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The neutron emission spectrum can be modified from Gaussian due to excited Alfven eigenmodes (AEs). We evaluate the neutron emission spectrum when the fuel-ion velocity distribution functions are distorted by AEs, assuming an ITER-like deuterium–tritium tokamak plasma. When shear AEs are excited by energetic particles in a plasma, the non-Maxwellian tails are created in the fuel-ion distribution functions in directions that are parallel and antiparallel to the magnetic field lines. Due to formation of these tails, the non-Gaussian components are formed in the neutron emission spectrum in the same and opposite directions of the toroidal axis. The anisotropic, non-Gaussian neutron emission spectrum can be used for experimental verification and diagnostics of the non-Maxwellian tails in the fuel-ion velocity distribution functions formed by AEs.

Analysis and experimental validation of energetic non-Maxwellian components formed in ion velocity distribution functions enhance our understanding of important physical phenomena in burning plasmas. As one such energetic component, knock-on tails appear due to nuclear elastic scattering (NES). It is important to experimentally validate the NES effects and analysis model of knock-on tails. For this purpose, we propose a method for determining the shape and size of a knock-on tail from the Doppler-broadened γ-ray emission spectrum in a proton-beam-injected deuterium plasma confined in an ITER-like experimental fusion device. In the proposed method, we adopt a two-temperature Maxwellian model and utilize the γ-ray-generating 6Li(d,nγ)7Be and 6Li(d,pγ)7Li nuclear reactions. We discuss both the validity of the proposed method and the expected accuracy of the shape and size of the measured knock-on tail.

It is well known that the influence of nuclear force, e.g., nuclear elastic scattering (NES), appears in an ion scattering process when ion energy increases. NES caused by high-energy particles forms the non-Maxwellian component in the ion distribution function. The non-Maxwellian component is named knock-on tail. The knock-on tail gives various effects on fusion plasma. Therefore, it is important to conduct an experiment in order to understand the impact of the NES effects. The NES effects are affected by the “shape and size” of the knock-on tail and the “shape and size” of the knock-on tail depends on plasma conditions. Therefore, we newly propose the method to observe the correlation between the NES effects and the plasma conditions by using Doppler effects for the γ-ray-generating reaction, i.e., 6 Li(d, p) 7 Li nuclear reaction, in ITER-like deuterium plasma. We can capture the impact of the NES effect caused by the change in the plasma conditions, i.e., electron temperature, deuteron density, proton beam power, and proton beam energy by capturing the change in the γ-ray spectrum. On the basis of the Boltzmann-Fokker-Planck model, we showed the validity of the method by simulation.

A possible scenario to observe a knock-on tail using anisotropic neutron emission spectrum in a proton-beam injected deuterium plasma is presented. On the basis of the ion trajectory analysis in ITER-like magnetic configuration, Boltzmann collision integral and Fokker-Planck simulation, the knock-on tail formation in deuteron distribution function due to nuclear elastic scattering, and the resulting modification of the “double differential” neutron emission spectrum are examined. As a result of the beam injection with a specific direction, the neutron emission spectrum is modified in 2-D phase space. It is shown that the ratio of neutron emission rate with >2.8-MeV energy to the 2.45-MeV peak is increased almost 10 times compared with the 1-D modified neutron emission spectrum integrated over the emission angle, which implies the improvement of the accuracy in the neutron measurement. By using the anisotropic neutron emission adjusting the relative positions between beam-injection port and the neutron detector, the possibility to catch the knock-on tail for various plasma conditions can be increased.

The fast deuteron (non-Maxwellian component) diagnostic method, which is based on the higher resolution optical spectroscopic measurement, has been developed as a powerful tool. Owing to a decrease in the D–H charge-exchange cross section, the diagnostic ability of conventional optical diagnostic methods should be improved for ∼MeV energy deuterons. Because the 3He–H charge-exchange cross section is much larger than that of D–H in the ∼MeV energy range, the visible light (VIS) spectrum of 3He produced by the dueteron–dueteron (DD) reaction may be a useful tool. Although the density of 3He is small because it is produced via the DD reaction, improvement of the emissivity of the VIS spectrum of 3He can be expected by using a high-energy beam. We evaluate the VIS spectrum of 3He for the cases when a fast deuteron tail is formed and not formed in the ITER-like beam injected deuterium plasma. Even when the beam energy is in the MeV energy range, a large change appears in the half width at half maximum of the VIS spectrum. The emissivity of the VIS spectrum of 3He and the emissivity of bremsstrahlung are compared, and the measurable VIS spectrum is obtained. It is shown that the VIS spectrum of 3He is a useful tool for the MeV beam deuteron tail diagnostics.

