Collisionless current generation in the center of the tokamak plasma by an isotropic source of α-particles

The density of the noninductive current generated due to collisionless motion of α-particles in the tokamak magnetic field is calculated. The analysis is based on fully three-dimensional calculations of charged particle trajectories without simplifying assumptions typical for drift and neoclassical approaches. The current is calculated over the entire cross section of the plasma column, including the magnetic axis. It is shown that the current density is not a function of a magnetic surface and is strongly polarized over the poloidal angle. The current density distribution in the tokamak poloidal cross section is obtained, and the current density as a function of the safety factor, the tokamak aspect ratio, and the ratio of the particle Larmor radius on the axis to the tokamak minor radius is determined. It is shown that, when the source of α-particles is spatially nonuniform, the current density in the center of the tokamak is nonzero due to asymmetry of the phase-space boundary between trapped and passing particles. The current density scaling in the tokamak center differs from the known approximations for the bootstrap current and is sensitive to the spatial distribution of α-particles.     

Formation of an internal transport barrier and magnetohydrodynamic activity in experiments with the controlled density of rational magnetic surfaces in the T-10 Tokamak

Results are presented from experiments on the formation of an internal electron transport barrier near the q = 1.5 rational surface in the T-10 tokamak. The experiments were carried out in the regime with off-axis electron cyclotron resonance (ECR) heating followed by a fast plasma current ramp-up. After suppressing sawtooth oscillations by off-axis ECR heating, an internal transport barrier began to form near the q = 1.5 rational surface. In the phase of the current ramp-up, the quality of the transport barrier improved; as a result, the plasma energy confinement time increased 2–2.5 times. The intentionally produced flattening of the profile of the safety factor q(r) insignificantly affected magnetohydrodynamic activity in the plasma column in spite of the theoretical possibility of formation of substantial m/n = 3/2 and 2/1 magnetic islands. Conditions are discussed under which the flattening of the profile of the safety factor q near low-order rational surfaces leads to the formation of either an internal transport barrier or the development of an island magnetic structure induced by tearing modes.     

Reversed-shear experiments in the T-10 tokamak

Results from T-10 experiments in regimes with nonmonotonic plasma current profiles are presented. The possibility of controlling the current profile j(r) by electron-cyclotron current drive is demonstrated experimentally. Nonmonotonic q profiles with the reversed shear are obtained in which the q _min value varies in a wide range, q _min=1–2.3. It is shown that the current profiles with q _min～2 (in this case, there are two resonant magnetic surfaces q=2 in the plasma) can cause the onset of MHD instabilities. The possibility of the formation of an internal transport barrier in reversed-shear discharges in the T-10 tokamak is analyzed. In T-10, electron transport is governed by short-wavelength electron turbulence. As a result, there is no clear evidence of the formation of an inner transport barrier in these experiments.     

Formation of self-consistent pressure profiles in simulation of turbulent convection in tokamak plasmas

The formation of pressure profiles in turbulent tokamak plasmas in ohmic heating regimes and transient regimes induced by turning-on of electron-cyclotron resonance (ECR) heating is investigated. The study is based on self-consistent modeling of low-frequency turbulent plasma convection described by an adiabatically reduced set of hydrodynamic-type equations. The simulations show that, in the ohmic heating stage, turbulence forms and maintains profiles of the total plasma pressure corresponding to turbulentrelaxed states. These profiles are close to self-consistent profiles of the total plasma pressure experimentally observed on the T-10 tokamak in ohmic regimes with different values of the safety factor q _L at the limiter. Simulations of nonstationary regimes induced by turning-on of on- and off-axis ECR heating show that the total plasma pressure profiles in the transient regimes remain close to those in the turbulent-relaxed state, as well as to the profiles experimentally observed on T-10.     

On local isodynamicity in tokamaks

It is shown that local isodynamicity (i.e., the constancy of the absolute value of the magnetic field on a magnetic surface) can take place at the periphery of the tokamak near the separatrix with an internal X point. An isodynamic layer including several magnetic surfaces cannot exist in a tokamak because the safety factor q is too low and the shape of the surfaces is predetermined. The layered and global isodynamicity is possible in pinches with low values of q (Palumbo’s configuration).     

