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.     

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.     

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.     

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.     

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.     

First results obtained with a sweeping pulsed radar reflectometer in the Globus-M tokamak

A weeping pulsed radar reflectometer designed for measuring the spatial electron density distribution in the Globus-M spherical tokamak with a minor plasma radius of a=24 cm, a major radius of R=36 cm, a toroidal field of B _T=0.5 T, a plasma current of I _p=200 kA, and an average density of n=(3–10)×10¹³ cm^?3 is described. The reflectometer operation is based on the reflection of microwaves with a carrier frequency f from a plasma layer with the critical density n=(0.0111f)², where n is the electron density in units of 10¹⁴ cm^?3 and f is the microwave frequency in GHz. By simultaneously probing the plasma at different frequencies, it is possible to recover the electron density profile. Microwave pulses with different frequencies are obtained by frequency sweeping. To increase the range of measured densities, channels with fixed frequencies are also used; as a result, the instrument has eleven frequency channels: a 19.5-GHz channel, eight channels in the 26-to 40-GHz frequency range, a 51.5-GHz channel, and a 60-GHz channel, which corresponds to eleven points in the density profile: 0.47×10¹³ cm^?3, eight points in the (0.8–1.95)×10¹³-cm^?3 range, 3.27×10¹³ cm^?3, and 4.5×10¹³ cm^?3. The reflectometer allows detailed measurements of the density profile with a time resolution of several tens of microseconds, which can be useful, in particular, in studying the processes related to the formation of an internal transport barrier in plasma. The first results obtained using this reflectometer in the Globus-M tokamak under various operating conditions are discussed.     

Excitation of Langmuir oscillations by a laser pulse in a semi-infinite dense plasma

A study is made of the nonlinear mechanism for the excitation of Langmuir waves in a dense plasma by an intense laser pulse with the frequency ω = ω_p/2 (where ω_p is the electron plasma frequency).     

Quasi-optics near the plasma frequency of a CuBr vapor laser

The kinetic parameters of the plasma of a CuBr vapor laser with a molecular hydrogen additive are determined by time measurements of the plasma transmittance at probing frequencies close to the plasma frequency. The measurements were performed across the discharge at frequencies of 94 and 142 GHz within the time interval 2–85 μs. The measurement results are used to calculate the time dependences of the electron density, electron temperature, and electron momentum relaxation time.     

Displacement of the electron cyclotron resonance heating region and time evolution of the characteristics of short-wavelength turbulence in the 3D magnetic configuration of the L-2M stellarator

Reflection of the heating extraordinary microwave incident obliquely onto the surface of the electron cyclotron resonance (ECR) at the second harmonic of the electron gyrofrequency in the 3D magnetic configuration of the L-2M stellarator was studied experimentally. The plasma was heated using two gyrotrons with a total power of 600–700 kW, the specific heating power being 2.4–2.8 MW/m³. The displacement of the ECR region in the course of heating was monitored by measuring the phase of the reflected extraordinary wave. It is found that the growth of the plasma density is accompanied by the displacement of the ECR heating region from the center of the plasma column toward its periphery. The coefficient of reflection of the heating microwave beam from the ECR region was measured. The spectra of short-wavelength (k _s ≈ 30 cm^?1) plasma density fluctuations were explored by analyzing backscattered microwave radiation. A tenfold increase in the energy of short-wavelength density fluctuations and the growth of the spectral density of fluctuations in the frequency range of 0.3–1.5 MHz were observed.     

Estimates of the local parameters of plasma density fluctuations by reflectometry measurements

The question is considered of how to estimate the parameters of local plasma density fluctuations from reflectometry measurements made by probing the plasma with an extraordinary electromagnetic wave. In the geometrical-optics approximation, a formula is derived that relates the fluctuation amplitude of the phase of the reflected signal to the amplitude of local plasma density fluctuations and the range of its applicability is considered. The spectral sensitivity of reflectometry measurements in a reflection region of finite dimensions to poloidal perturbations with wavenumbers k _⊥ ? k ₀ is estimated by the phase-screen method, and the expressions obtained are compared with the results of numerical simulations. Based on the relationships derived, an algorithm is proposed for recovering the amplitude of the local plasma density fluctuations from the fluctuations in the reflected reflectometer signal. The results obtained are compared with the results of the full-wave simulations of the reflection of microwaves from a turbulent plasma. Finally, an example is given of how to recover the data on the amplitude of the local plasma density fluctuations in the T-10 tokamak plasma.     

