Operation of a tokamak reactor in the radiative improved mode

The operation of a nuclear fusion reactor has been simulated within a model based on experimental results obtained at the TEXTOR-94 tokamak and other facilities in which quasistationary regimes were achieved with long confinement times, high densities, and absence of the edge-localized mode. The radiative improved mode of confinement studied in detail at the TEXTOR-94 tokamak is the most interesting such regime. One of the most important problems of modern tokamaks is the problem of a very high thermal load on a divertor (or a limiter). This problem is quite easily solved in the radiative improved mode. Since a significant fraction of the thermal energy is reemitted by an impurity, the thermal loading is significantly reduced. As the energy confinement time τ_E at high densities in the indicated mode is significantly larger than the time predicted by the scaling of ITERH-98P(y, 2), ignition can be achieved in a facility much smaller than the ITER facility at plasma temperatures below 20 keV. The revealed decrease in the degradation of the confinement time τ_E with an increase in the introduced power has been analyzed.     

Decay of enhanced density and damping of plasma flows after the electrode biasing termination on the CASTOR tokamak

Electrode biasing is a standard tool for modification of both edge and global plasma parameters on the CASTOR tokamak (R=0.4 m,a=85 mm,B _T=1.3 T,I _p1≈9 kA,q _a≈10). During a steady state phase of a discharge, a polarization voltage is applied on an electrode immersed into the edge plasma. This voltage causes radial currents that create radial electric field and, due to theE×B drift, they cause an enhanced rotation. Then, as a consequence, the interaction with walls decreases and particle confinement and density increase. Recently, the decay of plasma density and plasma flows after the termination of the biasing period was investigated on the CASTOR tokamak. These observations are linked to processes and mechanisms that control generation of radial electric fields in plasmas and damping ofE×B sheared flows and that therefore represent a key issue for understanding the transition to improved confinements modes. In the contribution, measured time scales of the transition to the ohmic regime after the biasing termination will be shown. Further, possible consequences of these measured scales for the valuation and explanation of important processes in the plasma will be discussed.     

CARS study of deuterium clusters stabilized in solid helium

Solid deuterium clusters that for the first time have been isolated in a matrix of solid helium have been investigated at T=1.3 K and P=3 MPa by the coherent anti-Stokes Raman spectroscopy (CARS) technique. The vibronic Q₁((J=0) and Q₁(J=1) line intensity, shape, and positions have been studied as functions of ortho and para content in the solid, as well as of the size of clusters. The strong effect of Raman scattering cross-section sensitivity to the molecular environment nuclear spin state has been found in CARS: the ratio of probabilities for the scattering by para(J=1) and ortho(J=0) deuterium, which is equal to 1 in a gas, is as high as 10000 in nearly pure ortho deuterium, whereas it is about 50 in spontaneous Raman scattering. This effect has been shown to occur starting from a cluster size corresponding to the onset of the phonon band.     

Pioneering experiments on atomic-beam-assisted generation of drag currents in the Globus-M spherical tokamak

Research data for drag currents in the Globus-M spherical tokamak are presented. The currents are generated by injecting atomic beams of hydrogen and deuterium. Experiments were carried out in the hydrogen and deuterium plasma of the tokamak. It has a divertor configuration with a lower X-point, a displacement along the larger radius from–1.0 to–2.5 cm, and a toroidal field of 0.4 T at a plasma current of 0.17–0.23 MA. The beam is injected into the tokamak in the equatorial plane tangentially to the magnetic axis of the plasma filament with an impact diameter of 32 cm. To provide a 28-keV 0.5-MW atomic beam with geometrical sizes of 4 × 20 cm (at a power level of 1/e), an IPM-2 ion source is used. The generation of noninductive currents is detected from a rise in the loop current and a simultaneous dip of the loop voltage. The injection of the hydrogen and deuterium atomic beams into the deuterium plasma results in a noticeable and reproducible dip of the loop voltage (up to 0.5 V). Using the ASTRA transport code, a model is constructed that allows rapid calculation of noninductive currents. Calculations performed for a specific discharge confirm that the model adequately describes the effect of drag current generation.     

