Tokamak Research Research Articles

Deutelio approach to fusion energy with the Polomac

Deutelio is a private initiative promoting an alternative path to fusion energy. The Tokamak research line pursued worldwide since 1970 met several difficulties, heavily jeopardising the objective of commercial energy production from fusion before 2050, as a support to the global effort towards Net Zero Emissions. As a result, new plasma magnetic confinement concepts, such as Stellarators or overlooked alternatives like the poloidal confinement are being pursued to achieve more efficiency and better performance. The Polomac is a poloidal magnetic configuration where the outboard magnetic lines are deviated aside together with the plasma, to open some accesses to the dipole coils located inside the plasma. These accesses, called magnetic tunnels, are used to support, feed and cool the dipole coil. They avoid the impact with plasma which led to abandon past poloidal experiments, despite their good stability and confinement efficiency. The poloidal confinement can achieve Deuterium-Tritium reactor conditions with a magnetic field 3 times weaker than the Tokamak, in steady state rather than pulsed. With the same high field as in the Tokamak the poloidal confinement can achieve Deuterium-Deuterium reaction, thus avoiding the development of the breeding blanket to produce the Tritium. This paper presents the Polomac system, explains the development strategy of Deutelio through a small prototype focused to tune and assess the magnetic tunnels, and describes the possibility of deuterium-deuterium reaction.

Electron cyclotron emission calibration with Thomson scattering using a wide scan of toroidal magnetic field of KSTAR.

The Korea Superconducting Tokamak Advanced Research (KSTAR) tokamak is capable of operating at a wide range of toroidal magnetic fields up to 3.5T at the major radius. The electron cyclotron emission (ECE) diagnostic on KSTAR is required to cover a broad frequency range for electron temperature profile measurements in both the low and high field sides. To meet these broadband requirements, the ECE system consists of W-band (78-110GHz) and D-band (110-162GHz) heterodyne radiometers. The two radiometers are connected to 28 and 48 detection channels, respectively. However, since the absolute ECE calibration based on the hot-cold calibration has been very challenging, an alternative method of calibration was performed using Thomson scattering measurements and varying toroidal magnetic fields. As the toroidal magnetic field is scanned from 1.6 to 3.2T in steps of 0.2T, most of the 76 ECE channels are calibrated relatively by the electron temperature values of Thomson scattering in a narrow region (0.2 < r/a <0.6). In this article, the methodological details of the ECE calibration are described. In addition, to demonstrate the robustness of the ECE calibration factors, the calibrated electron temperature profiles from ECE measurements are compared with the ion temperature profiles in terms of the plasma position as the plasma positon shifts outward.

RFX-mod2 as a flexible device for reversed-field-pinch and low-field tokamak research

The RFX-mod2 installation is planned to be completed by 2024 and the start of operations is expected in 2025. The high flexibility of the machine (already tested in the previous RFX-mod experiment) allows operation in Reversed Field Pinch and tokamak configuration as well as ultra-low q pulses. In this work we present predictive analysis on transport, performances and plasma control in RFX-mod2 in view of the first experimental campaigns.

The effect of blanket system and port plugs on the harmonic components of error field and optimizing approach investigation

The fusion plasma is sensitive to the penetration of the toroidal mode numbers harmonic components of the error fields (EFs), and the toroidal mode components of the EFs are closely tied to the toroidal distribution of the magnetic field source. The primary source of EFs within the magnetic field sources is the current source, such as the magnet system, while the magnetic field produced by magnetized ferromagnetic materials may also generate EFs. The ferromagnetic field source, such the reduced-activation ferritic-martensitic steel, represent a smaller portion of the EFs source. However, the use of ferromagnetic materials is expected to increase significantly as tokamak research transitions from experimental devices to demonstration and commercial reactors, particularly for the structural materials of in-vessel components and port plugs. Predictably, the EFs induced by ferromagnetic materials will increase and may even surpass the design specifications. In this study, the EFs introduced by the water-cooling ceramic breeder blanket system and the vacuum vessel port plugs of China Fusion Engineering Test Reactor are comprehensively analyzed by an analytical approach and finite element numerical approach, which is based on the Fourier decomposition. The results reveal a clear linear relationship between the EFs formed by the saturated magnetization module and its rigid displacement deviating from periodic symmetry, as well as the same behavior in EFs and overall magnetization intensity. Compared to the assembly error of the blanket system, the EFs that may be introduced by the equatorial ports and plugs are substantial, including larger toroidal mode harmonic components that can lead to lock mode and disruption. Moreover, using the correlation between harmonic components and symmetrical periods, specific toroidal mode components can be selectively shielded.

