Effect of density variations along ion drift trajectories on the poloidal and toroidal rotation velocities of a collisionless tokamak plasma

The effect of plasma density variations along ion drift trajectories on the ion velocity distribution function at a given point on a tokamak magnetic surface is studied. The observed distortion of the distribution function can be interpreted as a poloidal (or toroidal) plasma rotation that is additional to the neoclassical rotation. Due to this additional rotation, the velocity of the toroidal plasma rotation is different on the low-and high-field sides of the same magnetic surface. In the case of large ion density gradients, the poloidal rotation velocity on the same magnetic surface can have different signs at different poloidal angles.     

Calculation of one-dimensional plasma flows with allowance for the kinetics of ion collisions

The influence of kinetic effects on the generation of line X radiation during the spherical implosion of a laser corona plasma with two ion species is studied under the conditions prevailing in experiments with thin-wall spherical targets in the Iskra-5 laser facility of the All-Russia Research Institute of Experimental Physics (Sarov, Russia). Kinetic processes occurring in a multicharged plasma are investigated using a specially devised code for solving one-dimensional Landau equations for a nondegenerate multicomponent plasma by the Monte Carlo method (the KIN-MC code). The code was developed using the quasineutral plasma approximation under the assumption that the electron distribution function is locally equilibrium. The model equations are presented, the scheme of numerical solution is described, and the calculated results are discussed.     

Calculation of the energy confinement time and power threshold for L-H transitions in a tokamak with allowance for the parameters of the transport barrier

The ASTRA-ETL code is used to simulate L-H transition scenarios and calculate the energy confinement time and the threshold power of the L-H transition as functions of the averaged electron density 〈n〉, the averaged magnetic field B, the neutral density n _n , and the neutral temperature T _n , as well as the values of T _Se , T _Si , and n _S at the separatrix. It is shown that the linear dependence of the threshold power of the L-H transition on the averaged electron density, Q _L-H∝〈n〉, is associated with an increase in the viscosity of a poloidally rotating plasma due to charge exchange and is governed exclusively by an increase in the neutral density n _n . When the averaged electron density 〈n〉 is low, the threshold power rises because T _Si and T _Se increase. The accuracy of predictions for the power threshold of the L-H transition can be improved if the scaling of Q _L-H versus 〈n〉 and B is derived by processing experimental data from discharges with close parameter values at the separatrix. The hysteresis effect during an L-H-L transition triggered by varying the input power is modeled. The global energy confinement time τ_E is shown to increase linearly with 〈n〉 in the range 〈n〉<3.6×10¹⁹ m^?3 and to saturate at higher electron densities; this behavior is found to be characteristic of the Ohmic, L-, and H-modes. The saturation is associated with the fact that losses via the ion channel (when the transport coefficients are density-independent) dominate over losses via the electron channel. The dependence of τ _E on the input power is determined from the calculated database and is found to be τ _E =0.12Q _L-H ^?0.46 at a fixed averaged electron density 〈n〉. In the simulations of the L-H transition, the energy confinement time τ _E increases by a factor of 2 only if the thermal diffusivity inside the transport barrier is lower than that in the central plasma by a factor of more than 6.     

Simulation of plasma density evolution in the T-10 tokamak

Analysis of the experimental profiles of the plasma density and pressure in the T-10 tokamak shows that in the plasma core they are close to the corresponding canonical profiles. This allows one to construct an expression for the particle flux in terms of the canonical profile model. T-10 experiments performed with ohmic discharges have revealed transitions from improved to low particle confinement, similar to the effect of the density pump-out from the central part of the plasma upon switching-on of the electron cyclotron resonance heating (ECRH). It is shown that such a change in the particle confinement is associated with the deviation of the radial pressure profile from the canonical one. A nonlinear model of particle transport in discharges with density variations that allows for the transition effects is proposed. The plasma density evolution is numerically simulated for a number of ohmic and ECRH T-10 discharges.     

Time-of-flight measurements of the plasma density in the T-11M tokamak

The average plasma density in the T-11M tokamak is determined by means of an O-mode time-of-flight refractometer measuring the propagation time τ of microwave pulses through the plasma. Since the front duration τ_fr of these pulses is shorter than 2 ns, filtering the measured signal cannot reduce the signal-to-noise ratio below a certain level. This circumstance impedes the use of this diagnostics in larger devices, where the signals may be substantially attenuated because of the larger chamber size and larger waveguide losses. There are several ways to overcome these difficulties: to raise the microwave power, to increase the sensitivity of the receivers, etc. In this paper, a technique is described that is based on the differential method for determining the propagation time of a microwave signal through the plasma. In this method, the plasma is probed by two continuous microwaves with close frequencies and the phase difference between them Δφ₁₂ is measured. As long as the condition Δφ₁₂ < 2π is satisfied, the measurements are unambiguous, because there are no phase jumps by a value multiple of 2π, as is usually the case in conventional interferometers at an increased level of MHD activity, in regimes with a rapid density growth, etc. This method allows the signal to be filtered, thereby ensuring an appreciable improvement in the signal-to-noise ratio in comparison with the pulsed methods. The first measurements of the average density along the +3-cm chord were performed with the help of this new differential time-of-flight refractometer in the T-11M tokamak. The refractometry data agree well with the interferometric data and are used to recover the plasma-density profile.     

