Investigation of the plasma radiation power in the Globus-M tokamak by means of SPD silicon photodiodes

Radiation losses from the plasma of the Globus-M tokamak are studied by means of SPD silicon photodiodes developed at the Ioffe Institute, Russian Academy of Sciences. The results from measurements of radiation losses in regimes with ohmic and neutral beam injection heating of plasmas with different isotope compositions are presented. The dependence of the radiation loss power on the plasma current and plasma–wall distance is investigated. The radiation power in different spectral ranges is analyzed by means of an SPD spectrometric module. Results of measurements of radiation losses before and after tokamak vessel boronization are presented. The time evolution of the sensitivity of the SPD photodiode during its two-year exploitation in Globus-M is analyzed.     

Turbulent dynamics of helical perturbations in the edge plasma of the T-10 tokamak

Turbulent dynamics of the edge plasma in the T-10 tokamak is simulated numerically by solving nonlinear MHD equations in the framework of the four-field {?, n, p _e , p _i } reduced two-fluid Braginskii hydro-dynamics. It is shown that the transition from ohmic to electron-cyclotron heating is accompanied by a decrease in the amplitudes of turbulent fluctuations in plasma. This is caused by the enhancement of longitudinal dissipation due to the increase in the electron temperature. However, phase relations between potential fluctuations of different modes change in such a way that the Reynolds turbulent force increases, which leads to an increase in the poloidal velocity in the direction of ion diamagnetic drift. Since the poloidal and ion diamagnetic drift velocities enter into the equation of the radial force balance for ions with different signs, the radial electric field decreases. The simulation results agree qualitatively with the results of experiments in the T-10 tokamak. The dependence of the radial electric field on the plasma density, ion pressure, and neutral density is also calculated.     

Study of plasma confinement in the L-2M stellarator during the formation of an edge transport barrier

A plasma confinement mode characterized by the formation of an edge transport barrier (ETB) was discovered in the L-2M stellarator after boronization of the vacuum vessel wall. The transition into this mode is accompanied by a jump in the electron temperature by 100–200 eV at the plasma edge and a sharp increase in the gradient of the electron temperature T _e in this region. The threshold power for the transition into the ETB confinement mode with an increased electron temperature gradient is P _thr ^?Te = (60 ± 15)n _e [10¹⁹ m^?3] kW. The formation of the ETB manifests itself also in a substantial change in the electron density profile. A density peak with a steep gradient at the outer side forms at the plasma edge. The threshold power for the transition into the ETB confinement mode corresponding to a substantial increase in the plasma density gradient near r = a is P _thr ^?Te = (67 ± 9)n _e [10¹⁹ m^?3] kW, which agrees to within experimental error with the threshold power for the transition into the ETB confinement mode determined from the sharp increase in the gradient of the electron temperature T _e . The value of P _thr for the L-2M stellarator agrees to within 25% with that obtained from the tokamak scaling. In the ETB confinement mode, the plasma energy W and the energy confinement time τ _E determined from diamagnetic measurements increase by 20–30% as compared to those obtained from the stellarator scaling for the confinement mode without an ETB. When the heating power increases by a factor of 2–3 above the threshold value, the effects related to improved energy confinement disappear.     

Pulsed time-of-flight refractometry measurements of the electron density in the T-11M tokamak

A new method for measuring the plasma density in magnetic confinement systems—pulsed time-of-flight refractometry—is developed and tested experimentally in the T-11M tokamak. The method is based on the measurements of the time delay of short (with a duration of several nanoseconds) microwave pulses propagating through the plasma. When the probing frequency is much higher than the plasma frequency, the measured delay in the propagation time is proportional to the line-averaged electron density regardless of the density profile. A key problem in such measurements is the short time delay of the pulse in the plasma (～1 ns or less for small devices) and, consequently, low accuracy of the measurements of the average density. Various methods for improving the accuracy of such measurements are proposed and implemented in the T-11M experiments. The measurements of the line-averaged density in the T-11M tokamak in the low-density plasma regime are performed. The results obtained agree satisfactorily with interferometric data. The measurement errors are analyzed, and the possibility of using this technique to measure the electron density profile and the position of the plasma column is discussed.     

