstration of Fuel Hot-Spot Pressure in Excess of 50 Gbar for Direct-Drive, Layered Deuterium-Tritium Implosions on OMEGA [Phys. Rev. Lett. 117, 025001 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.025001.

Demonstration of Fuel Hot-Spot Pressure in Excess of 50 Gbar for Direct-Drive, Layered Deuterium-Tritium Implosions on OMEGA.

A record fuel hot-spot pressure P_{hs}=56±7 Gbar was inferred from x-ray and nuclear diagnostics for direct-drive inertial confinement fusion cryogenic, layered deuterium-tritium implosions on the 60-beam, 30-kJ, 351-nm OMEGA Laser System. When hydrodynamically scaled to the energy of the National Ignition Facility, these implosions achieved a Lawson parameter ∼60% of the value required for ignition [A. Bose et al., Phys. Rev. E 93, 011201(R) (2016)], similar to indirect-drive implosions [R. Betti et al., Phys. Rev. Lett. 114, 255003 (2015)], and nearly half of the direct-drive ignition-threshold pressure. Relative to symmetric, one-dimensional simulations, the inferred hot-spot pressure is approximately 40% lower. Three-dimensional simulations suggest that low-mode distortion of the hot spot seeded by laser-drive nonuniformity and target-positioning error reduces target performance.

Bound on hot-spot mix in high-velocity, high-adiabat direct-drive cryogenic implosions based on comparison of absolute x-ray and neutron yields.

In laser-driven implosions for laboratory fusion, the comparison of hot-spot x-ray yield to neutron production can serve to infer hot-spot mix. For high-performance direct-drive implosions, this ratio depends sensitively on the degree of equilibration between the ion and electron fluids. A scaling for x-ray yield as a function of neutron yield and characteristic ion and electron hot-spot temperatures is developed on the basis of simulations with varying degrees of equilibration. We apply this model to hot-spot x-ray measurements of direct-drive cryogenic implosions typical of the direct-drive designs with best ignition metrics. The comparison of the measured x-ray and neutron yields indicates that hot-spot mix, if present, is below a sensitivity estimated as ∼2% by-atom mix of ablator plastic into the hot spot.

Thermal decoupling of deuterium and tritium during the inertial confinement fusion shock-convergence phase.

A series of thin glass-shell shock-driven DT gas-filled capsule implosions was conducted at the OMEGA laser facility. These experiments generate conditions relevant to the central plasma during the shock-convergence phase of ablatively driven inertial confinement fusion (ICF) implosions. The spectral temperatures inferred from the DTn and DDn spectra are most consistent with a two-ion-temperature plasma, where the initial apparent temperature ratio, T_{T}/T_{D}, is 1.5. This is an experimental confirmation of the long-standing conjecture that plasma shocks couple energy directly proportional to the species mass in multi-ion plasmas. The apparent temperature ratio trend with equilibration time matches expected thermal equilibration described by hydrodynamic theory. This indicates that deuterium and tritium ions have different energy distributions for the time period surrounding shock convergence in ignition-relevant ICF implosions.

FES and spasticity.

A model of hemiplegic spasticity based on electromyographical and biomechanical parameters measured during passive muscle stretching is presented. Two components of spasticity can be distinguished--phasic and tonic. This classification depends on the pattern of stretch reflex activity which can be either phasic or tonic as well as on the muscle stretch/tension characteristic. Stretch reflex, as a control loop, is in phasic spasticity characterized by increased sensitivity to velocity of stretching. In tonic spasticity, sensitivity to length of stretching is increased. After the injury, phasic spasticity appears first and invokes monosynaptic reflex pathways. The intensity of tonic spasticity increases with the duration of disability and hence causes changes in muscle fiber biomechanical properties. The model mentioned above has been used to evaluate the effects of FES on spasticity. Hemiplegic patients with implanted peroneal nerve stimulator for gait correction were followed up for one year starting a week before implantation. Long-term use of FES resulted in decrease of tonic spasticity in both ankle joint antagonistic muscle groups. In stimulated tibialis anterior muscle, the phasic type of spasticity increased. To obtain the correlation between changes in spasticity and functional abilities of patients, the maximal voluntary isometric contraction of both muscle groups was also measured. An improvement in voluntary strength was also observed. This can be taken as additional evidence that tonic spasticity is of greater physiological and clinical significance than phasic spasticity. It may be concluded that use of FES can decrease tonic spasticity and, if applied early after the injury, can prevent the appearance of tonic spasticity.

Application of a programmable dual-channel adaptive electrical stimulation system for the control and analysis of gait.

A dual-channel electrical stimulation system with a stimulator and a programmer/stride analyzer was designed for clinical rehabilitation of gait and for subsequent daily use as an orthotic aid. The stimulator, with controls to adjust amplitude only (50 mA), adapts chosen stimulation sequences to the walking rate of a patient. Pulse duration (50-500 microseconds), frequency (5-120 Hz), shape (symmetrical biphasic, monophasic), stimulation sequences (16 stride segments) and their cycle (2-12 sec), and right/left foot-switch choices are selected for each patient and programmed into a separate unit. The programming unit also statistically processes the foot-switch data collected by the stimulator. The device was evaluated with regard to the programmable parameters, effectiveness during gait, and feasibility in clinical use. It was applied to 11 stroke patients and 10 brain injury patients during gait, stimulating 22 combinations of peroneal nerve and hamstring, quadriceps, triceps brachii, and gluteus maximus muscles. Forces on both feet, equinovarus, knee extension and hyperextension, elbow flexion, and hip extension were corrected. Selection of the stimulation sequences, their adaptation, range of pulse duration, and valid statistics were verified. Improved forces and joint angles were recorded together with significant changes in the stride time, length, and velocity by the stimulation.