Calculation of transport coefficients with allowance for the chemical composition of a low-temperature high-density metal plasma

The model proposed by Ichimaru for calculating transport coefficients is generalized to describe a plasma containing neutral atoms and ions with different charges. Ichimaru's model was developed for a fully ionized two-component (electrons and a single ion species) plasma with a temperature above 10⁵ K. Taking into account several species of positive ions and neutral atoms makes it possible to extend Ichimaru's model to a partially ionized plasma. Transport coefficients calculated from different models are compared with the experimental data.     

Toroidal inhomogeneity of plasma density fluctuations during ECR plasma heating in the L-2M stellarator

Correlation between short-wavelength (k_⊥ ≈ 20–30 cm^–1) and long-wavelength (k_⊥ ≈ 1–2 cm^–1) plasma density fluctuations in two poloidal cross sections of the stellarator chamber separated by 1/14 or 5/14 of the torus perimeter was studied using collective scattering of radiation of two 75-GHz gyrotrons and radiation of a 37-GHz Doppler reflectometer at an ECR heating power density of 1.6–3.2 MW/m³. It is found that excitation of turbulent fluctuations is bursty in character and that fluctuations excited in different L-2M cross sections are uncorrelated. It is shown that the energy of turbulent fluctuations is modulated by a low frequency of 5–20 kHz. An idea is put forward that anomalous transport is toroidally inhomogeneous.     

Correction of the axial asymmetry of the poloidal magnetic field in the Globus-M spherical tokamak

The toroidal inhomogeneity of the poloidal magnetic field—the so-called error fields that arise due to imperfections in manufacturing and assembling of the electromagnetic system-was measured in the Globus-M spherical tokamak. A substantial inhomogeneity corresponding to the n = 1 mode, which gave rise to a locked mode and led to discharge disruption, was revealed. After compensation of this inhomogeneity with the help of special correction coils, the discharge duration increased and the global plasma parameters improved substantially. A technique for determining and compensating the n = 1 mode inhomogeneity is described, the measured dependences of the penetration threshold of the m = 2/n = 1 mode on the plasma parameters are given, and results of experiments in which record parameters for the Globus-M tokamak were achieved after correction of the poloidal magnetic field are presented.     

Measurements of the plasma density in the FTU tokamak by a pulsed time-of-flight X-wave refractometer

On-line control over the plasma density in tokamaks (especially, in long-term discharges) requires reliable measurements of the averaged plasma density. For this purpose, a new method of density measurements—a pulsed time-of-flight plasma refractometry—was developed and tested in the T-11M tokamak. This method allows one to determine the averaged density from the measured time delay of nanosecond microwave pulses propagating through the plasma. For an O-wave, the measured time delay is proportional to the line-averaged density and is independent of the density profile (f?f _p ) τ_o ≈ k _o \(\tfrac{1}{{f^2 }}\mathop \smallint \limits_l \) N(x dx. A similar formula is valid for an X-wave: τ_X = ≈ k _x \(\tfrac{{f^2 + f_c^2 }}{{(f^2 - f_c^2 )^2 }}\mathop \smallint \limits_l \) N(x)dx. Here, f is the frequency of the probing wave, f _p is the plasma frequency, l= 4 a is the path length for two-pass probing in the equatorial plane, a is the plasma minor radius, k _O and k _X are numerical factors, f _c is the electron-cyclotron frequency at the axis of the plasma column, and f _p ?f _c , f. Measurements of the time delay provide the same information as plasma interferometry, though they do no employ the effect of interference. When the conditions f _p ?f _c , f are not satisfied, the measured time delay depends on the shape of the density profile. In this case, in order to determine the average density regardless of the density profile, it is necessary to perform simultaneous measurements at several probing frequencies in order to determine the average density. In ITER (Bt ～ 5T), a spectral window between the lower and upper cutoff frequencies in the range of 50–100 GHz can be used for pulsed time-of-flight X-wave refractometry. This appreciably simplifies the diagnostics and eliminates the problem of the first mirror. In this paper, the first results obtained in the FTU tokamak with a prototype of the ITER pulsed time-of-flight refractometer are presented. The geometry and layout of experiments similar to the planned ITER experiments are described. The density measured by pulsed time-of-flight refractometry is shown to agree well with the results obtained in FTU with a two-frequency scanning IR interferometer. The results obtained are analyzed, and the future experiments are discussed.     

Effect of the radial electric field on the results of measurements of the poloidal rotation of a tokamak plasma by charge exchange recombination spectroscopy

Abtract The effect of the radial electric field E _r on the results of measurements of the poloidal rotation of a tokamak plasma by charge exchange recombination spectroscopy is considered. It is shown that the emission line shift arising from the finite lifetime of the excited state of the ions is proportional to E _r. For helium ions, the maximum shift corresponds to the poloidal rotation velocity, which is about one-third of the drift velocity in the crossed radial electric (E _r) and toroidal magnetic (B _t) fields. __________ Translated from Fizika Plazmy, Vol. 27, No. 11, 2001, pp. 1050–1052. Original Russian ? 2001 by Romannikov, Chernobai.     