Drift-Alfvén turbulence in a tokamak wall plasma

The behavior of turbulent fluxes in the vicinity of a resonant point m/n=q(x _res) in a plane wall plasma layer in a tokamak is studied by numerically analyzing the nonlinear MHD equations in a four-field electromagnetic model. Simulations show that, as the electron temperature at the plasma edge increases, the intensity of turbulent particle flux decreases, reaching its minimum value, and then increases. Such behavior is found to be due to the stabilizing effect of the electron drift velocity (V _y0∼dT _e0/dx) in the equation for the longitudinal component of the magnetic potential. It is shown that, at a strong toroidal magnetic field, turbulent transport processes conform to the gyro-Bohm scaling, which gradually passes over to the Bohm scaling as the field decreases. __________ Translated from Fizika Plazmy, Vol. 30, No. 5, 2004, pp. 387–397. Original Russian Text Copyright ￠ 2004 by Shurygin.     

Influence of the plasma density and heating power on the intensity of electron cyclotron emission in the L-2M stellarator

Results are presented from experiments on studying the plasma behavior in the L-2M stellarator in regimes with a high power deposition in electrons during electron cyclotron heating at the second harmonic of the electron gyrofrequency (X mode) at heating powers of P _in=120–400 kW and average plasma densities from n _e≤3×10¹⁹ to 0.3×10¹⁹ m^?3. It is shown that, as the plasma density decreases and the heating power increases, the electron cyclotron emission spectrum is modified; this may be attributed to a deviation of the electron energy distribution from a Maxwellian and the generation of suprathermal electrons. At low plasma densities, the emission intensity at the second harmonic of the electron gyrofrequency increases, whereas the plasma energy measured by diamagnetic diagnostics does not increase. This poses the question of the correctness of determining the plasma electron temperature by electron cyclotron emission diagnostics under these conditions.     

Langmuir probe study of an inductively coupled magnetic-pole-enhanced helium plasma

This study reports the effects of RF power and filling gas pressure variation on the plasma parameters, including the electron number density n _e , electron temperature T _e , plasma potential V _p , skin depth δ, and electron energy probability functions (EEPFs) in a low-pressure inductively coupled helium plasma source with magnetic pole enhancement. An RF compensated Langmuir probe is used to measure these plasma parameters. It is observed that the electron number density increases with both the RF power and the filling gas pressure. Conversely, the electron temperature decreases with increasing RF power and gas pressure. It is also noted that, at low RF powers and gas pressures, the EEPFs are non-Maxwellian, while at RF powers of ≥50 W, they evolve into a Maxwellian distribution. The dependences of the skin depth and plasma potential on the RF power are also studied and show a decreasing trend.     

Parameters of a tokamak reactor operating at a fixed fusion power as functions of the aspect ratio

Such parameters of a tokamak reactor as the major radius, plasma current, reactor volume, neutron load to the first wall, heat load to the divertor plates, and bootstrap current are studied as functions of the aspect ratio, assuming that the reactor operates at a fixed power. The conclusion is drawn that a demonstrative prototype reactor should be based on a large aspect ratio tokamak.     

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.     

CXSFIT Code Application to Process Charge-Exchange Recombination Spectroscopy Data at the T-10 Tokamak

The applicability of the CXSFIT code to process experimental data from Charge-eXchange Recombination Spectroscopy (CXRS) diagnostics at the T-10 tokamak is studied with a view to its further use for processing experimental data at the ITER facility. The design and operating principle of the CXRS diagnostics are described. The main methods for processing the CXRS spectra of the 5291-Å line of C⁵⁺ ions at the T-10 tokamak (with and without subtraction of parasitic emission from the edge plasma) are analyzed. The method of averaging the CXRS spectra over several shots, which is used at the T-10 tokamak to increase the signal-to-noise ratio, is described. The approximation of the spectrum by a set of Gaussian components is used to identify the active CXRS line in the measured spectrum. Using the CXSFIT code, the ion temperature in ohmic discharges and discharges with auxiliary electron cyclotron resonance heating (ECRH) at the T-10 tokamak is calculated from the CXRS spectra of the 5291-Å line. The time behavior of the ion temperature profile in different ohmic heating modes is studied. The temperature profile dependence on the ECRH power is measured, and the dynamics of ECR removal of carbon nuclei from the T-10 plasma is described. Experimental data from the CXRS diagnostics at T-10 substantially contribute to the implementation of physical programs of studies on heat and particle transport in tokamak plasmas and investigation of geodesic acoustic mode properties.     