Study on Resonance Phenomenon Caused by Voltage Fluctuation of Power Supply in JT-60SA EF Coil

For the large research Tokamak JT-60SA, evaluating the withstand voltage between conductors is one of the most critical factors for the coil design. The power supply feeding the coil injects a wide spectrum of frequency components. The transient response and resonance phenomena induce a non-uniform voltage distribution in the coil. The transiently concentrated voltage can cause the insulation breakdown between conductors, and JT-60SA may not be able to operate safely. This study conducted an impulse test to evaluate the withstand voltage between adjacent conductors for an equilibrium field (EF) coil. The actual power supply voltage for the EF coil was measured to investigate the ramp rate (dv/dt) and frequency spectrum. In addition, based on the results of a resonance test of the EF dummy coil, a circuit simulation model for the EF coil was developed to evaluate the effect of the transient response and resonance phenomenon on the voltage in the coil. The results of this study provide fundamental data that can be used to ensure that the EF coil does not cause insulation breakdown.

Determining plasma boundary in Alvand-U tokamak

One of the major topic of tokamak research is the determination of the magnetic profile due to magnetic coil fields and plasma current by mean of data from magnetic probes. The most practical approach is to use the current filament method, which models the plasma column with multiple current carrying filaments and the total current of these filaments is equal to the plasma current. Determining the plasma boundary in Alvand-U tokamak is the main purpose of this paper. In order to determine the magnetic field profile and plasma boundary, information concerning the magnetic coils, their position, and current is required in the computing code. Then, the plasma shape is determined and finally the plasma boundary is extracted by the code. In the conducted research, we discuss how to determine the plasma boundary and the performance of the computing code for extraction of the plasma boundary. The developed algorithm shows to be effective by running it in the regular pc machine with characteristics of Intel (R) core (TM) i3-10100 CPU @3.60 GHz and 8.00 GB of RAM. Finally, we present results of a test run for computing code using a typical experimental pulse.

Polarized fusion and potential in situ tests of fuel polarization survival in a tokamak plasma

The use of spin-polarized fusion fuels would provide a significant boost towards the ignition of a burning plasma. The cross section for D + T → α + n, would be increased by 1.5 if the fuels were injected with parallel polarization. Furthermore, our simulations demonstrate additional non-linear power gains in large-scale machines such as ITER, due to increased alpha heating. Such benefits require the survival of spin polarizations for periods comparable to the particle confinement time. During the 1980s, calculations predicted that polarizations could survive a plasma environment, although concerns persisted regarding the cumulative impacts of wall recycling. In that era, technical challenges prevented direct tests and left the large scale fueling of a power reactor beyond reach. Over the last decades, this situation has changed dramatically. Detailed simulations of ITER have predicted negligible wall recycling in a high-power reactor, and recent advances in laser-driven sources project the capability of producing large quantities of ∼100% polarized D and T. The remaining crucial step is an in-situ demonstration of polarization survival in a plasma. For this, we outline a measurement strategy using the isospin-mirror reaction, D + 3He → α + p. Polarized 3He avoids the complexities of handling tritium, while encompassing the same spin-physics. We evaluate two methods of delivering deuterium, using dynamically polarized Lithium-Deuteride (with vector polarization PV D of 70%) or frozen-spin Hydrogen-Deuteride (with PV D of 40%), together with a method of injecting optically-pumped 3He (with 65% polarization). Pellets of these materials all have long polarization decay times (∼6 min for LiD at 2 K, ∼2 months for HD at 2 K, and ∼3 d for 3He at 77 K), all far greater than a plasma shot in a research tokamak such as DIII-D (∼20 s). Both species can be propelled from a single cryogenic injection gun. We review plasma requirements and strategies for detecting polarization survival. Polarization alters both fusion yields and the angular distribution of fusion products, and each of these provides a potential signal. In this paper we simulate a selection of shots with similar characteristics in a future high-Tion H plasma, and find ratios of yields from shots with fuel spins parallel and antiparallel reaching 1.3 (HD + 3He) to 1.6 (LiD + 3He) over a wide range of poloidal angles. (A companion paper finds sensitivity to fusion product angular distributions as reflected in the pitch angles of protons and alphas reaching the plasma facing wall.)