In this work, energetic-ion confinement and loss due to energetic-ion driven magnetohydrodynamic modes are studied using comprehensive neutron diagnostics and orbit-following numerical simulations for the Large Helical Device (LHD). The neutron flux monitor is employed in order to obtain global confinement of energetic ions and two installed vertical neutron cameras (VNCs) viewing different poloidal cross-sections are utilized in order to measure the radial profile of energetic ions. A strong helically-trapped energetic-ion-driven resistive interchange mode (EIC) excited in relatively low-density plasma terminated high-temperature state in LHD. Changes in the neutron emission profile due to the EIC excitation are clearly visualized by the VNCs. The reduction in the neutron signal for the helical ripple valley increases with EIC amplitude, which reaches approximately 50%. In addition to the EIC experiment, orbit-following simulations using the DELTA5D code with EIC fluctuations were performed to assess the energetic-ion transport and loss. Two-dimensional temporal evolution results show that the neutron emissivity at the helical ripple decreases significantly due to the EIC. The rapid reduction in neutron emissivity shows that the helically-trapped beam ions immediately escape from the plasma. The reduction in the VNC signals for the helical ripple valley and the total neutron emission rate increase with increasing EIC amplitude, as observed in the experiment. Calculated line-integrated neutron emission results show that the profile measured by VNC1 has one peak, whereas the profile measured by VNC2 has two peaks, as observed in the experiment. Although the neutron emission profile for VNC2 has a relatively wide peak compared with the experimental results, the significant decrease in neutron signal corresponding to the helical ripple valley was successfully reproduced.

We developed an analysis model to predict and describe neutron emission anisotropy caused by anisotropy of energetic deuterons in the large helical device (LHD), by considering energetic-ion distribution functions, the differential cross-section of fusion reactions, and the exact shape of the vacuum vessel of the LHD. Neutron emission anisotropy that can be observed by the neutron activation system is evaluated numerically assuming deuterium-beam-injected deuterium plasmas confined by the LHD using the model. We demonstrate the dependence of neutron emission anisotropy on the beam-injection direction and the electron temperature. Based on this estimation, we propose an experimental scenario to validate the analysis model and easily understand energetic-ion anisotropy caused by the neutral beam injection.

Fuel-ion velocity distribution functions can be distorted from a Maxwellian by Alfven eigenmodes when the mode amplitudes are large, and the fusion reaction rate coefficient can be enhanced by the distortion. Assuming an ITER-like deuterium–tritium plasma containing an excited Alfven eigenmode, we have investigated the modified deuteron and triton velocity distribution functions and the resulting fusion reaction rate coefficient. It is found that the non-Maxwellian components in the distribution functions form in directions parallel and antiparallel to the magnetic field lines due to the toroidal Alfven eigenmodes or the ellipticity-induced Alfven eigenmodes. Focusing on the effect of the distortion of the distribution functions, we discuss the dependence of the enhancement of the fusion reaction rate coefficient on the mode amplitudes and determine the threshold amplitude necessary to enhance the rate coefficient.

A new method to diagnose the degree of electron degeneracy in compressed fuel for fast-ignition inertial confinement fusion is proposed We focus on 4.44-MeV γ-rays emitted in the reaction 9 Be(a, nγ) 12 C governed by fusion-produced energetic alpha-particles in a laser-imploded DT fuel pellet admixed with a small amount of 9 B. In this case the compressed fuel pellet is not subjected to any heating laser pulse. We have evaluated the probability P α-Be that the a+9B e reaction occurs during the slowing down of a-particle. It is found that the reaction probability depends strongly on the degeneracy parameter Θ, which is defined as the ratio of electron temperature to the Fermi energy. We show the possibility of diagnosing the electron degeneracy from the P α-Be - Θ diagram by detecting the 4.44-MeV γ-quanta and DT neutrons emitted from the dense core plasma.

