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Vol 45, No 12 (2019)

Tokamaks

V. D. Shafranov and Necessary Conditions for Fusion Energy

Zakharov L.E.

Abstract

By the presented paper I tried to express my deep appreciation to Vitaly D. Shafranov who was my supervisor, friend and mentor. The great value of his equilibrium theory is widely recognized as one of the pillar of tokamaks. At the same time, it may look like the importance of contribution of founders of tokamak physics is diminishing in favor on new research results and models. The paper shows that this is not the case: after six decades of tokamak fusion, the program is incapable to demonstrate fusion power exceeding the applied plasma heating. In contrast to this situation, the return to fundamentals of tokamak physics suggests much more efficient approach with order of magnitude better confinement, consistent with burning plasma.

Plasma Physics Reports. 2019;45(12):1087-1092
pages 1087-1092 views

Equations of Plasma Equilibrium in a Magnetic Field with Three-Dimensional Magnetic Surfaces

Sorokina E., Ilgisonis V.

Abstract

A system of equations that describe the static equilibrium of plasma in a magnetic field with three-dimensional magnetic surfaces of toroidal topology is obtained. The approach is based on the mixed representation for the magnetic field; the representation is similar to that used in the derivation of the classical Grad–Shafranov equation but modified with allowance for the possible axial asymmetry of magnetic surfaces. The system consists of three differential equations for three scalar functions; two of the equations can be written in the form of magnetic differential equations and the third one (the balance of forces in the direction perpendicular to the surface) serves as an analogue of the Grad–Shafranov equation. The obtained equations allow a simple transition to the limiting case of axial symmetry. An example of a solution of the Hill vortex type is presented under the assumption of weak axial asymmetry of the problem. The paper is dedicated to the memory of the brilliant physicist Vitaly D. Shafranov, who could think simply and very precisely.

Plasma Physics Reports. 2019;45(12):1093-1098
pages 1093-1098 views

On the Influence of the SOL Region on Core-Plasma Energy Confinement Time in Simulation of Turbulent Transport Processes in Tokamaks

Pastukhov V.P., Kirneva N.A., Smirnov D.V.

Abstract

The influence of the scrape-off layer (SOL) on the energy confinement time of the core plasma is analyzed by using computer simulation of the self-consistent evolution of turbulence and anomalous transport. The simulation is performed for the conditions of a series of discharges with auxiliary heating in the T‑10 tokamak. It is demonstrated that the role of the SOL region in core-plasma confinement increases considerably relative to the conventional diffusion model of transport processes in the presence of turbulent convection that maintains self-consistency of pressure profiles in plasma. In this case, the influence of the SOL region on the energy confinement time of the core plasma is modeled by nonlinear boundary conditions of the third type at the boundary between the core plasma and the SOL region in which the heat fluxes at the SOL boundary are expressed in the form of power-law dependences on local values of the electron and ion temperatures. The specific form of this power-law dependence is related to power-law scaling for effective plasma confinement time in the SOL. The results of numerical simulation of turbulent-plasma evolution revealed that such an approach allows to provide self-consistent evolution of the energy confinement time τE in transient regimes with auxiliary heating, resulting in τE attaining stationary values close to those observed in real experiments.

Plasma Physics Reports. 2019;45(12):1099-1113
pages 1099-1113 views

Extension of Shafranov’s Equilibrium Theory to the Description of Current Quenches Affected by Resistive Wall Dissipation in Tokamaks

Pustovitov V.D.

Abstract

An equation for the plasma column position in a tokamak is derived with account of the resistive wall reaction on the changes in the plasma. A similar problem was considered by V.D. Shafranov [J. Nucl. Energy C 5, 521 (1963)] but for a fixed plasma current. Here, this current is treated as time-dependent, which allows to cover the current quenches and expand the study to the analysis of disruptions. It is shown that the net toroidal current induced in the wall during the current quench (which is not accounted for in the mentioned and related existing analytical models) can strongly affect the plasma equilibrium. A general algorithm applicable to arbitrary tokamaks is presented. For a large-aspect-ratio “circular” tokamak a full cycle of the step-by-step reduction of a problem is carried out down to the equation for the plasma shift evolution. The technique and results are ready for use with standard equilibrium solvers and models.

Plasma Physics Reports. 2019;45(12):1114-1127
pages 1114-1127 views

Strong Isotope Effect in Energy Confinement at the FT-2 Tokamak

Kuprienko D.V., Altukhov A.B., Gurchenko A.D., Gusakov E.Z., Esipov L.A., Kaledina O.A., Tropin N.V., Lashkul S.I., Troshin G.A., Shatalin S.V.

Abstract

The effect of the isotope content of plasma (hydrogen/deuterium) on energy confinement time was studied at the FT-2 tokamak. A strong isotope effect is discovered, which is manifested in the deuterium plasma in high-density regimes. A correlation is shown between the improvement of the energy confinement in deuterium and the drop in the turbulence level at the plasma periphery.

