Magnetic Confinement Systems Research Articles

Surface Heating Calculation of Composite Material Under the Influence of an Electron Beam on the Surface

Introduction. Modern plasma magnetic confinement systems use tungsten as a material in contact with plasma. Under the influence of high-density plasma irradiation, tungsten undergoes cracking, intense erosion, and macro-particle emission. High-temperature ceramics are considered a promising material for protective coating of plasma components, as they are resistant to thermal loads. One possible solution could be a boron carbide coating, which has a high melting temperature.Materials and Methods. The impact of an electron beam on samples of rolled tungsten and boron carbide and tungsten composite was studied in experiments on the BETA setup. The heat from the beam propagates into the samples, with the maximum temperature reached at the center and decreasing towards the edges. The modeling area represents a cross-section of the samples, optimal for a task with a cylindrical coordinate system. The numerical implementation is based on the correction scheme and the marching method.Results. A new model of heating the boron carbide and tungsten composite sample under the influence of surface heating by an electron beam is presented. The model is based on solving the heat conduction equation in an axially symmetric setup with constant values of specific heat capacity, density, and thermal conductivity of metals.Discussion and Conclusions. An analysis of the model of heating the composite material under the influence of surface heating by an electron beam at constant values of density, thermal conductivity, and specific heat capacity has been conducted. The modeling results are in demand for analyzing experimental results and planning experiments at the Beam of Electrons for Materials Test Applications (BETA) facility, created at the Budker Institute of Nuclear Physics SB RAS.

Comparing neutron and helium ion irradiation damage of REBa2Cu3O coated conductor using x-ray absorption spectroscopy

Understanding the effects of high energy neutron damage on REBa2Cu3O (REBCO) coated conductor is of vital importance for the design of the magnetic confinement systems for compact nuclear fusion power plants. However, neutron irradiation campaigns can only be carried out in a few facilities, and the experiments are very slow and expensive partly because the samples become radioactive. Ion irradiation provides an easily accessible alternative route to studying the effects of radiation on high temperature superconductors, which not only increases the volume of technical data that can be obtained but also enables more complex experiments such as in situ cryogenic irradiation. The question is, does ion damage offer a good proxy for neutrons? Here we use high energy resolution fluorescence detected x-ray absorption spectroscopy to probe the effects of fast neutron irradiation on the local environment around the copper ions in the REBCO layer of coated conductor tapes. We find that the spectral changes are similar to those induced by helium ion irradiation, suggesting that both projectiles produce the same types of structural defect in the REBCO lattice, although there is some evidence of an additional type of defect present in the sample heavily damaged by He+ ion irradiation. It is also shown that the linear degradation of superconducting transition temperature (T c ) of coated conductors with the calculated number of displacements per atom occurs at the same rate for neutrons and helium ions. Together these results provide new evidence suggesting that helium ions can emulate neutron point defect damage in REBCO high temperature superconductor reasonably well, increasing confidence that helium ions could be used as a useful proxy for neutrons in future experiments.

Radiation Limit for the Energy Gain of the p–11B Reaction

The feasibility of positive energy yield in systems with the p–11B reaction is considered here by considering refined (optimistic) data on the reaction rate. The analysis was carried out within the traditional framework for magnetic confinement systems, but without taking into account a particular type of plasma configuration. The energy balance was considered both for the ions and electrons. The balance of particles includes all species as well as the products of fusion (alpha particles). Calculations have shown that accounting for the content of thermalized reaction products (alpha particles) leads to an increase in radiation losses and a decrease in gain to Q < 1. In the steady-state scenario, the energy gain Q~5–10 can be obtained in p–11B plasma, if only the fast (high-energy) population of fusion alpha particles is considered. For pulsed modes, the gain value is proportional to the content of alpha particles, and it is limited by the complete burn of one of the fuel components (boron), so it does not exceed unity. In the analysis we did not rely on any assumptions about the theoretically predicted mechanisms for increasing the cross section and the reaction rate, and only radiation losses (primarily bremsstrahlung) dramatically affect the gain Q. Thus, the regimes found can be considered as limiting in the framework of the classical concepts of processes in hot fusion plasma.