The alpha-particle emission spectrum in beam-injected deuterium-tritium (DT) plasma is examined by solving the Boltzmann-Fokker-Planck (BFP) equations for deuteron, triton and alpha-particle simultaneously. It is shown that owing to the existence of energetic component in fuel-ion energy distribution functions due to neutral-beam injection (NBI) and/or nuclear elastic scattering (NES), the fraction of the energetic (> 3.52MeV) alpha-particle generation rate increases significantly compared with the case for Gaussian distribution. Aiming at an application to plasma diagnostics, correlation between the modification of the emission spectrum and the gamma(y)-ray generation rate from 9 Be(a,nγ) 12 C reaction is studied.

Fast neutral generation by charge exchange reaction in inertial electrostatic confinement plasmas is studied by solving the Poisson equation and the Boltzmann equation for fast neutrals. Fusion reactions carried by the charge exchange fast neutrals become appreciable compared with ion-background fusion reaction. It is shown that the fusion reaction between fast neutral and background gas is sensitively affected by experimental parameters (grid voltage, background gas pressure) and ion distribution function.

An effect of the nuclear elastic scattering (NES) on the neutral beam injection (NBI) plasma heating was examined by solving the Boltzmann-Fokker-Planck (BFP) equation for beam ion in the deuterium-tritium (DT) thermonuclear plasmas. The BFP calculations show that the enhancement in the fraction of the NBI heating power deposited to ions due to NES becomes appreciable when beam energy is larger than 1MeV, and the enhancement is strongly influenced by plasma parameters.

The radial profile of the neutron production rate in spherical inertial electrostatic confinement (SIEC) plasmas is numerically investigated for various device parameters, i.e., grid cathode current, grid voltage, etc. The electrostatic potential is obtained by solving the Poisson equation; and using the potential, the fuel-ion velocity distribution function is determined at each radial point. From the space-dependent velocity distribution function, the radial profile of the neutron production rate is evaluated. The influence of the broadness of the electron angular momentum distribution on the radial profile of the neutron production rate is also examined. It is shown that the height of the peak of the neutron production rate and its radial position are strongly influenced by the device parameters and the electron distribution.

The effect of magnetic field on the velocity distribution function of tritons in D-3He fuelled/field reversed configuration (FRC) plasmas is investigated. Some of the tritons produced by D(d,p)T reactions in the FRC are immediately and asymmetrically lost from the device without any interaction with background charged particles, and then non-symmetric loss causes a distortion of the velocity distribution function as well as a decrease in the number of trapped tritons. Using the distorted triton distribution, the 14 MeV neutron generation rate is estimated and compared with the values for Maxwellian plasmas (the effect of the magnetic field is neglected). It is found that in a typical ignited D-3He/FRC plasma, for example, Ti = Te = 80 keV, nD = 2n3He = 0.5ne = 3 × 1020m-3, τE = 0.5τP = 3 s, rs = 1.6 m and BW = 6 T, the reduction in 14 MeV neutron generation is about 20%.

Formation of an effective ion tail due to neutral beam injection heating during startup in D-[sup 3]He plasmas is investigated. The main idea is to reduce the energy input required for startup heating as well as the 14-MeV neutron yield by creating an effective tail. The optimal beam injection energy and beam species are first estimated by solving the steady-state Fokker-Planck equations for the injected species and for tritons. The startup of D-[sup 3]He plasma is simulated by simultaneously solving the time-dependent power balance and particle conservation equations together with the Fokker-Planck equations. As a result of tail formation in the fuel ion distribution, both the total input energy and the 14-MeV neutron yield during the startup phase are reduced by [approximately]20% from the values for Maxwellian plasma. 12 refs., 10 figs., 3 tabs.

Distortion in the fuel-ion (deuteron and triton) velocity distribution functions due to nuclear elastic scattering (NES) by beam ion and alpha-particle during neutral-beam-injection (NBI) plasma heating operation is studied by simultaneously solving the Boltzmann-Fokker-Planck (BFP) equations for deuteron, triton, alpha-particle and beam ion in the deuterium-tritium (DT) thermonuclear plasmas. Using the obtained distribution functions, enhancement in the T(d,n)4He fusion reaction rate coefficient between background deuteron and triton are estimated. It is shown that the enhancement in the T(d,n)4He reaction rate coefficient becomes appreciable in low-density operations, i.e. neles5times1019 m-3