Theory of longitudinal plasma waves with allowance for ion motion

A study is made of the propagation of steady-state large-amplitude longitudinal plasma waves in a cold collisionless plasma with allowance for both electron and ion motion. Conditions for the existence of periodic potential waves are determined. The electric field, potential, frequency, and wavelength are obtained as functions of the wave phase velocity and ion-to-electron mass ratio. Taking into account the ion motion results in the nonmonotonic dependence of the frequency of the waves with the maximum possible amplitudes on the wave phase velocity. Specifically, at low phase velocities, the frequency is equal to the electron plasma frequency for linear waves. As the phase velocity increases, the frequency first decreases insignificantly, reaches its minimum value, and then increases. As the phase velocity increases further, the frequency continues to increase and, at relativistic phase velocities, again becomes equal to the plasma frequency. Finally, as the phase velocity approaches the speed of light, the frequency increases without bound.     

Resonance of the Larmor drift with plasma oscillations

Resonance phenomena arising when the Larmor drift velocity is locally equal to the phase velocity of plasma oscillations are analyzed. It is shown that, in a plasma with a nonuniform temperature, the wavelength of the oscillations sharply reduces at the resonant point, so that the oscillations convert into small-scale waves. In a plasma with a uniform temperature, Coulomb collisions cause the oscillations to dissipate at the resonant point. It is noted that a resonance with the Larmor drift can be used to heat the plasma.     

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.     

Mechanisms of dust grain charging in plasma with allowance for electron emission processes

The process of dust grain charging is described with allowance for secondary, ion-induced, photoelectric, and thermal electron emission from the grain surface. The roughness of the grain surface is taken into account. An intermediate charging regime involving ion–atom collisions and electron ionization in the perturbed plasma region is analyzed using the moment equations and Poisson’s equation. A calculation method is proposed that allows one to take into account the influence of all the above effects and determine the radius of the plasma region perturbed by the dust grain.     

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.     

Two-dimensional MHD simulations of a plasma focus with allowance for the acceleration mechanism for neutron generation

The problem is formulated and a numerical model is developed for calculating MHD flows in plasma-focus (PF) devices. An implicit (with respect to the magnetic field) difference scheme and a method for its numerical implementation are proposed. The scheme allows one to describe plasma flows with drastically different densities and, therefore, to take into account the presence of a vacuum region behind the PF current sheath. Taking into account this region is important to numerically simulate the focusing process and adequately describe the acceleration mechanism for the generation of fast ions and fusion neutrons. The results of calculations are compared with the experimental data on the plasma dynamics in two different types of PF device. A model of accelerated ions is proposed to estimate the contribution of the acceleration mechanism to the total neutron yield. The neutron yield calculated in the framework of this model for three different geometries of the PF chamber at currents of 0.5–1.5 MA differs from the measured values by less than a factor of 2.     

Measurements of the load resistance of a poloidal antenna and the phase velocity of fast magnetosonic waves during ICR plasma heating in the L-2M stellarator

The propagation and damping of waves excited by a poloidal antenna in a hydrogen plasma at the ion cyclotron resonance (ICR) frequency were investigated. The longitudinal wavenumber and damping length of waves excited in the ohmically heated plasma of the L-2M stellarator, the dependence of the damping length of fast magnetosonic waves on the magnetic field strength, and the dependence of the antenna load resistance on the plasma density were measured. It is the first time that such complex measurements were performed in experiments on ICR heating of a hydrogen plasma at the fundamental harmonic of the ion gyrofrequency in toroidal magnetic confinement systems.     

Identification of the plasma boundary shape and position in the Damavand tokamak

A series of experiments and numerical calculations have been done on the Damavand tokamak for accurate determination of equilibrium parameters, such as the plasma boundary position and shape. For this work, the pickup coils of the Damavand tokamak were recalibrated and after that a plasma boundary shape identification code was developed for analyzing the experimental data, such as magnetic probes and coils currents data. The plasma boundary position, shape and other parameters are determined by the plasma shape identification code. A free-boundary equilibrium code was also generated for comparison with the plasma boundary shape identification results and determination of required fields to obtain elongated plasma in the Damavand tokamak.     

Formation of an anisotropic electron velocity distribution function and production of multicharged ions in the micropinch discharge plasma

Analysis of the results of polarimetric measurements of X-ray line radiation of multicharged ions in a Z-pinch discharge indicates that the formation of an anisotropic electron velocity distribution in the neck of the current channel and the generation of highly charged ions are separated in time. The generation of a fast electron beam in the longitudinal ohmic electric field in the stage of plasma compression in the neck results in the polarization of X-ray bremsstrahlung continuum. In the stage of expansion of the hot dense micropinch plasma, the radial electric field prevails, due to which X-ray line radiation of multicharged ions becomes linearly polarized.