EPR and photoluminescence spectra of smooth CD<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> films from T-10 tokamak: The effect of iron impurity

The electron and spin structure of thick smooth hydrocarbon CD _x films (“flakes”) with a high relative deuterium concentration of x ~ 0.5, redeposited from deuterium plasma discharge onto the walls of the vacuum chamber of the T-10 tokamak and containing ~1 at % of 3d-metal impurities due to erosion of the chamber walls, are studied using electron paramagnetic resonance (EPR) and photoluminescence (PL). The resulting spectra are compared for the first time to the EPR and photoluminescence spectra of polymer (soft) a-C:H(D) films (H(D)/C ~ 0.5), which are considered model analogues of smooth CD _x films. A certain similarity of the CD _x films with a-C:H films was found in the electronic structure of the valence band. At the same time, the differences in the EPR and photoluminescence spectra were observed due to the presence of 3d-metal impurities in the CD _x samples, contributing to the conversion of sp ³ → sp ² in the formation of films in the tokamak and upon heating and thermal desorption. An impurity of, presumably, 3d metals was detected for the first time by EPR in the a-C:H films in an amount of approximately 0.2 ppm, related to the evaporation of graphite.     

Analysis of tokamak plasma confinement modes using the fast Fourier transformation

The Fourier analysis is a satisfactory technique for detecting plasma confinement modes in tokamaks. The confinement mode of tokamak plasma was analysed using the fast Fourier transformation (FFT). For this purpose, we used the data of Mirnov coils that is one of the identifying tools in the IR-T1 tokamak, with and without external field (electric biasing), and then compared it with each other. After the Fourier analysis of Mirnov coil data, the diagram of power spectrum density was depicted in different angles of Mirnov coils in the ‘presence of external field’ as well as in the ‘absence of external field’. The power spectrum density (PSD) interprets the manner of power distribution of a signal with frequency. In this article, the number of plasma modes and the safety factor q were obtained by using the mode number of q = m /n (m is the mode number). The maximum MHD activity was obtained in 30–35 kHz frequency, using the density of the energy spectrum. In addition, the number of different modes across 0–35 ms time was compared with each other in the presence and absence of the external field.     

COMPASS-D magnetic equilibria with lh and NBI current drive

Plasma equilibria are investigated numerically, using the ACCOME and ASTRA codes, on the COMPASS-D tokamak (R ₀ = 0:56 m, a = 0:17 m, B _T = 1:2 T, I _p = 200 kA, k = 1:7, δ_x = 0:4) for the planned Neutral Beam Injection (NBI) and Low Hybrid Current Drive (LHCD) systems. The LH system provides P _LH = 0:4 MW at n _∥ = 2:1 and f _LH = 1:3 GHz. The NBI system has two 40 keV deuterium beams in co-or counter-directions with a total power of 0.6 MW. The COMPASS-D tokamak can typically operate in two configurations-single null divertor (SND) and single null divertor with a higher triangularity (SNT). Higher triangularity provides access to higher confinement and improved stability, and leads to larger n _∥ up-shifts for better slow LH wave absorption.We investigate the range of densities n = 2 ÷ 6 × 10¹⁹ m^?3. Both the LH and NB driven currents decrease with density. The magnetic shear reverses with off-axis beam incidence. In the given plasma parameter range, typically up to 60 kA of bootstrap current is driven and with NB co-injection up to 80 kA of NB current is driven. LHCD is weak at f = 1:3 GHz and BT = 1:2 T, but at n = 3 × 10¹⁹ m^?3 the LH driven current is about 40 kA, so that the required plasma current of 200 kA is supported almost non-inductively.     

The analysis of the densities of <Emphasis Type="Italic">s</Emphasis>-wave neutron resonances separated with respect to spin

The density ratio of s-wave neutron resonances z=ρ(J₁)/ρ(J₂) was analyzed on the basis of the experimental data for 22 atomic nuclei and the Gilbert-Cameron formula for ρ(J). Here, J₁=I_x—1/2 and J₂=I_x+1/2, where I_x denotes the spin of the target nucleus in the ground state. Our aim was to verify whether the factor η(I_x), as a multiplier, can be applied in the expression describing ρ(J₁), with the assumption that ρ(J₂) values remain unchanged, or whether the factor 1η(I_x) can be applied, as a multiplier with ρ(J₂), while the ρ(J₁) values remain unchanged. The final conclusions, e.g., the confirmation or the negation of the fact that it may be necessary to apply the η(I_x) factor, depend on the values of “real” errors Δz of the z variable, which can be calculated if the optimal values of Δρ(J₁) and Δρ(J₂) are known.     

