Super-thermal particles in hot plasmas—Kinetic models,numerical solution strategies,and comparison to tokamak experiments

The excitation of collective instabilities by super-thermal particles in hot plasmas and the related transport processes attract increasing interest due to their fundamental challenges for theoretical models and their practical importance for burning fusion plasmas. In fact, the physics of a self-heated thermonuclear plasma due to fusion-born 3.5 MeV α$\alpha$-particles is one of the most important outstanding fundamental research topics on the way to a fusion power plant with magnetic confinement. Within the last 10 years significant advances on both the theoretical and the experimental sides have been made leading to a more detailed and quantitative understanding of fast-particle-driven instabilities. On the theoretical side, the crucial step was to move from fluid models for the plasma background with a hybrid kinetic expression for the energetic particles to a fully kinetic model for all the plasma species, i.e. background ions, background electrons, and fast ions. This improvement allows one to describe consistently the resonant interaction between global plasma waves such as shear Alfvén and Alfvén–acoustic waves, and the particles via Landau damping, i.e. the dynamics parallel to the magnetic background field. Also, mode conversion mechanisms require the inclusion of background ion scales in a kinetic, non-perturbative way. This accurate treatment of the plasma background leads not only to changes in the linear mode properties such as frequency, growth/damping rate, and mode structure but also influences the non-linear dynamics. Due to major advances, innovations and installation of diagnostics in present day experiments, this comparison can be carried out in a more detailed and comprehensive way than a few years ago. For example, the measurement of damping rates via active external antennas, the imaging of 2D mode structures via electron–cyclotron-emission spectroscopy, and the direct detection of escaping fast ions allow to diagnose various kinetic features of the plasma modes that are responsible for the transport of energetic particles. Furthermore, the fast particle distribution function itself can also be measured with much greater confidence. Therefore, the new physics accessible due to a more comprehensive model and numerical implementation can be directly verified and validated with experimental data.     

低杂波驱动电流在托卡马克中的分布

本文考虑了大振幅波场对电子的捕获引起的朗道阻尼共振区下限速度下移的机制,并用射线跟踪法计算了低杂波在托卡马克中传播轨迹上的能量沉积。根据能量沉积与低杂波驱动电流的焦耳热效应之间的关系,求出了驱动电流在托卡马克中的径向分布。计算结果与PLT,JFT-2的实验结果符合较好,对HL-1的计算结果也比较令人乐观。 关键词：     

Optimized calculation of the synergy conditions between electron cyclotron current drive and lower hybrid current drive on EAST

The optimized synergy conditions between electron cyclotron current drive(ECCD) and lower hybrid current drive(LHCD) with normal parameters of the EAST tokamak are studied by using the C3PO/LUKE code based on the understanding of the synergy mechanisms so as to obtain a higher synergistic current and provide theoretical reference for the synergistic effect in the EAST experiment. The dependences of the synergistic effect on the parameters of two waves(lower hybrid wave(LHW) and electron cyclotron wave(ECW)), including the radial position of the power deposition, the power value of the LH and EC waves, and the parallel refractive indices of the LHW(N) are presented and discussed.     

Finite motion of massive particles in the Kerr and Schwarzschild fields

In the weakly relativistic limit, an expression is obtained for the damping of quasistationary energy levels in Schwarzschild and Kerr fields due to capture by a collapsar. The strength of the damping in the Schwarzschild field decreases strongly with increasing angular momentum of the particle. If the condition < m_H is satisfied in the case of a rotating black hole, the damping can be replaced by excitation. A particle production process (Hawking process) is considered that leads to the accumulation of particles on quasistationary levels near the black hole. Dynamical equilibrium can be established in the system between the processes of production and capture of particles by the black hole.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, 109–114, September, 1978.     

Study of Electron Heat Pulse Propagation and Particle Diffusion During the Synergy of LHW and IBW Heating in the HT-7

A successful experiment on lower hybrid wave (LHW) and ion Bernstein wave (IBW) synergy has been carried out in the HT-7 superconducting tokamak. With 560KW of LHW heating power and 160 KW of IBW heating power, during the synergy of the LHW and IBW experiment we achieved an improved plasma: the electron density increased and peaked, the soft X intensity increased too. A five-channel far-infrared (FIR) hydrogen cyanide (HCN) laser interferometer was used to measure the electron density profile. The particle diffusion coefficient was studied for the experiment, and the result compared with the heat diffusion coefficient. With the same injected LHW and IBW power, high electron density n_e can deduce the electron pulse propagation and the particle diffusion.     

Electron current drive by fusion-product-excited lower hybrid drift instability

We present first principles simulations of the direct collisionless coupling of the free energy of fusion-born ions into electron current in a magnetically confined fusion plasma. These simulations demonstrate, for the first time, a key building block of some "alpha channeling" scenarios for tokamak experiments. Spontaneously excited obliquely propagating waves in the lower hybrid frequency range undergo Landau damping on resonant electrons, drawing out an asymmetric tail in the electron parallel velocity distribution, which carries a current.     