Py-EFIT: A new Python package for plasma equilibrium reconstruction on EAST tokamak

Plasma equilibrium is the basis for various tokamak research topics, such as plasma performance evaluation, plasma control, and physical analysis of instability, etc. In this study, we have developed a Python-based toolkit with a graphical user interface (GUI) to reconstruct the tokamak plasma equilibrium, which is called the Py-EFIT program. The main implementation steps of Py-EFIT program are introduced. Firstly, various magnetic diagnostic signals and machine structure of Experimental Advanced Superconducting Tokamak (EAST) are utilized as the inputs for computation. Secondly, the plasma magnetic flux distribution is numerically determined based on these inputs according to the plasma equilibrium reconstruction principle. Finally, a GUI of Py-EFIT program is developed for function execution and visualization of results. This program provides a convenient and user-friendly platform for plasma equilibrium calculation. It has been successfully applied for experimental analysis and plasma equilibrium reconstruction on EAST, which also indicates its potential for practical applications in more tokamak devices. Program summaryProgram title: Py-EFITCPC Library link to program files:https://doi.org/10.17632/85f8kj7hvp.1Licensing provisions: GNU General Public License 3Programming language: PythonNature of problem: Plasma equilibrium is the basis for many tokamak research topics, such as plasma performance evaluation, plasma control, physical analysis, etc. But plasma equilibrium cannot be obtained from experimental measurements directly, it has to be calculated through ‘equilibrium reconstruction’ technique. This program (Py-EFIT) provides an efficient, open-source, user-friendly, expandable, and portable computation platform for equilibrium reconstruction calculation.Solution method: 1. Code initialization, including grid mesh division and parameter declaration; 2. Give flux function an initial guess; 3. Construct plasma current matrix and response matrix; 4. Solve for plasma current based on diagnostic signals; 5. Calculate updated flux function based on Green-function method; 6. Refine flux value at magnetic axis and X-points; 7. Evaluate the difference between two iteration steps; 8. Output results until convergence condition is satisfied.

Design of a Novel Variable Geometry Divertor for Tokamaks

The divertor is a key component of fusion reactors, allowing exhaust of gas, impurities, and helium ash to preserve plasma purity. The divertor geometry strongly affects plasma performance, and it is designed to be compatible with different plasma shapes in present-day fusion experiments. We present a novel concept for a variable geometry divertor, in which the divertor baffle tiles are reorientable by external actuation. Implementation of this concept in a medium-sized research tokamak would uniquely provide the flexibility to tailor divertor geometry to the plasma configuration and also enable study of the effect of divertor closure on plasma performance. To ensure compatibility with typical tokamak operations, the adjustable divertor must withstand the effects of significant mechanical and thermal stresses such as MW/m2-scale heat fluxes and large electromagnetic fields, e.g., disruption forces. The technological solutions for actuation mechanisms, cooling system, gas baffling and plasma-facing components are assessed. A functional reduced-scale model with movable outer divertor target baffle tiles is developed and the actuation mechanism is tested.