Implantable stimulator for selective stimulation of the common peroneal nerve: a preliminary report.

We present details of the modelling, design, and experimental testing of an implantable system with a monopolar half-cuff electrode for selective stimulation of fibres within certain superficial regions of the human common peroneal nerve which is capable of making a selective activation of muscles, thus contributing to strong dorsal flexion and moderate eversion of the hemiplegic foot. The development of the cuff electrode was based partly on data obtained from histological examination of human common peroneal nerves, and from previously described models of excitation of myelinated nerve fibres. The modelling objectives were to determine the electric field that would be generated within the deep peroneal branch of the nerve by a monopolar half-cuff electrode installed on the nerve behind the lateral head of the fibula. The extent of initial excitation of the nerve fibres within the superficial region of the deep peroneal branch elicited by a monopolar half-cuff electrode was predicted. In the past 6 months two systems were implanted. In both patients significant improvements of gait dynamics were observed.

Evaluation of gait with multichannel electrical stimulation.

Short, intensive multichannel electrical stimulation therapy was evaluated in 14 hemiplegics after stroke or head injury. The stimulation of the peroneal nerve, soleus, quadriceps, hamstring, gluteus maximus, and triceps brachii muscles with individually preprogrammed sequences was applied by surface electrodes at the beginning of gait rehabilitation. The patients started walking with the support of a therapist, gradually increased the walking distance and all reached independent ambulation with a crutch after an average of 14 stimulation sessions. A portable microprocessor six-channel stimulator/stride analyzer enabled the collection of gait parameters and recording of statistical mean values of stride time, gait symmetry, right and left stance times, and their standard deviations. Without additional equipment, several hundred stimulated strides were measured during each stimulation session.

Enhanced rehabilitation of gait after stroke: a case report of a therapeutic approach using multichannel functional electrical stimulation.

The beneficial effects of using multichannel functional electrical stimulation (MFES) for gait rehabilitation in nonambulatory hemiplegic patients have already been shown. The methodology of application and the results presented were pooled for the whole group of participants, which blurs the exact picture of each particular subject and many vital details are not presented. The purpose of this article is to focus on a single subject from the study and to present all the details of the treatment. The presented subject participated six weeks in the study, first three weeks in MFES therapy and second three weeks in conventional therapy. The effects of each therapy were evaluated by the following measures: temporal-distance parameters of gait, ground reaction forces, goniograms in hip knee and ankle, and assessment of the physical status of the patient according to the Fugl-Meyer evaluation scale. An analysis of the measured parameters showed improved performance of the patient during MFES therapy and stagnation or even slight recession during conventional therapy. The patient achieved independent gait during the three weeks of MFES therapy. At 30 months after the beginning of therapy, the patient was still able to ambulate independently without any significant changes in his gait pattern. The accomplishment was mainly attributed to the avoidance of pathological gait pattern development by using MFES assisted gait training and to the high motivation of the patient to walk and exercise during therapy as well as after he was released to go home.

EMG monitoring of stimulating electrode position in implantation of subcutaneous peroneal stimulators.

Implantation of subcutaneous peroneal stimulators requires careful positioning to obtain a good response. With the patient lying down during the surgical procedure, ankle dorsal flexion was not always satisfactory during gait. Instead of dorsal flexion the stimulus could give an excessive eversion or a coactivation of ankle antagonists. To select the correct electrode position, the responses to single stimulation pulses were monitored in the tibialis anterior, peroneus longus and triceps surae muscles by surface EMG electrodes. With the patient standing, a strong contraction of the anterior tibial muscle without excessive contraction of the peroneus longus muscle was first determined by surface stimulation. The EMG responses were then recorded with the patient lying in the position required for implantation. The records were used as a guideline during surgery, during which positioning of the electrodes was monitored by the EMG responses. The method, tested on 2 healthy adults and 13 patients, resulted in reliable positioning of the stimulating electrodes.

Chronic electrical stimulation for the modification of spasticity in hemiplegic patients.

The effects of long-term electrical stimulation on reflex hyperactivity and voluntary muscle control were studied. Eight hemiplegic patients with implanted peroneal stimulator were included. After six months of functional electrical stimulation (FES) there was a decrease of tonic activity in both tibialis anterior and triceps surae muscles. The phasic stretch reflex activity in the stimulated tibialis anterior muscle increased. The resulting resistance during passive movements decreased due to diminution of tonic activity. The absence of tonic activity also resulted in improvement of voluntary control, particularly in the tibialis anterior muscle.

Therapeutic effects of multisite electric stimulation of gait in motor-disabled patients.

Therapeutic effects in ten hemiplegic patients and one paraparetic patient treated by multisite electric stimulation of gait were compared with effects in ten hemiplegic patients treated by standard rehabilitation methods after 2.6 months of extensive therapy. Average step length and gait velocity, ground reaction forces and their distribution under both feet, and crutch loading were measured; goniograms of joint angles, kinesiologic gait analysis, and EMG recordings from the main muscles used in ambulation and in standing, were made while patients in both groups walked without stimulation. Quantitative measurements before, during, at the end, and 8.4 months posttherapy were taken based on at least 40 strides per patient. The results for the stimulated group in midtherapy indicated faster recovery rates (3.15 times in step length and 2.25 times in gait velocity) than in the control group, and at the end of therapy the stimulated group had higher improvement levels (2.14 times in step length, 1.42 times in gait velocity, and 1.63 times in kinesiologic gait analysis). The differences between the two groups faded after 8.4 months without treatment, and some kinesiologic deficits reappeared, mostly those in the more distal muscle groups. These findings indicate a need for a simpler orthotic electric stimulation after multisite therapy in several cases. Immediate effects of the six-site stimulation were also considered for orthotic possibilities after the therapy.