Charge exchange radiation diagnostic with gas jet target for measurement of plasma flow velocity in the linear magnetic trap

The ambipolar electrostatic potential rising along the magnetic field line from the grounded wall to the centre in the linear gas dynamic trap, rules the available suppression of axial heat and particle losses. In this paper, the visible range optical diagnostic is described using the Doppler shift of plasma emission lines for measurements of this accelerating potential drop. We used the room temperature hydrogen jet puffed directly on the line of sight as the charge exchange target for plasma ions moving in the expanding flux from the mirror towards the wall. Both bulk plasma protons and He2+ ions velocity distribution functions can be spectroscopically studied; the latter population is produced via the neutral He tracer puff into the central cell plasma. This way, potential in the centre and in the mirror area can be measured simultaneously along with the ion temperature. A reasonable accuracy of 4 ÷ 8% was achieved in observations with the frame rate of ≈1 kHz. Active acquisitions on the gas jet also provide the spatial resolution better than 5 mm in the middle plane radial coordinate because of the strong compression of the object size when projected to the centre along the magnetic flux surface. The charge exchange radiation diagnostic operates with three emission lines: H-α 656.3 nm, He-I 667.8 nm and He-I 587.6 nm. Recorded spectra are shown in the paper and examples for physical dependences are presented. The considered experimental technique can be scaled to the upgraded multi-point diagnostic for the next generation linear traps and other magnetic confinement systems.

Editorial: 16th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems—Theory of Plasma Instabilities

Editorial: 16th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems—Theory of Plasma Instabilities

Summary of the 16th IAEA technical meeting on energetic particles in magnetic confinement systems—theory of plasma instabilities

This report summarizes the contributions presented at the 16th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems—Theory of Plasma Instabilities, held in Shizuoka, Japan, 3–6 September 2019. The meeting brought together about 100 experts from nuclear fusion research sites worldwide to discuss the physics of energetic particles and plasma instabilities, at the first joint meeting from the two scientific disciplines. The main topics of the meeting were: alpha particles physics; transport of energetic particles; effects of energetic particles in magnetic confinement fusion devices; collective phenomena such as Alfvén eigenmodes, energetic particle modes and others; runaway electrons and disruptions; diagnostics for energetic particles; control of energetic particles confinement; multiscale physics and instabilities in burning plasmas.

Heavy ion–acoustic rogue waves in magnetized electron–positron multi‐ion plasmas

AbstractNon‐linear heavy ion‐acoustic waves (HIAWs) are studied in a homogeneous magnetized four‐component multi‐ion plasma composed of inertial heavy negative ions, light positive ions, and inertia‐less non‐extensive electrons and positrons. The non‐linear Schrödinger equation is derived in this model using the perturbation method. The criteria for modulational instability of HIAWs and the basic features of finite‐amplitude heavy ion acoustic rogue waves (HIARWs) are investigated. The presence of the magnetic field was found to reduce the amplitude of HIARWs and enhances the stability. It is interesting to note that increasing positive ion mass causes decreases in the amplitude and width of rogue waves, which is opposite behaviour to that demonstrated in the previous study of these waves in an unmagnetized plasma. Furthermore, it is also shown that striking parameters, such as the non‐extensive parameter, the positron number density, the electron number density, the electron temperature, and the magnetic field parameter, play an undeniable role on the stability of waves packets. The findings of the present investigation may be of wide relevance to some plasma environments, such as active galactic nuclei, pulsar magnetospheres, and other magnetic confinement systems.

Experimental analysis of self-organized structure and transport on the magnetospheric plasma device RT-1

Dipole plasma exhibits strong heterogeneities in field strength, density, temperature and other parameters, while maintaining a holistic balance. Our study of the internal structures reveals the fundamental self-organizing mechanisms operating in their simplest realization (as commonly observed in astronomical systems). Three new findings are reported from the RT-1 experiment. The creation of a high-energy electron core (similar to the radiation belts in planetary magnetospheres) is observed for the first time in a laboratory system. High-energy electrons (3–15 keV), produced by electron cyclotron heating, accumulate in a ‘belt’ located in the low-density region (high-beta value ~1 is obtained by increasing the high-energy component up to 70% of the total electrons). The dynamical process of the ‘up-hill diffusion’ (a spontaneous mechanism of creating density gradient) has been analyzed by perturbing the density by gas injection. The spontaneous density formation in the laboratory magnetosphere elucidates the self-organized plasma transport relevant to a planetary magnetosphere. The coherence-imaging spectroscopy visualized the two-dimensional profiles of ion temperature and flow velocity in the ion cyclotron resonance frequency heating. The ion temperature and flow were enhanced globally, and particularly along the magnetic field lines near the levitation magnet. These results advance our understanding of transport and self-organization not only in dipole plasmas, but in general magnetic confinement systems relevant to fusion plasmas.