Fast-ion orbit analysis in Thailand Tokamak-1

Thailand Tokamak-1 (TT-1) will be a small research tokamak being operated by the Thailand Institute of Nuclear Technology (TINT) in Nakhonnayok province, Thailand. The device partly uses the infrastructure of the former HT-6M alongside new hardware. Auxiliary heating sources, such as ion cyclotron range of frequency (ICRH) and/or neutral beam injection (NBI), maybe also included in subsequent operations. This study aims to investigate the characteristics and behavior of fast ions produced by NBI heating in various operation scenarios. This work employs the collisionless Lorentz-orbit (LORBIT) code for simulating the motion of ions in the TT-1. When a hydrogen ion (H+) with an energy of 20 keV travels in the plasma with the plasma current of 100 kA, the toroidal magnetic field of 1.0 T, the average Larmor radius is found to approximately be 0.48 cm for a passing transit particle and 2.17 cm for a trapped particle. The Larmor radius reduces as the plasma current is increased or a stronger magnetic field is used. Furthermore, when the ion has pitch angles in the range of 85∘−100∘, the ion orbit clearly demonstrates a banana shape with a width and height of 7.0 and 18.8 cm, respectively. The size of the banana orbit shows an inverse correlation with the plasma current. In the last part of this work, we investigate the motion of ions that had initial positions along the paths of a co-current and counter-current NBI. It is shown that the number of lost ions can be reduced if the initial radial positions of the ions are in the range of 0.64–0.68 m.

Optimizing detachment control using the magnetic configuration of divertors

As tokamak research moves to reactor conditions, the control of a stable, optimally-detached divertor plasma has become increasingly relevant. Simple predictions of such detachment control have been performed previously using the detachment location sensitivity (DLS) model (Lipschultz et al 2016 Nucl. Fusion 56 056007). In this study the DLS model is extended and combined with SOLPS-ITER simulations of isolated divertor grids to study the effects of alternate divertor magnetic field properties on detachment control. The DLS model predicts that divertors can achieve easier access to detachment through a long connection length, a high total flux expansion, and a high average magnetic field in the divertor compared with that at the x-point. SOLPS-ITER simulations suggest an even stronger impact of total flux expansion and connection length on detachment access than the DLS model predicts. In terms of detachment evolution, both simulation and modelling show a high gradient in the total magnetic field and low are able to more easily keep a detachment front at a desired poloidal location. Regions with no stable detachment front locations can arise for high magnetic field gradients directed towards the target. Significant differences have been found between impurity scan simulations and the DLS model. These differences may be attributed to sources and sinks of power and electron pressure, and should be explored further in future work.

Overview of coordinated spherical tokamak research in Japan

Spherical tokamak (ST) research in Japan has produced many innovative results: (i) plasma start-up to I p > 70 kA was achieved by electron cyclotron wave (ECW) with N ∥ = 0.75, while electron heating to T e > 500 eV was achieved with N ∥ = 0.26 on QUEST. (ii) The radiofrequency (RF)-induced transport model was combined with the x-ray emission model, and extended magnetohydrodynamics equilibrium with kinetic electrons was developed to interpret fast-electron-dominated lower hybrid wave sustained plasmas on TST-2. (iii) Density as high as 30 times the cutoff density was achieved by electron Berstein wave current drive combined with electron beam injection on LATE. (iv) Multiple plasmoids formed by tearing instability in the elongated current sheet were observed, and flux closure and ion heating by plasmoid-mediated fast magnetic reconnection were observed on HIST. (v) Optimization of ECW-assisted inductive start-up with a vertical field with positive decay index was performed on TST-2. (vi) Stabilization of the vertical displacement event by a set of upper and lower helical field coils was demonstrated on TOKASTAR-2. (vii) A 6 h discharge was achieved by cool-down of the center stack cover on QUEST, where the plasma duration limit was consistent with the wall saturation time estimated by modeling. (viii) Extension of ion heating by plasma merging was achieved on TS-3U, TS-4U, UTST, MAST, and ST40.