Calculation of<Emphasis Type="Italic">Z</Emphasis><Subscript>eff</Subscript> from plasma resistivity in IR-T1 tokamak

The effective ion charge,Z _eff, represents the average charge of ionsZ _i of gasses inside the system, which indicates the level of the impurities in the plasma. Several techniques have been applied to estimateZ _eff, like mass spectroscopy, anomaly factor and Bremsstrahlung radiation.

We estimatedZ _eff in the IR-T1 tokamak through anomaly factor. The IR-T1 tokamak is a small air-core transformer tokamak with circular cross section and with out conducting shell and divertor. Its aspect ratio is

$$\frac{R}{a} = \frac{{45 cm}}{{12.5 cm}}.$$

For a tokamak discharge of 30 kA plasma current and 1.5 V of loop voltage and by anomaly factor we observed thatZ _eff value is about 1.5.     

Influence of Fuel Ratio in D–<Superscript>3</Superscript>He/ST Fusion Power Reactor

The effect of different fuel ratio f³ (the ratio between the ³He and D densities) on D–³He fusion reaction in spherical tokamak has been considered. By solving the zero dimensional particle and power equations numerically the temporal evolution plasma parameters such as the fusion power, synchrotron power and radiation power for different fuel ratios are calculated and compared to each others.     

High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice

The low-energy constants, namely the staggered magnetization density M? _s per spin, the spin stiffness ρ _s , and the spinwave velocity c of the two-dimensional (2-d) spin-1/2 Heisenberg model on the honeycomb lattice are calculated using first principles Monte Carlo method. The spinwave velocity c is determined first through the winding numbers squared. M? _s and ρ _s are then obtained by employing the relevant volume- and temperature-dependence predictions from magnon chiral perturbation theory. The periodic boundary conditions (PBCs) implemented in our simulations lead to a honeycomb lattice covering both a rectangular and a parallelogram-shaped region. Remarkably, by appropriately utilizing the predictions of magnon chiral perturbation theory, the numerical values of M? _s , ρ _s , and c we obtain for both the considered periodic honeycomb lattice of different geometries are consistent with each other quantitatively. The numerical accuracy reached here is greatly improved. Specifically, by simulating the 2-d quantum Heisenberg model on the periodic honeycomb lattice overlaying a rectangular area, we arrive at M? _s = 0.26882(3), ρ _s  = 0.1012(2)J, and c = 1.2905(8)Ja. The results we obtain provide a useful lesson for some studies such as simulating fermion actions on hyperdiamond lattice and investigating second order phase transitions with twisted boundary conditions.     

Peculiarities of magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Eu<Subscript>0.55</Subscript>Sr<Subscript>0.45</Subscript>MnO<Subscript>3</Subscript>

Magnetic, elastic, magnetoelastic, transport, and magnetotransport properties of the Eu_0.55Sr_0.45MnO₃ ceramics have been studied. A break was detected in the temperature dependence of electrical resistivity ρ(T) near the temperature of the magnetic phase transformation (41 K), with the material remaining an insulator down to the lowest measurement temperature reached (ρ=10⁶ Ω cm at 4.2 K). In the interval 4.2≤T≤50 K, the isotherms of the magnetization, volume magnetostriction, and ρ were observed to undergo jumps at the critical field H_C1, which decreases with increasing T. For 50≤T≤120 K, the jumps in the above curves persist, but the pattern of the curves changes and H_C1 grows with increasing T. The magnetoresistance Δρ/ρ = (ρ _H ?ρ_H=0)/ρ _H is positive for H<H_C1 and passes through a maximum at 41 K, where Δρ/ρ = 6%. For H>H_C1, the magnetoresistance is negative, passes through a minimum near 41 K, and reaches a colossal value of 3×10⁵ % at H=45 kOe. The volume magnetostriction is negative and attains a giant value of 4.5×10^?4atH=45 kOe. The observed properties are assigned to the existence of three phases in Eu_0.55Sr_0.45MnO₃, namely, a ferromagnetic (FM) phase, in which carriers are concentrated because of the gain in s-d exchange energy, and two antiferromagnetic (AFM) phases of the A and CE types. Their fractional volumes at low temperatures were estimated to be as follows: ～3% of the sample volume is occupied by the FM phase; ～67%, by the CE-type AFM phase; and ～30%, by the A-type AFM phase.     