Kinetic simulations of sheared flow stabilization in high-temperature Z-pinch plasmas

The first fully kinetic particle-in-cell (PIC) simulations of sheared flow stabilized Z-pinch plasmas show the suppression of the sausage instability by shear, ∂rvz ≠ 0, with flow Mach numbers ≲1, consistent with experimental observations. Experimental investigations of sheared-flow stabilized Z-pinches demonstrated stability for 10 s of microseconds, over 1000 Alfvén radial transit times, in quasi steady-state plasmas that are an intermediate between conventional inertial and magnetic confinement systems. The observed stability coincides with the presence of radial shear in axial flow profiles with peak speeds less than Mach 1, and experiments are underway to validate scaling this design to fusion conditions. The experimentally observed stability agrees with models of m = 1 kink mode suppression by sheared flows, but existing models of the m = 0 sausage mode underestimate the efficacy of sheared flow stabilization. These models rely on fluid approximations and find that stabilization requires flows ranging from Mach 1.7 to 4.3, and in some cases, stabilization is not reproduced in the models. This is faster than the measured flows in long-lived plasmas and would necessitate substantial energy convection out of the Z-pinch and the need to drive and sustain supersonic flows in future devices. The MHD models typically used in the literature are invalid in the high-temperature, high-current environments desirable for many Z-pinch applications, and they ignore large Larmor radius effects and viscous dissipation which are known to impact Z-pinch stability. PIC simulations can capture all these effects as well as kinetic instabilities that could influence the performance of high-temperature sheared flow stabilized Z-pinch plasmas. The PIC simulations presented here show the suppression and damping of m = 0 modes by sheared flows ∂rvz = 0.75vA/r0 with flow Mach numbers ≲1. Equivalent stability occurs under plasma conditions ranging from the limits of present-day experimental capabilities to the projected conditions of a sheared flow stabilized Z-pinch reactor.

Stable confinement of high-electron-temperature plasmas in the GDT experiment

Having the ability to control the operation of advanced plasma heating methods is essential for the achievement of fusion-relevant plasmas in open traps. We describe a technique to deal with the increased transport brought about by the electron cyclotron heating in axisymmetric magnetic mirror device. The technique is based on shaping of the plasma potential by means of a set of specifically biased electrodes facing plasma at both open ends of a trap. In the experiments with combined microwave and neutral beam plasma heating performed in the gas-dynamic trap (GDT) facility at the Budker Institute, we show that a value of on-axis electron temperature up to 450 eV at plasma density m−3 can be supported steadily for 1.5 ms limited by the available heating and magnetic confinement systems. Stable high-temperature discharge, no longer degraded by low-frequency instabilities, offered a unique opportunity to confirm quantitatively the gas-dynamic plasma confinement model in a new range of parameters.

Three Confinement Systems—Spherical Tokamak, Standard Tokamak, and Stellarator: A Comparison of Key Component Cost Elements

Since the 1950s “next-step” fusion devices and power plant studies have been developed for a number of magnetic confinement systems but an open question remains: can a magnetic fusion device be simplified to the point where it will be cost competitive and operate with high availability? Concept designs based on the ARIES advanced tokamak, spherical tokamak (ST), and the quasi-axisymmetric (QAS) stellarator option have progressed in recent years through a series of Princeton Plasma Physics Laboratory (PPPL) studies with an underlying intent to improve the engineering feasibility of each, giving special attention to concepts that simplify the device configuration and improve maintenance features. For the ST option, design details centered on a 3-m Fusion Nuclear Science Facility that evolved to incorporate vertical maintenance, high temperature superconductor magnets, a small inboard duel coolant lead lithium blanket, and a liquid metal divertor. In collaboration with the Korean fusion demonstration reactor (K-DEMO) and CFETR concept study teams the tokamak design has evolved to increase plasma component access within a vertical maintenance approach using enlarged toroidal field coils incorporating a low- and high-field Nb3Sn winding pack that provide a peak field of 16 T. A recent PPPL stellarator study focused on simplifying the stellarator winding topology to improve access to in-vessel components; combining coil optimization with winding surfaces that incorporated geometry constraints specified by engineering. This paper centered on a 1000-MW power plant design with a tokamak like vertical maintenance scheme that allows access to remove large internal blanket sectors. Results of three confinement studies (PPPL developed ST, K-DEMO, and QAS stellarator) will be presented to highlight concepts that simplify each device configuration and improved their maintenance features. Scaling each option to a common 1000-MW net electric power plant mission allows comparisons to be made of key cost elements such as the size of major core components, sizing of the reactor hall, or external facilities needed to handle and store activated in-vessel components.

Modeling of the mode dynamics generated by Madison Symmetric Torus machine utilizing a modified sine-Gordon equation

In this paper, a new dynamic model is presented for the experimental data generated by the Madison Symmetric Torus (MST) machine. The model is based on a modified sine-Gordon (SG) dynamic equation. The modified sine-Gordon equation model effectively captures the behavior of the slinky mode in reversed-field pinch experiments. In addition, this paper demonstrates how the derived model accurately describes the behavior of the localized magnetohydrodynamic mode (slinky mode) that appears in reversed-field pinch toroidal magnetic confinement systems. The modified SG equation model is solved analytically by using the perturbation method. The resulting model is fit to match a variety of experimental results in the MST reversed-field pinch experiment. The efficacy of the newly developed model in effectively representing the slinky mode is verified by comparing obtained analytical solution to experimentally measured data.