A study of low-frequency microturbulence by CO2-laser collective scattering in the FT-2 tokamak

Results are presented from studies of small-scale plasma density fluctuations in the FT-2 tokamak by the method of far-forward CO₂-laser collective scattering. The frequency and wavenumber spectra of fluctuations are measured using parallel k analysis at various positions of the scattering volume in the plane of the minor cross section of the torus. The data obtained are interpreted using numerical simulations. In phenomenological models, plasma fluctuations are substituted by a superposition of two-dimensional noninteracting cells with Gaussian profiles. A comparison of the calculated and experimental spectra shows that plasma fluctuations should be described based on the concept of strong microturbulence. The poloidal rotation velocity and the characteristic scale length of the scattering fluctuations, as well as the radial position of the region where they are located, are determined. The diffusion coefficient of the cells introduced in the model turns out to be close to the thermal diffusivity determined from the electron energy balance in the ohmic phase of the discharge.     

Analysis of the efficiency of lower hybrid current drive in the FT-2 tokamak

Results are presented from experimental studies of the efficiency of lower hybrid current drive (LHCD) in the FT-2 tokamak. The dependence of the LHCD efficiency on the grill phasing Δφ and RF oscillator power was determined experimentally in a wide range of plasma densities. It is shown that, at high plasma currents (i.e., at sufficiently high electron temperatures), current drive is suppressed when the plasma density reaches its resonance value n _LH for the pumping wave frequency, rather than when parametric decay comes into play (as was observed in regimes with lower plasma currents and, accordingly, lower electron temperatures T _e ). In order to analyze the experimentally observed effect of LHCD and its dependence on the value and sign of the antenna phasing, the spectra of the excited LH waves, P(N _z ), were calculated. Simulations using the FRTC code with allowance for the P(N _z ) spectrum and the measured plasma parameters made it possible to calculate the value and direction of the LH-driven current, which are determined by the spectrum of the excited LH waves. It is shown that the synergetic effect caused by the interaction between different spectral components of the excited RF wave plays a decisive role in the bridging of the gap in the wave spectrum.     

Microwave measurements of the time evolution of electron density in the T-11M tokamak

Unambiguous diagnostics intended for measuring the time behavior of the electron density and monitoring the line-averaged plasma density in the T-11M tokamak are described. The time behavior of the plasma density in the T-11M tokamak is measured by a multichannel phase-jump-free microwave polarization interferometer based on the Cotton-Mouton effect. After increasing the number of simultaneously operating interferometer channels and enhancing the sensitivity of measurements, it became possible to measure the time evolution of the plasma density profile in the T-11M tokamak. The first results from such measurements in various operating regimes of the T-11M tokamak are presented. The measurement and data processing techniques are described, the measurement errors are analyzed, and the results obtained are discussed. We propose using a pulsed time-of-flight refractometer to monitor the average plasma density in the T-11M tokamak. The refractometer emits nanosecond microwave probing pulses with a carrier frequency that is higher than the plasma frequency and, thus, operates in the transmission mode. A version of the instrument has been developed with a carrier frequency of 140 GHz, which allows one to measure the average density in regimes with a nominal T-11M plasma density of (3–5)×10¹³ cm^?3. Results are presented from the first measurements of the average density in the T-11M tokamak with the help of a pulsed time-of-flight refractometer by probing the plasma in the equatorial plane in a regime with the reflection of the probing radiation from the inner wall of the vacuum chamber.     