Advances in the long-pulse steady-state high beta H-mode scenario with active controls of divertor heat and particle fluxes in EAST

Since the last IAEA-Fusion Energy Conference, the Experimental Advanced Superconducting Tokamak (EAST) research program has been, in support of ITER and CFETR, focused on development in terms of the long-pulse steady-state (fully noninductive) high beta H-mode scenario with active controls of the stationary and transient divertor heat and particle fluxes. The operational domain of the steady-state H-mode plasma scenario has been significantly extended with ITER-like tungsten mono-block divertor, plasma control and heating schemes. EAST has achieved several important milestones in the development of high β p H-mode scenario and its key physics and technologies. A 60 s-scale long-pulse steady-state high β p H-mode discharge with the major normalized plasma parameters similar to the designed performance of the CFETR 1 GW fusion power operation scenario has been successfully established and sustained by pure RF heating and current drive. Several feedback control schemes have been developed for a sustained detachment with good core confinement. This includes control of the total radiation power, target electron temperature, and particle flux measured using divertor Langmuir probes or a combination of the control of target electron temperature and AXUV radiation near the X point. The detachment feedback control schemes have been integrated with small-ELM regimes and high β p scenario via neon seeding, enabling a core and edge compatible integrated high-beta scenario applicable to long-pulse operations. ELM suppression has been achieved using various methods, including resonant magnetic perturbations and impurity seeding. Full suppression of ELMs by using n = 4 RMPs has been demonstrated for ITER for the first time in low input torque plasmas in EAST. EAST has been operated with helium to support the ITER research requirements for the first time. For a long-pulse, high bootstrap current fraction operation, a new lower tungsten divertor with active water-cooling has been installed, along with improvements in the heating and current drive capability.

On similarity scaling of tokamak fusion plasmas with different aspect ratio

Previously, tokamak research has been focused mainly on large aspect ratio devices where the vessel/plasma major radius is about a factor three larger than the plasma radius. This research culminated in the design and construction of the international thermonuclear experimental reactor, ITER. Spherical tokamaks (ST), with aspect ratio below two, represent an attractive alternative to large aspect ratio tokamaks as, in our opinion, provide a faster, more economical and compact solution on the path to a fusion reactor. STs are the focus of research at Tokamak Energy Ltd with its present device ST40 in operation and the first ST reactor being designed, taking advantage of the high temperature superconductor (HTS) technology. HTS allow to design a ST with magnetic field/comparable or exceeding that of present-day large aspect ratio tokamaks. However, plasma studies carried out so far on compact, low aspect ratio tokamaks have been limited to small, low magnetic field, low plasma-current devices and therefore the data available for extrapolating to large scale ST plasmas is limited. This paper addresses the problem of scaling the results of large aspect ratio tokamak and existing ST plasmas to a high field ST reactor using plasma-similarity arguments in order to mitigate its design and operational risks. The role of the plasma aspect ratio in scaling burning plasmas as well as conventional experiments in deuterium is highlighted. We find that the scaling for fusion-reactor plasmas exhibit a stronger dependence on the magnetic field and aspect ratio than the one of conventional non-burning plasmas. The parameters of a ST having the same fusion gain Q fus of ITER under different confinement assumptions and for different aspect ratios are presented and discussed.

Calculating the linear critical gradient for the ion-temperature-gradient mode in magnetically confined plasmas

A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized ‘spikes’ in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that localize within bad drift curvature wells that have a critical gradient set by peak drift curvature are also observed. A case study of near-helical stellarators of increasing field period demonstrates that the critical gradient can indeed be controlled by manipulating the magnetic geometry, but underscores the need for a general framework to evaluate the critical gradient. We conclude that average curvature and global shear set the correlation length of resonant ITG modes near the absolute critical gradient, the physics of which is included through direct solution of the gyrokinetic equation. Our method, which handles the general geometry and is more efficient than conventional gyrokinetic solvers, could be applied to future studies of stellarator ITG turbulence optimization.