Alpha channeling in mirror machines

The injection of radio frequency waves can cool charged particles trapped in a magnetic mirror. This cooling effect relies upon waves with azimuthal and axial phase velocities resonating with ions in different axial locations. The ions are then forced to diffuse along highly constrained orbits, such that they can only exit the magnetic trap at low energy. This cooling effect may have application to magnetic fusion mirror machines, where the free energy of the fusion by-products, the alpha particles, might be channeled into the waves that effect the cooling, thereby both extracting the fusion ash quickly and making that energy available in a convenient form for more useful purposes.     

Time-resolved laser optoacoustic tomography of inhomogeneous media

The methods of time-resolved laser optoacoustic tomography of inhomogeneous media and related problems are reviewed. Time-resolved laser optoacoustic tomography allows one to measure the distribution of light absorption in turbid media with depth resolution up to several microns in real time. The theory of laser excitation of acoustic waves by absorbing of light in particles, dispersed in transparent, light-absorbing or scattering media, is developed. The distribution of light absorption can be obtained from the temporal course of acoustic pressure. Two schemes of acoustic wave detection — in the medium under testing (direct detection) and in transparent medium, coupled to the investigated one (indirect detection) — are discussed. In both cases the reconstruction of light absorption can be made by simple calculations. Test experiments with homogeneous and layered media confirm the proposed theoretical models and the possibility of using the proposed experimental schemes. Light absorption in homogeneous, inhomogeneous media and in absorbing particles dispersed in turbid media was investigated. The experimental setup allows one to measure the absorption coefficients over the range 1-500 cm^–1 with the depth resolution 10–15 m over the depth 1–1.5 mm.     

HT-7 Tokamak离子回旋波和低杂波等离子体逃逸电子行为研究

HT-7 Tokamak拥有离子回旋波(ICRF)和低杂波(LHW)两套加热系统.ICRF主要对加热离子有比较好的加热效果,LHW则主要是通过电子Landau阻尼加热电子.除此之外,在ICRF和LHW协同加热的条件下,可以对等离子体产生更有效的加热效果,增加等离子体的聚变反应截面,增加聚变中子产额.本文报道了LHW对改善ICRF和等离子体耦合的重要作用,ICRF和LHW加热等离子体中电子温度随时间的演化过程,计算了放电过程中电子逃逸的阈值能量,分析了逃逸电子的产生过程,以及放电过程中的中子产额.研究结果发     

Measurements of the diffusion parameters in diphenyl at temperatures from 20 °C to 170 °C

Diffusion coefficient, mean life time of thermal neutrons, coefficient of diffusion cooling and diffusion length in diphenyl at temperatures 20°, 40°, 60°, 80°, 110°, 140° and 170° C were measured by the pulse method. Their dependence on the temperature of diphenyl was deduced in an analytic form and the change of the neutron transport length was determined experimentally. No discontinuity of the diffusion coefficient at the melting point of diphenyl apart from that caused by density change was observed. The energy exchange cross sectionM ₂ is practically independent of temperature in the range from 20 °C to 170 °C and the deduced microscopic absorption cross section for hydrogen equals 337±2 millibarns. The thermalization of neutrons in diphenyl proceeds more slowly than in water and neutrons loose their energy predominantly by interaction with the C—H group of the diphenyl molecule.We are indebted to Mr. J.Jadavan and Mr. J.Jirou for their technical assistance during the measurements and setting up the measuring apparatus.     

Creep of a Cu-2·5 at. pct. Al alloy at high temperatures

The creep of a Cu-2·5 at.pct. Al alloy has been investigated by the isothermal tests technique. Two dislocation mechanisms operate in parallel in the investigated temperature region. In the region of lower minimum creep rates ( <3×10^–5 sec^–1) — region 1 — the activation energy of creep is close to the expected value of the activation enthalpy of the lattice self-diffusion of copper in the alloy. The stress dependence of the minimum creep rate can be described by a power function of the ⁿ type, where n=n₁=5·8. The results for region 1 can be satisfactorily correlated with the model of nonconservative motion of jogs on screw dislocations dependent on lattice self-diffusion. If a power function of the ^m type is used to describe the minimum creep rate dependence on the stacking fault energy, thenm is equal to –0.66.In the region of higher minimum creep rates — region 2 — the apparent activation energy is higher than the expected value of the activation enthalpy of lattice self-diffusion of any component in the investigated alloy. The dislocation mechanism dominating in region 2 has not been identified.The influence of stacking fault energy on the minimum creep rate in region 2 is weak or even zero.     

The vibration and rotation of piezoelectric particles in high frequency electric fields observed by a thermoacoustic method

We have observed, by a thermoacoustic method, the acoustic resonance vibration of small (diameter 115 m) piezoelectric particles in high frequency (15 MHz) electric fields. The frequency dependence of the thermoacoustic signal gives direct information about the size distribution of the particles.In very strong rf electric fields we also observed a rotation of the vibrating particles by large angles — as originally suggested by Melcher and Shiren [3] — orienting the initially random rf dipoles parallel to the rf electric fields.The observed strong forces acting on vibrating piezoelectric particles in rf fields can probably be used as a new method of selectively extracting particles of a given size from a broad distribution of very small particles.     