Behavior of small-scale density fluctuations in discharges with off-axis electron-cyclotron resonance heating in the T-10 tokamak

In experiments on off-axis electron-cyclotron resonance heating in the T-10 tokamak, a steep gradient of the electron temperature was observed to form for a short time at a relative radius of ρ ≈ 0.25 after the heating power was switched off. Small-scale fluctuations of the electron density were studied with the help of correlation reflectometry. It was found that, in a narrow region near ρ ≈ 0.25, the amplitude of the density fluctuations was two times lower than that in the ohmic heating phase. Quasi-coherent fluctuations were suppressed over a period of time during which the steep temperature gradient existed. Measurements of the poloidal rotation velocity of turbulent fluctuations show that there is no velocity shear after the heating is switched off. An analysis of the linear growth rates of instabilities shows that the ion-temperature-gradient mode is unstable at ρ ≈ 0.25 throughout the entire discharge phase. The effect observed can be explained by an increase in the distance between the rational surfaces near the radius at which the safety factor is q = 1 due to the temporary flattening of the q profile after the off-axis electron-cyclotron resonance heating is switched off.     

First results from plasma density measurements in the FTU tokamak by means of a two-frequency pulsed time-of-flight refractometer

A pulsed time-of-flight refractometer was developed and tested to determine the mean plasma density in the T-11M tokamak by measuring the propagation time of nanosecond microwave pulses in plasma. Later, it was also proposed to use such an instrument to measure and control the mean plasma density in the ITER tokamak by probing the plasma with an extraordinary wave, the electric field of which is perpendicular to the magnetic field in plasma, in the transparency window at frequencies of 50–100 GHz. To avoid the effect of the density profile shape on the measurement results in the nonlinear mode of refractometer operation (near the cutoff), a system operating at two different probing frequencies was developed and tested. Such a system provides two values of the time delay, which can be used to estimate the peaking factor of the density distribution α and correctly determine the linear density 〈Nl〉, regardless of the density profile (assuming a smooth density profile of the form of N(ρ) = N(0)(1 − ρ²)^α, where N(0) is the central plasma density and ρ = r/a is the normalized plasma radius). The first experiments on density measurements in the FTU tokamak performed with this refractometer are described, and results from these experiments are presented. The formation of a thin dense plasma layer in the zone of a strong magnetic field (the so-called MARFE layer) at a relatively low (for FTU) plasma density of ∼6 × 10¹⁹ m⁻³ was detected. The thickness of this layer, determined from the refractometry data, agrees well with the data obtained using a digital camera.     

Reconstruction of the q and p profiles in ITER from external and internal measurements

A method is developed for calculating uncertainties in reconstructing the equilibrium profiles of the safety factor q and plasma pressure p in the ITER device from external magnetic measurements and from motional Stark effect line polarization (MSE-LP) and motional Stark effect line shift (MSE-LS) signals from excited NBI atoms inside the plasma core. It is shown that, with MSE-LP signals, as well as with MSE-LS signals (the use of which was recently proposed by Nova Photonics, Inc.), it is possible to substantially improve the reconstruction of the profiles that determine the plasma magnetic configuration.     

Numerical simulation of drift-resistive ballooning turbulence in the presence of the GA mode in the plasma edge tokamak

Drift-resistive ballooning turbulence is simulated numerically based on a quasi-three-dimensional computer code for solving nonlinear two-fluid MHD equations in the scrape-off layer plasma in a tokamak. It is shown that, when the toroidal geometry of the magnetic field is taken into account, additional (geodesic) flux terms associated with the first poloidal harmonic (∼sinθ) arise in the averaged equations for the momentum, density, and energy. Calculations show that the most important of these terms is the geodesic momentum flux (the Stringer-Windsor effect), which lowers the poloidal rotation velocity. It is also shown that accounting for the toroidal field geometry introduces experimentally observed, special low-frequency MHD harmonics—GA modes—in the Fourier spectra. GA modes are generated by the Reynolds turbulent force and also by the gradient of the poloidally nonuniform turbulent heat flux. Turbulent particle and heat fluxes are obtained as functions of the poloidal coordinate and are found to show that, in a tokamak, there is a “ballooning effect” associated with their maximum in the weak magnetic field region. The dependence of the density, temperature, and pressure on the poloidal coordinate is presented, as well as the dependence of turbulent fluxes on the toroidal magnetic field.     