Diagnostics of a nonequilibrium nitrogen plasma from the emission spectra of the second positive system of N2

A method is proposed for determining the electron density N _e and the electric field E in the non-equilibrium nitrogen plasma of a low-pressure discharge from the spectra of the second positive system of N₂. The method is based on measuring the specific energy deposition in the plasma and the distribution of nitrogen molecules over the vibrational levels of the C ³Π _u state, as well as on modeling this distribution for a given energy deposition. The fitting parameters of the model are the values of N _e and E. A kinetic model of the processes governing the steady-state density of the C ³Π _u nitrogen molecules is developed. The testing of this method showed it to be quite reliable. The method is of particular interest for diagnosing electrodeless discharges and provides detailed information on the processes occurring in the discharge plasma. Preliminary data are obtained on the plasma parameters in a cavity microwave discharge and an electrode microwave discharge. In particular, it is found that the electric field in an electrode microwave discharge in nitrogen is lower than that in a hydrogen discharge. This effect is shown to be produced by stepwise and associative processes with the participation of excited particles in nitrogen.     

Effect of the transverse magnetic field on turbulence and parameters of a plasma column in the L-2M stellarator

The influence of magnetic configurations with magnetic hills or wells on the parameters of a plasma column and turbulence characteristics were studied in experiments in which the plasma was created and heated by a microwave beam at the second harmonic of the electron cyclotron frequency. Calculations show that, for 〈β〉=(1.5?2)×10^?, a configuration with a magnetic well takes place and the Mercier criterion for stability of the ideal MHD modes is satisfied. It is shown that the compensation of the Shafranov shift of the plasma column by a transverse (vertical) field (B _v /B ₀ =5×10^?3) leads to a configuration with a magnetic hill in which the Mercier stability criterion is violated in the central region of the plasma column. It is experimentally shown that the stored plasma energy in the magnetic-hill configuration is reduced by one-half in comparison with the magnetic-well configuration. In the case of a magnetic hill, the energy of fluctuations increases both in the plasma core and near the separatrix, and the quasi-regular components of the wavelet spectra grow. When the Shafranov shift is compensated only partially (B _v/B ₀～3×10^?3) and the system is near the instability threshold, the stored plasma energy and the central electron temperature are somewhat higher, and the radiation power of fast electrons from non-Maxwellian tails at the second harmonic of the electron gyrofrequency decreases. It is found that the wavelet spectra of fluctuations change, the coherence coefficient for spectral components increases, and the radial electric field near the separatrix decreases.     

Broadband Wide-Angle Second Harmonic Generation in Magnetized Plasma: Double Resonant Effect

Conditions for the phase synchronism between high-frequency electromagnetic waves with frequencies ω and 2ω propagating in magnetized plasma are investigated. The variety of the values of the plasma density and magnetic field, as well as of wave polarizations, obeying the synchronism conditions are shown to provide resonant broadband wide-angle nonlinear generation of the second harmonic of the pumping wave. Special attention is given to oblique propagation of interacting waves. The coupling strengths for the resonant mode conversion in magnetized collisional plasma are obtained. The double resonance ensuring efficient nonlinear generation of extraordinary mode in the vicinity of the electron cyclotron resonance (ω(2k) = ω _ce ) is considered. Examples illustrating these nonlinear phenomena for some plasma and radiation parameters are presented.     

Reflection and backscattering of microwaves under doubling of the plasma density and displacement of the gyroresonance region during electron cyclotron resonance heating of plasma in the l-2M stellarator

Reflection and backscattering of high-power (400 kW) gyrotron radiation creating and heating plasma at the second harmonic of the electronic cyclotron frequency in the L-2M stellarator have been investigated experimentally. The effect of the displacement of the gyroresonance region from the axis of the plasma column under doubling of the plasma density on the processes of reflection and backscattering of microwave radiation has been examined. A near doubling of short-wavelength (k _⊥ ≈ 30 cm^–1) turbulent density fluctuations squared is observed. The change in the energy confinement time under variations of plasma parameters and characteristics of short-wavelength turbulence is discussed. A discrepancy between the measured values of the reflection coefficient from the electron cyclotron resonance heating region and predictions of the one-dimensional model is revealed.     