Effect of the magnetic field structure on the intensity of electron cyclotron emission from the plasma of the L-2M stellarator

Results are presented from experimental studies of the influence of the stellarator magnetic field structure on the plasma behavior in electron-cyclotron resonance regimes with a high heating power per electron. The magnetic field structure was changed by varying the induction current I _p from ?14 to +14 kA. The plasma electrons were heated at the second harmonic of the electron gyrofrequency by an X-mode microwave beam with a power of P ～ 200 kW, the average plasma density being in the range n _e = (0.5–2) × 10¹³ cm^?3. At I _p = 0, the rotational transform varies from $\rlap{--} \iota $ (0) = 0.2 on the magnetic axis to 0.8 at the plasma boundary. At a positive current of I _p = 13.5 kA, the rotational transform was $\rlap{--} \iota $ (0) = 0.8 on the axis and $\rlap{--} \iota $ (a _p) = 0.9 at the plasma boundary. Experiments with a positive current have shown that the radiative temperature first increases with current. When the current increases to I _p = 11–14 kA, strong modulation appears in the electron cyclotron emission signals received from all the plasma radii, the emission spectrum changes, and the emission intensity decreases. At a negative current of I _p = ?(6.5–13.5) kA, the rotational transform vanishes at r/a _p = 0.4–0.6. In this regime, the number of suprathermal electrons is reduced substantially and the emission intensity decreases at both low and high plasma densities.     

Study of Current Sheets in Three-Dimensional Magnetic Fields with an X-Line by Holographic Interferometry

Results are presented from experimental studies of the spatial electron density distribution in current sheets formed in three-dimensional magnetic configurations with X-lines. The electron density is measured by using two-exposure holographic interferometry. It is shown that plasma sheets can form in a magnetic configuration with an X-line in the presence of a sufficiently strong longitudinal magnetic-field component B_∥ when the electric current is excited along the X-line. As the longitudinal magnetic-field component increases, the electron density decreases and the plasma sheet thickness increases; i.e., the plasma is compressed into a sheet less efficiently.     

Transition into the improved core confinement mode as a possible mechanism for additional electron heating observed in the lower hybrid current drive experiments at the FT-2 tokamak

In experiments on lower hybrid current drive (LHCD) carried out at the FT-2 tokamak, a substantial increase in the central electron temperature T _e (r = 0 cm) from 550 to 700 eV was observed. A complex simulation procedure is used to explain a fairly high LHCD efficiency and the observed additional heating, which can be attributed to a transition into the improved core confinement (ICC) mode. For numerical simulations, data obtained in experiments with deuterium plasma at 〈n _e 〉 = 1.6 × 10¹⁹ m^–3 were used. Simulations by the GRILL3D, FRTC, and ASTRA codes have shown that the increase in the density and central temperature is apparently caused by a significant suppression of heat transport in the electron component. The mechanism for transition into the improved confinement mode at r < 3 cm can be associated with the broadening of the plasma current channel due to the lower hybrid drive of the current carried by superthermal and runaway electrons. In this case, the magnetic shear s = (r/q)(dq/dr) in the axial region of the plasma column almost vanishes during the RF pulse. In this study, the effect of lower hybrid waves on the plasma parameters, resulting in a transition into the ICC mode, is considered. New experimental and calculated data are presented that evidence in favor of such a transition. Special attention is paid to the existence of a threshold for the transition into the ICC mode in deuterium plasma.     

Characteristics of discharge disruptions in the T-10 tokamak

The results of experimental studies of discharge disruptions in the T-10 tokamak at the limiting plasma density are presented. On the basis of measurements of the generated soft X-ray emission, for a group of “slow” disruptions, the dynamics of the magnetic configuration of the central part of the plasma column is studied and the possible role of the m/n = 1/1 mode in the excitation of predisruptions or the final stage of disruption is analyzed. It is shown that the characteristics of plasma electron cooling in predisruptions correspond to those of electron cooling upon pellet injection into T-10 and in discharge predisruptions occurring in regimes with the “quiet mode.” It is found that, in the latter case, the reason for predisruptions and fast electron cooling in the plasma core is the instability of the m/n = 2/1 mode, its spontaneous spatial reconstruction, and the generation of a “cooling wave” during this process. Measurements of the electron temperature (determined from the plasma radiation intensity at the second electron cyclotron harmonic) in the zone of the m/n = 2/1 mode have shown that the transformation of the m/n = 2/1 mode leads to the excitation of predisruptions and the final phase of disruption not only in regimes with the “quiet mode,” but also in disruptions of ordinary ohmic discharges. The experimental results obtained in this work make it possible to determine the scenario of the development of “slow” discharge disruptions in the T-10 tokamak at the limiting plasma density.     