ECE measurements via B-X-O mode conversion: A proposal to diagnose the q profile in spherical tokamaks

Generation of electron Bernstein waves by the ordinary-extraordinary-Bernstein (O-X-B) mode conversion process has been successfully demonstrated on W7-AS. According to Kirchoff’s law, the inverse process of plasma EC emission by B-X-O mode conversion at particular angles must take place in tokamak plasmas. The optical depth at electron cyclotron harmonics is generally very high for electron Bernstein waves in tokamak plasmas. Consequently the O-mode ECE spectrum measured below the plasma frequency will show steps in the emitted power when each EC harmonic coincides with the upper hybrid resonance zone, where the mode conversion occurs, giving a local measurement of the relationship between the total magnetic field and plasma density. In a spherical tokamak, there are several EC harmonics below the plasma frequency, so several such steps can be observed via the B-X-O mode conversion mechanism. This is a very promising way to get information about the q profile in ST plasmas.     

Kinetic models of current sheets with a sheared magnetic field

Thin current sheets, whose existence in the Earth’s magnetotail is confirmed by numerous spacecraft measurements, are studied analytically and numerically. The thickness of such sheets is on the order of the ion Larmor radius, and the normal component of the magnetic field (B _z ) in the sheet is almost constant, while the tangential (B _x ) and shear (B _y ) components depend on the transverse coordinate z. The current density in the sheet also has two self-consistent components (j _x and j _y , respectively), and the magnetic field lines are deformed and do not lie in a single plane. To study such quasi-one-dimensional current configurations, two kinetic models are used, in particular, a numerical model based on the particle-in-cell method and an analytical model. The calculated results show that two different modes of the self-consistent shear magnetic field B _y and, accordingly, two thin current sheet configurations can exist for the same input parameters. For the mode with an antisymmetric z profile of the B _y component, the magnetic field lines within the sheet are twisted, whereas the profiles of the plasma density, current density component j _y , and magnetic field component B _x differ slightly from those in the case of a shearless magnetic field (B _y = 0). For the symmetric B _y mode, the magnetic field lines lie in a curved surface. In this case, the plasma density in the sheet varies slightly and the current sheet is two times thicker. Analysis of the dependence of the current sheet structure on the flow anisotropy shows that the sheet thickness decreases significantly with decreasing ratio between the thermal and drift plasma velocities, which is caused by the dynamics of quasi-adiabatic ions. It is shown that the results of the analytical and numerical models are in good agreement. The problems of application of these models to describe current sheets at the magnetopause and near magnetic reconnection regions are discussed.     

Resistive drift-alfvén turbulence in a tokamak edge plasma

The behavior of turbulent fluxes in the vicinity of a resonant point m/n = q(x _res) in a plane edge plasma layer in a tokamak is studied by numerically analyzing the nonlinear MHD equations in a five-field electromagnetic model. Simulations show that the heat and electron turbulent fluxes decrease with increasing ion temperature at the plasma edge. It is shown that these fluxes are suppressed due to the stabilization mechanism associated with an increase in the shear of the E × B drift velocity, which in turn increases with increasing ion pressure gradient. The effect of the zonal magnetic field on turbulent transport is also investigated. It is shown that an increase in this field stabilizes edge plasma turbulence.     

Analysis of electron thermal diffusivity and bootstrap current in ohmically heated discharges after boronization in the HT-7 tokamak

Significant improvements of plasma performance after ICRF boronization have been achieved in the full range of HT-7 operation parameters. Electron power balance is analyzed in the steady state ohmic discharges of the HT-7 tokamak. The ratio of the total radiation power to ohmic input power increases with increasing the central line-averaged electron density, but decreases with plasma current. It is obviously decreased after wall conditioning. Electron heat diffusivity χ_e deduced from the power balance analysis is reduced throughout the main plasma after boronization. χ_e decreases with increasing central line-averaged electron density in the parameter range of our study. After boronization, the plasma current profile is broadened and a higher current can be easily obtained on the HT-7 tokamak experiment. It is expected that the fact that the bootstrap current increases after boronization will explain these phenomena. After boronization, the plasma pressure gradient and the electron temperature near the boundary are larger than before, these factors influencing that the ratio of bootstrap current to total plasma current increases from several percent to above 10%.     