Spatial distribution of the RF power absorbed in a helicon plasma source

The spatial distributions of the RF power absorbed by plasma electrons in an ion source operating in the helicon mode (ω _ci < ω < ω _ce < ω _pe ) are studied numerically by using a simplified model of an RF plasma source in an external uniform magnetic field. The parameters of the source used in numerical simulations are determined by the necessity of the simultaneous excitation of two types of waves, helicons and Trivelpiece-Gould modes, for which the corresponding transparency diagrams are used. The numerical simulations are carried out for two values of the working gas (helium) pressure and two values of the discharge chamber length under the assumption that symmetric modes are excited. The parameters of the source correspond to those of the injector of the nuclear scanning microprobe operating at the Institute of Applied Physics, National Academy of Sciences of Ukraine. It is assumed that the mechanism of RF power absorption is based on the acceleration of plasma electrons in the field of a Trivelpiece-Gould mode, which is interrupted by pair collisions of plasma electrons with neutral atoms and ions of the working gas. The simulation results show that the total absorbed RF power at a fixed plasma density depends in a resonant manner on the magnetic field. The resonance is found to become smoother with increasing working gas pressure. The distributions of the absorbed RF power in the discharge chamber are presented. The achievable density of the extracted current is estimated using the Bohm criterion.     

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.     

Generation of dense multicharged ion flows from an ECR plasma confined in a quasi-gas-dynamic magnetic cusp trap

The possibility of generating dense multicharged ion beams with a current density as high as ～1 A/cm² from an ECR plasma confined in a quasi-gas-dynamic cusp trap is studied both theoretically and experimentally. The most important advantages of this type of ion source are that the plasma in the cusp is stabile against MHD perturbations and that a trap intended to operate at fairly high pump-field frequencies (above 30 GHz) is relatively inexpensive. A theoretical model of confinement of a high-density nonequilibrium ECR plasma (T _e ? T _i ) in an open magnetic trap is proposed and results are presented from model experiments with an ～30-cm-long cusp trap (here, by the cusp length is meant the volume of a paraxial magnetic tube divided by the area of its cross sections in magnetic mirrors) pumped by a pulsed microwave field with a frequency of 37.5 GHz and power of 100 kW. The possibility of achieving a quasi-gas-dynamic regime of plasma confinement of an ECR plasma in a cusp trap is demonstrated. Ion beams with a average ion charge number of 2–4 (depending on the sort of working gas) and current densities unprecedented for ECR sources are obtained. Good agreement between theoretical and experimental results makes it possible to reliably predict the ion beam parameters that can be achieved at even higher microwave frequencies.     

Determination of the electron density and electric field in the plasma of a low-pressure microwave electrode discharge in hydrogen from the measured spectral line intensities

The parameters of the plasma of a microwave electrode discharge in hydrogen at pressures of 1–8 torr and incident powers of 20–80 W are measured by the so-called “relative intensity” method. The method allows one to determine the electron density and electric field in plasma by measuring the relative intensities of the H_α, H_β, and 763.5-nm Ar line emission and calculating the electron-impact rate constants from the homogeneous Boltzmann equation. The measurements show that there are regions in the discharge where the electron density is higher (a bright electrode sheath) and lower (a spherical region) than the critical density for the frequency 2.45 GHz (n_cr～7×10¹⁰ cm^?3). Inside the spherical region, the electric field varies slightly over the radius and the electron density increases as the discharge boundary is approached. The observed discharge structure can be attributed to the presence of a self-sustained discharge zone (electrode sheath); a non-self-sustained discharge zone (spherical region); and a decaying plasma region, which is separated from the active discharge zone by an electric double layer.     

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.     

Multichannel Thomson scattering diagnostics for the GOL-3 facility

A multichannel Thomson scattering diagnostics for measuring the plasma parameters in the GOL-3 facility was designed and created at the Budker Institute of Nuclear Physics of the Siberian Division of the Russian Academy of Sciences. The diagnostics operates at the fundamental harmonic of a neodymium laser (1.06 μm) and allows one to perform measurements over a wide range of electron temperatures and densities with high spatial and time resolutions. A special multipulse oscillator is developed that makes it possible to perform up to 20 measurements of the plasma temperature and density over a period of 300 μs during one shot. The laser used to generate probing radiation, the recording system, and the calibration procedure are described. Results from measurements of the temporal evolution of the plasma density in the GOL-3 in different stages of the discharge are presented to illustrate the system operation. Original Russian Text ? S.V. Polosatkin, A.V. Burdakov, M.V. Ivantsivskiĭ, V.S. Koĭdan, V.K. Ovchar, A.F. Rovenskikh, V.V. Semionov, M.G. Fedotov, 2006, published in Fizika Plazmy, 2006, Vol. 32, No. 2, pp. 128–133.