In highly-compressed plasmas as realized in inertial confinement fusion, the wave nature of electrons becomes noticeable and Pauli’s exclusion principle restricts the energy transition of electrons remarkably. Such a state is called “electron degeneracy”. In addition, the electron degeneracy may affect the energy distribution and temperature of coexisting ions through Coulombic ion-electron interaction. In order to evaluate these effects, we developed and solved the model equation for the distribution function of ions in degenerate electron plasmas. As a result, it is shown that the ion distribution function maintains a Maxwellian form at a temperature equal to that of degenerate electrons in thermal equilibrium because two effects of electron degeneracy—spectral hardening and Pauli blocking—counteract each other. Furthermore the electron degeneracy slows temperature relaxation between ions and electrons in non-thermal equilibrium. c

Alpha-particle slowing-down behaviors at low-temperature, high-density operation points in force-free helical reactors (FFHRs) are examined on the basis of a Fokker-Planck (FP) simulation that simultaneously consider the balance among generation, slowing down, and loss from the plasma in parallel with the density dependence of the Alfven speed. An accurate treatment of the boundary velocity region between thermal and non-thermal components is shown to be important in evaluating the alpha particle population that can induce instability. In a typical high-density, low-temperature operation point in an FFHR, this population is reduced.

A possibility of distortion in bulk-electron velocity distribution function due to injection of intense laser-induced (LI) fast electrons is examined. The Fokker-Planck (FP) equations for LI-fast and bulk electrons are simultaneously solved consistently considering the time evolution of Rosenbluth potentials in two-dimensional (2D) velocity space. The FP simulation shows that an asymmetric distortion of bulk-electron distribution function becomes appreciable when number density of the fast electrons relative to bulk plasma is increased, and that when bulk electrons are assumed to be Maxwellian, the propagation distance of LI-fast electron tends to be shorter due to overestimated power deposition compared with the case when distortion process of the bulk electron distribution is considered.

The alpha (α)-particle and neutron emission spectra in a deuterium-tritium plasma accompanied with neutral-beam-injection (NBI) heating are evaluated in a consistent way by solving the Boltzmann–Fokker–Planck equations for deuteron, triton, and α-particle simultaneously. It is shown that owing to the existence of non-Maxwellian tail component in fuel-ion distribution function due to NBI and/or nuclear elastic scattering, the generation rate of the energetic (≥4 MeV) α-particle increases significantly. When 20 MW intense deuterium beam with 1 MeV beam-injection energy is injected into an 800 m3 plasma (Te=10 keV, ne=6.2×1019 m−3), the enhancement of the fraction of the power carried by α-particles with energy above 4 (3.9) MeV to total α-particle power is almost twice (1.5 times) as much from the value for Gaussian distribution. A verification scenario for the modification of the emission spectrum by using the gamma (γ)-ray-generating B9e(α,nγ)C12 reaction is also presented.

The γ-ray emission rate by 6Li(d,p)7 Li*, 7Li* → 7Li+γ reaction when 50∼250 keV proton beam is injected into 6Li containing deuterium plasmas (ne ∼1019 m-3 and Te = 1∼10 keV) is evaluated by simultaneously solving the Boltzmann-Fokker-Planck (BFP) equations for deuteron and proton. A possible experiment to verify the BFP simulations, e.g. knock-on tail effect on T(d,n)4 He reaction rate coefficient and/or plasma diagnostics which utilize the tail formation in ion distribution function, is proposed.

Effects of nuclear elastic scattering (NES) on the neutral beam injection (NBI) and α-particle plasma heating operations are examined by solving the Boltzmann–Fokker–Planck (BFP) equations for beam ions and α-particles in deuteron–triton thermonuclear plasmas. The BFP calculations show that the enhancement in the fraction of the NBI and α-particle heating powers deposited to ions due to NES can be appreciable in reactor-grade plasmas.

An effect of nuclear elastic scattering (NES) on the energy transfer to plasma ions and electrons during (a) neutral beam injection (NBI) and (b) α-particle heating operations is examined on the basis of the Boltzmann-Fokker-Planck (BFP) equation for a beam ion and an α-particle in deuterium-tritium thermonuclear plasmas. The BFP calculations show that the enhancement in the fraction of the NBI heating power deposited to ions due to NES becomes appreciable when the beam energy is larger than 1MeV. How the NES effect is influenced by the plasma condition is discussed.