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.

Control and data acquisition system for SCR-1 Stellarator

The design and implementation of a small-size modular stellarator’s (SCR-1) control and data acquisition system is introduced and discussed in this article. The described development includes the validation and integration of vacuum pumping, gas injection, Electron Cyclotron Heating (ECH), diagnostics, and magnetic confinement systems of the SCR-1.The control system was implemented on a National Instruments® PXIe® platform. By data flow programming, it was possible to develop different algorithms for the simultaneous execution of four threads during the plasma discharge sequence (device safety, gas injection, data acquisition and plasma discharge), where the primary goal is to implement a robust and secure system considering the integrity and safety of the SCR-1 work team and the hardware involved. Through the implementation of this control and data acquisition system, it was possible to perform the first plasma discharge and, therefore, obtain first data of device operation.

Evolution of views on the structure of the ambipolar electric field in toroidal magnetic confinement systems

Various methods of determining the ambipolar electric field in toroidal magnetic systems (predominantly, in stellarators) and the evolution of views on this problem are discussed. Paradoxes encountered in solving this problem are analyzed, and ways of resolving them are proposed.

Determination of broken KAM surfaces for particle orbits in toroidal confinement systems

The destruction of Kolmogorov–Arnold–Moser surfaces in a Hamiltonian system is an important topic in nonlinear dynamics, and in particular in the theory of particle orbits in toroidal magnetic confinement systems. Analytic models for transport due to mode-particle resonances are not sufficiently correct to give the effect of these resonances on transport. In this paper we compare three different methods for the detection of the loss of stability of orbits in the dynamics of charged particles in a toroidal magnetic confinement device in the presence of time dependent magnetic perturbations.

Islands and ergodicity of the plasma current in toroidal magnetic confinement systems

Magnetic and current structures arising due to resonant perturbations of an equilibrium current-carrying magnetic configuration are analyzed using the Hamiltonian formalism. Special attention is paid to axisymmetric tokamak and pinch configurations. It is shown that, due to the very different dependences of the magnetic and current rotational transforms on the plasma pressure, the resonances (islands) of the magnetic field may not coincide with those of the current. The perturbed force-free equilibrium of a cylindrical pinch in which the field and current islands overlap is analyzed. The long-lived ribbon structures observed in the JET tokamak are explained as a manifestation of a force-free magneto-current island.

Calculation of the charged particle source in a toroidal magnetic confinement system (hydrodynamic approach)

In order to model transport processes in magnetic confinement systems, it is necessary to have information on the charged particle source. This in turn requires calculation of the inward flux of neutral particles. In this paper, a method for solving this problem in the hydrodynamic approach for the neutral gas is proposed. The average velocity of neutral particles and the spatial distribution of their density are determined. The obtained expression for the neutral density almost completely coincides with that calculated previously by solving the kinetic equation. However, the computational time required to solve the problem in the proposed hydrodynamic approach is much shorter than that in the kinetic approach.

Pressure-driven reconnection and quasi periodical oscillations in plasmas

This paper presents a model for an ohmically heated plasma in which a feedback exists between thermal conduction and transport, on one side, and the magneto-hydro-dynamical stability of the system, on the other side. In presence of a reconnection threshold for the magnetic field, a variety of periodical or quasi periodical oscillations for the physical quantities describing the system are evidenced. The model is employed to interpret the observed quasi periodical oscillations of electron temperature and perturbed magnetic field around the so called “Single Helical” state in the reversed field pinch, but its relevance for other periodical phenomena observed in magnetic confinement systems, especially in tokamaks, is suggested.

Canonical Hamiltonian mechanics of Hall magnetohydrodynamics and its limit to ideal magnetohydrodynamics

While a microscopic system is usually governed by canonical Hamiltonian mechanics, that of a macroscopic system is often noncanonical, reflecting a degenerate Poisson structure underlying the coarse-grained phase space. Probing into symplectic leaves (local structures in a foliated phase space), we may be able to elucidate the order of transition from micro to macro. The Lagrangian guides our analysis. We formulate canonized Hamiltonian systems of Hall magnetohydrodynamics (HMHD) which have a hierarchized set of canonical variables; the simplest system is the subclass in which the ion vorticity and magnetic field have integral surfaces. Renormalizing the singularity scaled by the reciprocal Hall parameter (as the ion vorticity surfaces and the magnetic surfaces are set to merge), we delineate the singular limit to ideal magnetohydrodynamics (MHD). The formulated canonical equations will be useful in the study of ordered structures and dynamics (with integrable vortex lines) in HMHD and their singular limit to MHD, such as magnetic confinement systems, shocks or vortical dynamics.