Experimental investigation of extinction cross-section of single vegetation elements using open resonator

The experimental results of investigation of the total cross — section of scattering and absorption (extinction cross — section) _t of stalks and strip leaves of grass in millimeter waves range are presented. The investigation was carried out using open quasioptical resonator with spherical mirrors. Measirements were carried out as by absolute method as using the relative method. Experimental results obtained by two different methods showed that in spite of some data differences obtained by absolute and relative methods the latter may be used for estimation of the extinction cross — section _t of vegetation elements.     

Spin waves on chains of YIG particles: dispersion relations,Faraday rotation,and power transmission

We calculate the dispersion relations for spin waves on a periodic chain of spherical or cylindrical Yttrium Iron Garnet (YIG) particles. We use the quasistatic approximation, appropriate when kd ? 1, where k is the wave number and d the interparticle spacing. In this regime, because of the magnetic dipole-dipole interaction between the localized magnetic excitations on neighboring particles, dispersive spin waves can propagate along the chain. The waves are analogous to plasmonic waves generated by electric dipole-dipole interactions between plasmons on neighboring metallic particles. The spin waves can be longitudinal (L), transverse (T), or elliptically polarized. We find that a linearly polarized spin wave undergoes a Faraday rotation as it propagates along the chain. The amount of Faraday rotation can be tuned by varying the off-diagonal component of the permeability tensor. We also discuss the possibility of wireless power transmission along the chain using these coupled spin waves.     

On the transport coefficients of interacting Brownian particles

A macroscopic argument shows that the ratios between the coefficients of particle transport are given by the equation of state of the diffusing substance, which may interact both by classical and by quantum mechanical effects. This fact is compared with the results of two microscopic treatments: first it agrees with the diffusion equation for interacting particles, and — on a less coarse-grained level — it can also be inferred from Boltzmann's transport equation.Work supported by the Swiss National Science Foundation     

Discretization of the thermal excitation in highly excited matter

In this paper the thermal energy diffusion for quantum particles is described. The quantum heat transport equation is obtained. It is shown that, for a short-time thermal excitation (of the order of the relaxation time), the excited matter response is quantized on the different levels (atomic, nuclear, quark) with quantum thermal energy equalE ^atomic 9 eV,E ^nuclear 7 MeV, andE ^quark 139 MeV.     

Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws

We study the large-time behaviors of solutions of viscous conservation laws whose inviscid part is a nonstrictly hyperbolic system. The initial data considered here is a perturbation of a constant state. It is shown that the solutions converge to single-mode diffusion waves in directions of strictly hyperbolic fields, and to multiple-mode diffusion waves in directions of nonstrictly hyperbolic fields. The multiple-mode diffusion waves, which are the new elements here, are the self-similar solutions of the viscous conservation laws projected to the nonstrictly hyperbolic fields, with the nonlinear fluxes replaced by their quadratic parts. The convergence rate to these diffusion waves isO(t ^–3/4+1/2p+) inL ^p , 1p, with >0 being arbitrarily small.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38     

Accumulation of Particles and Formation of a Dissipative Structure in a Nonequilibrium Bath

The standard textbooks contain good explanations of how and why equilibrium thermodynamics emerges in a reservoir with particles that are subjected to Gaussian noise. However, in systems that convert or transport energy, the noise is often not Gaussian. Instead, displacements exhibit an α-stable distribution. Such noise is commonly called Lévy noise. With such noise, we see a thermodynamics that deviates from what traditional equilibrium theory stipulates. In addition, with particles that can propel themselves, so-called active particles, we find that the rules of equilibrium thermodynamics no longer apply. No general nonequilibrium thermodynamic theory is available and understanding is often ad hoc. We study a system with overdamped particles that are subjected to Lévy noise. We pick a system with a geometry that leads to concise formulae to describe the accumulation of particles in a cavity. The nonhomogeneous distribution of particles can be seen as a dissipative structure, i.e., a lower-entropy steady state that allows for throughput of energy and concurrent production of entropy. After the mechanism that maintains nonequilibrium is switched off, the relaxation back to homogeneity represents an increase in entropy and a decrease of free energy. For our setup we can analytically connect the nonequilibrium noise and active particle behavior to entropy decrease and energy buildup with simple and intuitive formulae.     

Ignition curves for deuterium/helium-3 fuel in spherical tokamak reactor

In this paper, ignition curve for deuterium /helium-3 fusion reaction is studied. Four fusion reactions are considered. Zero-dimensional model for the power balance equation has been used. The closed ignition curves for ρ=constant (ratio of particle to energy confinement time) have been derived. The results of our calculations show that ignited equilibria for deuterium /helium-3 fuel in a spherical tokamak is only possible for ρ= 5.5 and 6. Then, by using the energy confinement scaling and parameters of the spherical tokamak reactor, the plasma stability limits have been obtained in n_e, T plane and, to determine the thermal instability of plasma, the time-dependent transport equations have been solved.