Characteristics of major plasma discharge disruption in the Globus-M spherical tokamak

The characteristics of the major disruption of plasma discharges in the Globus-M spherical tokamak are analyzed. The process of current quench is accompanied by the loss of the vertical stability of the plasma column. The plasma boundary during the disruption is reconstructed using the algorithm of movable filaments. The plasma current decay is preceded by thermal quench, during which the profiles of the temperature and electron density were measured. The data on the time of disruption, the plasma current quench rate, and the toroidal current induced in the tokamak vessel are compared for hydrogen and deuterium plasmas. It is shown that the disruption characteristics depend weakly on the ion mass and the current induced in the vessel increases with the disruption time. The decay rate of the plasma toroidal magnetic flux during the disruption is determined using diamagnetic measurements. Such a decay is a source of the poloidal current induced in the vessel; it may also cause poloidal halo currents.     

Current density distribution during disruptions and sawteeth in a simple model of plasma current in a tokamak

The processes that are likely to accompany discharge disruptions and sawteeth in a tokamak are considered in a simple plasma current model. The redistribution of the current density in plasma is supposed to be primarily governed by the onset of the MHD-instability-driven turbulent plasma mixing in a finite region of the current column. For different disruption conditions, the variation in the total plasma current (the appearance of a characteristic spike) is also calculated. It is found that the numerical shape and amplitude of the total current spikes during disruptions approximately coincide with those measured in some tokamak experiments. Under the assumptions adopted in the model, the physical mechanism for the formation of the spikes is determined. The mechanism is attributed to the diffusion of the negative current density at the column edge into the zero-conductivity region. The numerical current density distributions in the plasma during the sawteeth differ from the literature data.     

Simulation of internal transport barriers by means of the canonical profile transport model

Models with critical gradients are widely used to describe energy balance in L-mode discharges. The so-called first critical gradient can be found from the canonical temperature profile. Here, it is suggested that discharge regimes with transport barriers can be described based on the idea of the second critical gradient. If, in a certain plasma region, the pressure gradient exceeds the second critical gradient, then the plasma bifurcates into a new state and a transport barrier forms in this region. This idea was implemented in a modified canonical profile transport model that makes it possible to describe the energy and particle balance in tokamak plasmas with arbitrary cross sections and aspect ratios. The magnitude of the second critical gradient was chosen by comparing the results calculated for several tokamak discharges with the experimental data. It is found that the second critical gradient is related to the magnetic shear s. The criterion of the transport barrier formation has the form (a ²/r)d/drln(p/p _c ) > z ₀ (r), where r is the radial coordinate, a is the plasma minor radius, p is the plasma pressure, p _c is the canonical pressure profile, and the dimensionless function z _O(r) = C _O + C ₁ s (with C _0i ～1, C _0e ～3, and C _1i,e ～2) describes the difference between the first and second critical gradients. Simulations show that this criterion is close to that obtained experimentally in JET. The model constructed here is used to simulate internal transport barriers in the JET, TFTR, DIII-D, and MAST tokamaks. The possible dependence of the second critical gradient on the plasma parameters is discussed.     

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U₀. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2v_T/R (where v_T is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ? of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.     

Investigation of the Edge Plasma Parameters and Measurements of the Plasma Longitudinal Rotation Velocity by a Mach Probe in a Lithium Experiment on the T-11M Tokamak

The edge plasma parameters were measured by means of a Mach probe in a lithium experiment on the T-11M tokamak. The angular and radial distributions of the ion saturation current, along with the radial distribution of the electron temperature, were obtained in different modes of tokamak operation. The radial distributions of the electron temperature and ion saturation current in the main operating mode (L-mode) revealed a peak in the scrape-off-layer of the vertical limiter (lithium emitter), which can indicate the formation of a magnetic island in this region. The measured plasma flow velocity along the magnetic field was found to be close to one-half of the ion sound velocity for Li⁺ ions.     

Magnetic surfaces in an axisymmetric torus

A method is developed for specifying the boundary equilibrium magnetic surface in an axially symmetric torus by using the absolute values of the magnetic field B = B _s (θ) and the gradient of the poloidal flux ||?Ψ| = |?Ψ| _s (θ) in a special flux coordinate system. By setting two surface constants (e.g., the safety factor q and dp/dΨ) and matching the absolute values of the magnetic field and the flux gradient on a closed magnetic surface, it is possible to find all equilibrium magnetic functions (including n · ? ln B and the local shear s) and all constants (including the toroidal current J and the shear dμ/dΨ) on this surface. Such a non-traditional formulation of the boundary conditions in solving the stability problem in an axisymmetric torus allows one to impose intentional conditions on plasma confinement and MHD stability at the periphery of the system.