Application of motional Stark effect in situ background correction to a superconducting tokamak

A polychrometer-type motional Stark effect (MSE) diagnostic technique, originally developed for the Alcator C-Mod tokamak, has been extended and applied to the Korea Superconducting Advanced Tokamak Research (KSTAR) device, the long-pulse superconducting tokamak, for the first time. It demonstrates a successful in situ subtraction of the polarized reflections off the vacuum vessel wall, sometimes up to half the total signal in some sightlines. To avoid the secondary neutral beam emission that may contaminate conventional beam-into-gas calibrations, a new approach, where the beam-into-gas measurements are made at various torus pressures with fixed vacuum fields, has been devised, which is possible with the stable superconducting coil systems of KSTAR. The validity of this new calibration scheme has been checked via plasma jog experiments. The experimental evidence of the polarized background light and the necessity of its correction in the MSE measurements made in KSTAR are presented as well.

A Numerical Simulation for Fusion Reaction in Tokamak D-T Plasma

Fusion power, which generates electricity from the heat of fusion reactions, has the potential to solve the future energy crisis; hence, methods have been developed to study fusion reactions in a fusion reactor. For neutronic analyses of a fusion reactor, the reaction rate should be precisely calculated. The traditional calculation method has some defects. First, the deuterium-tritium fusion reaction cross-section data used are of the semiclassical model described by Gamow theory, which provides relatively accurate cross sections at energies below several hundreds of kilo-electron-volts in a center-of-mass frame. However, when energies increase, the data may be inaccurate. The ENDF/B-VI database provides accurate energies below 30 MeV. Since tokamak research always aims to raise the temperature inside, the ENDF/B-VI database may be more accurate at high temperatures and fit the research better. Second, adjacent plasmas with different temperatures and densities may influence each other and finally influence the reaction rate, which is not taken into account in the traditional calculation method. In this work, a numerical algorithm based on the ENDF/B-VI database employs both the Monte Carlo method and the discrete ordinates (SN) method, which is used to simulate the transportation process to obtain more accurate reaction rate results. Parameters of the European demonstration fusion power plant (DEMO) A-mode are used to calculate the reaction rate by both the traditional method and the new algorithm. The differences of the results are shown, and the total reaction rate of the new algorithm is 4.23% higher than that of the traditional method.

Experimental and theoretical investigation of EUV radiation behavior of laser-produced Zr plasmas

Extreme ultraviolet radiation of laser-produced zirconium (Zr) plasmas were measured in the 6.7–14.7 nm region using a spatio-temporally resolved laser-produced plasma spectroscopy technique. At shorter wavelengths, the spectrum was dominated by several lines attributed to the 4s-(6p,7p,8p) transition arrays of Zr6+ to Zr10+ ions. For the 4s-5p and 4p-6 s transitions, the spectral lines concentrated near 11.18 nm and smoothly move towards longer wavelengths with decreasing ion-charge-state, which are experimentally and theoretically investigated. The Hartree-Fok (HF) method with relativistic corrections (HFR) using the Cowan's codes and Flexible Atomic Code (FAC) were used to calculate and interpret the observed spectra, respectively. At relatively high temperatures, lines from 3p-3d transitions in Zr13+ and Zr14+ ions have been found to have an important contribution. A number of spectral lines are established in this study for the first time. Besides the atomic structure calculations, a numerical computation based on the assumption of a normalized Boltzmann distribution among the excited states associated with a steady-state collisional-radiative model (CR), has also been performed to obtain the plasma parameters by comparing the experimental and simulated spectra. The corresponding dominant ion stages and ion fractions for different ion stages were obtained. We have also provided the evolution of rate coefficients as a function of electron density and electron temperature. We reproduced synthetic spectra which are in good agreement with the experiment. Temporal and spatial evolution behavior about plasma parameters have been analyzed. The variation of electron plasma frequency and skin depth with plasma temperature were introduced. The results may be beneficial for spectroscopic diagnostics of hot plasmas in tokamak and fusion research.