Impact of magnetic field inhomogeneity on electron cyclotron radiative loss in tokamak reactors

The potential importance of electron cyclotron (EC) emission in the local electron power balance in the steady-state regimes of ITER operation with high temperatures, as well as in the DEMO reactor, requires accurate calculation of the one-dimensional (over magnetic surfaces) distribution of the net radiated power density, P _EC(ρ). When the central electron temperature increases to ∼30 keV, the local EC radiative loss comprises a substantial fraction of the heating power from fusion alphas and is close to the total auxiliary NBI heating power, P _EC(0) ≃ 0.3P _α(0) ≃ P _aux(0). In the present paper, the model of EC radiative transport in an axisymmetric toroidal plasma is extended to the case of an inhomogeneous magnetic field B(R, Z). The impact of such inhomogeneity on local and total power losses is analyzed in the framework of this model by using the CYNEQ code. It is shown that, for the magnetic field B, temperature T _e , density n _e , and wall reflection coefficient R _w expected in ITER and DEMO, accurate simulations of the EC radiative loss require self-consistent 1.5D transport analysis (i.e., one-dimensional simulations of plasma transport and two-dimensional simulations of plasma equilibrium). It is shown that EC radiative transport can be described with good accuracy in the 1D approximation with the surface-averaged magnetic field, B(ρ) = 〈B(R, Z)〉 _ms . This makes it possible to substantially reduce the computational time required for time-dependent self-consistent 1.5D transport analysis. Benchmarking of the CYNEQ results with available results of the RAYTEC, EXACTEC, and CYTRAN codes is performed for various approximations of the magnetic field.     

Nonquasineutral current equilibria as elementary structures of plasma dynamics

A study is made of the fundamental features of current filaments with a nonzero electron vorticity Ω _e ≡ B − (c/e) ▿ × p _ee ≠ 0 and the corresponding Lagrangian invariant I _e . Such current structures can exist on spatial scales of up to ω _pi ⁻¹. It is shown that the dissipative stage of the plasma evolution and the violation of Thomson’s theorem on vorticity conservation in an electron fluid are of fundamental importance for the onset of electron current structures. A key role of the screening of electric and magnetic fields at distances on the order of the magnetic Debye radius r _B = B/(4πen _e )—the main property of such current structures in a Hall medium with σB/(en _e c) ≫ 1—is stressed. Since the minimum size of a vortex structure is the London length c/ω _pe , the structures under consideration correspond to the condition r _B > c/ω _pe or B ² > 4πn _e m _e c ², which leads to strong charge separation in the filament and relativistic electron drift. It is demonstrated that the specific energy content in current structures is high at a filament current of 10–15 kA: from 100 J/cm³ at a plasma density of 10¹⁴ cm⁻³ (the parameters of a lightning leader) to 10⁷ J/cm³ for a fully ionized atmospheric-pressure air. Estimates are presented showing that the Earth’s ionosphere, circumsolar space, and interstellar space are all Hall media in which current vortex structures can occur. A localized cylindrical equilibrium with a magnetic field reversal is constructed—an equilibrium that correlates with the magnetic structures observed in intergalactic space. It is shown that a magnetized plasma can be studied by using evolutionary equations for the electron and ion Lagrangian invariants I _e and I _i . An investigation is carried out of the evolution of a current-carrying plasma in a cylinder with a strong external magnetic field and with a longitudinal electron current turned on in the initial stage—an object that can serve as the simplest electrodynamic model of a tokamak. In this case, it is assumed that the plasma conductivity is low in the initial stage and then increases substantially with time. Based on the conservation of the integral momentum of the charged particles and electromagnetic field in a plasma cylinder within a perfectly conducting wall impenetrable by particles, arguments are presented in support of the generation of a radial electric field in a plasma cylinder and the production of drift ion fluxes along the cylinder axis. A hypothesis is proposed that the ionized intergalactic gas expands under the action of electromagnetic forces.     

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.