Schrödinger’s Equation with Gauge Coupling Derived from a Continuity Equation

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ? S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out.     

Global transformations preserving Sturm–Liouville spectral data

We show the existence of a real analytic isomorphism between the space of the impedance function ρ of the Sturm–Liouville problem ?ρ ^?2(ρ ² f′)′ +uf on (0, 1), where u is a function of ρ, ρ′, ρ″, and that of potential p of the Schrödinger equation ?y″ +py on (0, 1), keeping their boundary conditions and spectral data. This mapping is associated with the classical Liouville transformation f → ρf, and yields a global isomorphism between solutions of inverse problems for the Sturm–Liouville equations of the impedance form and those of the Schrödinger equations.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

Quantifying Correlations via the Wigner-Yanase-Dyson Skew Information

In this paper, based on a discussion about the Wigner-Yanase-Dyson (WYD) skew information, the measure F_a,α(ρ_ab) for correlations in terms of the WYD skew information is introduced and discussed. The following conclusions are obtained. For a classical-quantum state ρ_ab, F_a,α(ρ_ab)=0 if and only if ρ_ab is a product state; F_a,α(ρ_ab) is locally unitary invariant and convex on the set of states with the fixed marginal ρ_a; F_a,α(ρ_ab) decreases under local random unitary operation on H_b; For a quantum-classical state ρ_ab, F_a,α(ρ_ab) decreases under local operation on H_b; Lastly, F_a,α(ρ_ab) is computed for the pure states and the Bell-diagonal states, respectively.     

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρ _s in the ordered phase and the vortex-condensate stiffness ρ _v in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρ _s,v /Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρ _s /ρ _v admits a quantitative measure of deviation from selfduality.     

A Family of Schrödinger Operators Whose Spectrum is an Interval

By approximation, I show that the spectrum of the Schrödinger operator with potential V(n) = f (n ^ρ (mod 1)) for f continuous and \({\rho > 0, \rho \notin \mathbb{N}}\) is an interval.     

Charged <Emphasis Type="Italic">ρ</Emphasis>-meson production in neutrino-induced reactions at &lt;<Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">ν</Emphasis></Subscript>&gt;≈ 10 GeV

The production of charged ρ mesons on nuclei and nucleons is investigated in charged current neutrino interactions at moderate energies (〈E _〉 ≈ 10 GeV), using the data obtained with SKAT bubble chamber. No strong nuclear effects are observed in ρ ⁺ and ρ ^? production. The fractions of charged and neutral pions originating from ρ decays are obtained and compared with higher-energy data. From analysis of the obtained and available data on ρ ⁺ and K*⁺(892) neutrino production, the strangeness suppression factor is extracted: λ _s = 0.18 ± 0.03. Estimation is obtained for cross section of coherent ρ ⁺ neutrino production on nuclei.     

Phase diagrams of bosonic AB<Subscript>n</Subscript> chains

The AB_{N ?1} chain is a system that consists of repeating a unit cell withN siteswhere between the A and B sites there is an energy difference ofλ. Weconsidered bosons in these special lattices and took into account the kinetic energy, thelocal two-body interaction, and the inhomogenous local energy in the Hamiltonian. We foundthe charge density wave (CDW) and superfluid and Mott insulator phases, and constructedthe phase diagram for N =2 and 3 atthe thermodynamic limit. The system exhibited insulator phases for densitiesρ =α/N, with α being an integer. Weobtained that superfluid regions separate the insulator phases for densities larger thanone. For any N value, we found that for integer densitiesρ, thesystem exhibits ρ +1 insulator phases, a Mott insulator phase, and ρ CDW phases. Fornon-integer densities larger than one, several CDW phases appear.