Power balance investigation in long-pulse high-performance discharges with ITER-like tungsten divertor on EAST

The Experimental Advanced Superconducting Tokamak (EAST) research program concentrates on demonstrating steady-state high-performance H-mode operations with ITER-like tungsten divertor. Calorimetry was applied to actively water-cool the plasma facing components (PFCs) by increasing the water temperature for power balance investigation. Considering the energy balance of EAST long-pulse high-performance discharges with upper single null (USN) configuration, thus far, approximately 78% of the injected energy could be accounted for. The method of estimation of heat flux on upper tungsten divertor target with a high time- and spatial-resolved infrared camera has been developed, and the sum of its heat load was found to be significantly consistent with that measured through calorimetry. The record longest steady-state H-mode plasma #73 999 was sustained for up to 101.2 s with net injected energy exceeding ∼0.25 GJ in the USN configuration. Heat load analysis of this discharge using calorimetric measurement indicates that the modification of heat load distribution was observed and this was induced by a slight change in the magnetic configuration. Not all temperature increments in the five cooling water modules reached the saturated state for the 100 s level discharge, which means that 100 s timescales are insufficient as compared to the thermal transport timescale in the targeted PFCs. The heat load on the tungsten divertor targets is not evenly distributed with the ratio of ∼2 in favour of the outer divertor.The experimental results and analysis of the physics involved in these USN configuration discharges are reported and discussed.

Малоракурсная реконструкция светимости плазмы для сферического токамака

Публикация посвящена применению методов вычислительной геометрии, интервального анализа и линейного программирования к задачам физики управляемого термоядерного синтеза. Рассмотрены геометрические аспекты проблемы, получены проекции светимостей различных объемов сферического токамака на плоскость матричного детектора, изучены изображения предполагаемых макроскопических структур и микроскопических включений. Для набора модельных распределений светимости объема токамака поставлена задача восстановления сигнала. Решение получено с использованием задач линейного программирования. The problems of reconstruction of plasma luminosity are important for physics and technology of power plants-tokamaks. The Globus-M research tokamak obtained a large amount of data using a matrix detector in pinhole camera geometry. From the mathematical point of view, finding the luminosity for different regions of the plasma volume according to the matrix detector is an inverse problem related to the field of integral geometry. An essential feature of the particular task is the use of a single fixed camera with a small viewing angle. In this regard, application of methods of harmonic analysis of data is not enough. The paper investigates the geometric aspects of the problem. In the general view, a threedimensional object is projected onto a two-dimensional plane through a diaphragm. Under the assumption of azimuthal symmetry, there is a central projection of the luminosity of the body of rotation onto a flat matrix detector. The initial information for the calculation is the plasma boundary obtained from magnetic sensors. There is no reliable information about the internal structure of the plasma, so its division into regions of the equal luminosity is not unambiguous. The paper presents an algorithm for finding the projections of the luminosity of plasma volumes on the plane of the matrix detector. A set of model direct problems for the construction of algorithms for their recognition according to the detector data was investigated. Images of supposed macroscopic structures and microscopic inclusions were obtained. The methodological basis of the work is the use of interval analysis methods for solving geometric and algebraic problems. This approach allows obtaining qualitative and quantitative results that takes into account the uncertainty of the input data with the minimum amount of computational costs. Algebraic solvability is investigated in the interval formulation using response functionality. Solutions for a set of test problems are obtained, which demonstrate the availability of successful reconstruction for real data. An important result of the study is an information about the presence of uncertainties in geometric data and related calculations by obtaining results about the luminosity of the plasma by solving linear programming problems.