Plasma Physics Reports. 2019;45(12):1128-1133
pages 1128-1133 views

Observation of Parametric Decay of a Pumping Wave in Lower Hybrid Wave Heating and Current Drive Experiments at the FT-2 Tokamak

D’yachenko V.V., Konovalov A.N., Stepanov A.Y., Altukhov A.B., Gusakov E.Z., Esipov L.A., Lashkul S.I., Shatalin S.V.

Abstract

The systematization of experimental data related to development of the parametric decay instability in tokamak plasma during RF power input within the lower hybrid frequency range was performed, which allows its characteristics to be compared with theoretical representations. The spectra of pumping waves and radiation from the plasma are obtained, which illustrate the appearance of satellites that are shifted from a pump frequency by a value that is a multiple of the ion cyclotron frequencies, toward the “red” and “blue” sides. It is noted that with a rise in density, a considerable broadening of the line of a pumping wave occurs. Values of the RF power and plasma density are observed, which are threshold values for the onset of the development of parametric decay instability. Using the diagnostic complex, the analysis of the low-frequency region of the plasma oscillation spectrum was carried out. The conditions of the development of instability were analyzed within the existing theoretical representations.

Plasma Physics Reports. 2019;45(12):1134-1141
pages 1134-1141 views

Plasma Cooling During Disruptions of Ohmic Discharges at the T-10 Tokamak

Stefanovskii A.M., Dremin M.M., Kakurin A.M., Kislov A.Y., Notkin G.E., Pavlov Y.D., Sushkov A.V.

Abstract

Experimental data on plasma cooling during slow discharge disruptions at the T-10 tokamak are analyzed. It is shown that, in the initial phase of thermal quench at T-10, two different scenarios of plasma cooling can take place. The first scenario is associated with energy transport due to heat conduction. It is initiated by the “cooling wave” that arises during the development of the m2/n1 mode instability or other plasma instabilities excited in the presence of the magnetic fields of this mode. The cooling wave rapidly propagates from the region where the instability develops into the plasma core and leaves plasma with enhanced electron thermal conductivity behind its front. The second scenario takes place when the cooling wave is so intense that it causes fast decay of the central helical magnetic structure created in the preliminary disruption phase by the magnetic fields of the m2/n1 mode. This stage is followed by the decay of the m2/n1 mode, after which the last phase of the plasma cooling begins: plasma mixing at the periphery of the plasma column and the beginning of plasma current disruption. Based on these scenarios, a general classification scheme of slow disruptions of ohmic discharges at the T-10 tokamak is proposed.

Plasma Physics Reports. 2019;45(12):1142-1163
pages 1142-1163 views

Plasma Column Position Determination Based on Electric Potential Profile Measurements on TUMAN-3M and Globus-M Tokamaks

Askinazi L.G., Abdullina G.I., Belokurov A.A., Gusev V.K., Zhubr N.A., Kornev V.A., Lebedev S.V., Patrov M.I., Petrov Y.V., Sakharov N.V., Tokarev V.A., Tukachinsky A.S., Khromov N.A.

Abstract

A method of plasma boundary location based on last closed magnetic surface position detection as a maximum of electrostatic potential measured using Langmuir probes is presented. It is demonstrated that the method can be used for an absolute calibration of magnetic diagnostics of plasma position (TUMAN-3M) and as an independent diagnostic tool (Globus-M).

Plasma Physics Reports. 2019;45(12):1164-1170
pages 1164-1170 views

Stellarators

The MHD Stability of Global Modes and Fast Particle Confinement in a Quasi-Axisymmetric Tokamak–Stellarator Hybrid

Mikhailov M.I., Nührenberg J., Zille R.

Abstract

The compatibility of global MHD modes stability and good collisionless confinement of fast particles is studied in a quasi-axisymmetric tokamak–stellarator hybrid. It is shown that both of these requirements can be satisfied at a relative plasma pressure up to \(\left\langle \beta \right\rangle \) ~ 0.02.

Plasma Physics Reports. 2019;45(12):1171-1176
pages 1171-1176 views

Oscillations and Waves in Plasma

On MHD Oscillations of a Plasma Column of Finite Conductivity with a Jump of Parameters in the Near-Wall Region

Arsenin V.V.

Abstract

In a straight-cylinder model in a strong longitudinal magnetic field, the MHD oscillations of a plasma of a finite conductivity are considered in a situation when there is no resonant surface in the plasma on which the component of the perturbation wave vector vanishes along the field. At high conductivity, there are large-scale oscillations with a radial wavelength on the order of the column radius, which in the entire volume differ little from those described by an ideal MHD. It is shown that with a jump in the density and electron temperature on a certain magnetic surface near the wall, another MHD mode may exist along with such oscillations due to the finite conductivity. In this mode, the perturbations are large-scale and almost ideal in most of the plasma volume, but small-scale in the radial coordinate and not ideal in the wall region.

Plasma Physics Reports. 2019;45(12):1177-1184
pages 1177-1184 views

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