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.     

Physical Parameters of a Reactor-Stellarator with Small Ripples of the Helical Magnetic Field

The paper describes the calculation data on the physical parameters of a reactor-stellarator, where the nonuniformities of the helical field are smaller than the toroidal magnetic field nonuniformities: ε_h < ε_t. Unlike the previous studies, where the ion-component transport coefficients had the collision frequency dependence proportional to ν^1/2, this being equivalent to the ε_h > ε_t case, in the present calculations, these coefficients were assumed to be in proportion to the first power of the collision frequency, D_i ∝ ν for ν_eff < 2ω_E, and to D_i ∝ ν^?1 for the inverse inequality. Here, ω_E is the rotation frequency of plasma in the radial electric field. As before, the plasma electrons corresponded to the mode of D_e ∝ ν^?1. As initial parameters for numerical calculations, a reactor with R = 8 m, r_p = 2 m, and B₀ = 5 Т was taken. A numerical code was used to solve the set of equations that describes the plasma space?time behavior in the reactor-stellarator under the conditions of equal diffusion fluxes. The start of reactor operation in the mode of thermonuclear burning was provided by heating sources with a power of several tens of megawatts. Steady-state operating conditions of a self-sustained thermonuclear reaction were attained by maintaining the plasma density through DT fuel pellet injection into the plasma.     

Effect of the radial electric field on lower hybrid plasma heating in the FT-2 tokamak

Conditions for efficient ion heating in the interaction of lower hybrid waves with plasma are experimentally determined. Experiments show that efficient lower hybrid heating stimulates a transition to the improved confinement mode. The formation of internal and external transport barriers is associated with strong central ion heating, which results in a change of the radial electric field E _r and an increase in the shear of the poloidal plasma velocity. The improved confinement mode in the central region of the discharge is attained under the combined action of lower hybrid heating and an additional rapid increase in the plasma current. A new mechanism for the generation of an additional field E _r is proposed to explain the formation of a transport barrier.     

Alfvén resonance heating in Uragan-2M torsatron

Uragan-2M is a medium-size torsatron with reduced helical ripples. This machine has the major plasma radius R = 1.7 m, the average minor plasma radius r _p ≤ 0.24 m and the toroidal magnetic field B ₀ ≤ 2.4 T. The Alfvén resonance heating in a high k _‖ regime is advantageous for small size machines since it can be realized at smaller plasma densities than the minority and second harmonic heating. The Alfvén resonance heating is examined numerically in the approximation of radially non-uniform plasma cylinder with identical ends. The numerical model for wave excitation and propagation accounts for the longitudinal electron thermal motion and the finite ion gyroradius which allow the model to treat correctly the propagation and damping of the kinetic Alfvén wave in hot plasma. A compact antenna consisting of four loop elements is chosen to provide operation in a high k _‖ regime. The major drawback of such an approach is the presence of plasma peripher y heating owing to unavoidable excitation of low k _‖ Alfvén resonances. Calculations show that, with the proper choice of heating regime, the periphery heating has an acceptable level and the major part of the power is deposited inside plasma column.     

On the nature of global plasma oscillations in a tokamak. Part II: Spatial structure and propagation of perturbations observed at the T-10 tokamak

Large-scale plasma oscillations (so-called MHD oscillations) observed at the T-10 tokamak are investigated. The central electron cyclotron heating was used to enhance oscillations at the m/n = 1/1 mode with the goal of determining the internal characteristics of the process. The spatially resolved electron cyclotron emission diagnostics allowed analyzing the propagation characteristics of plasma perturbations. The experiments have revealed that excitation of oscillations in a particular mode occur simultaneously in the entire area located within the corresponding rational magnetic surface. The propagation of plasma perturbations along the torus is found to be inhomogeneous. The electron cyclotron emission diagnostics allowed finding eigen (resonance) frequencies of plasma oscillations from the parameters of their inhomogeneous propagation in the plasma core and comparing them with spectra of oscillations of the magnetic field induced by the plasma current in the edge plasma, which were recorded by magnetic probes. It is established that the frequencies of eigenmodes are independent of the electron temperature, plasma density, and auxiliary heating power. Even spatial harmonics of the principal magnetic surface are observed under strong excitation of oscillations. The rational magnetic surfaces that determine oscillation harmonics retain their position during the entire steady-state phase of the total plasma current in spite of the strong sharpening of the temperature profile due to central heating.     

Effect of the periodic ripple in an axial confining magnetic field on the Alfvén heating of a cylindrical plasma

In a uniform axial magnetic field, the structure of local Alfvén resonance and the resonant absorption of RF power are governed by collisions, finite ion Larmor radius effects, and electron inertia. It is shown that, in a cylindrical plasma in a constant, periodically rippled, axial magnetic field, the structure of Alfvén resonance and the absorption of RF power can strongly depend on the ripple amplitude. The conditions under which the effect in question is dominant are intrinsic, e.g., to the modular Wendelstein stellarators.     

Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks

In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co-I _p direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with P _RF absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.     

Characteristic properties of fluctuating particle fluxes near the last closed flux surface in the course of lower hybrid heating and during a transition into the improved confinement mode in the FT-2 tokamak

Results are presented from experimental studies of the time behavior of the transport processes in the edge plasma of the FT-2 tokamak during auxiliary lower hybrid heating when an internal transport barrier and then an external transport barrier form in the plasma. An analysis of the data on turbulent particle transport in the edge plasma shows that the radial electric field generated inside the plasma column during auxiliary heating plays an important role in both the formation of a transport barrier and the suppression of anomalous transport at the plasma periphery in the postheating phase of the discharge. The mechanism for the formation of a negative radial electric field E _r near the last closed flux surface after the end of the lower hybrid heating pulse is considered. Fluctuation spectra of the particle density and poloidal electric field are presented that characterize the process of suppression of microturbulence at the plasma periphery. The experimental data were obtained with the use of movable multielectrode Langmuir probes.     

Effect of an External Magnetic Field on the Absorption Efficiency of the RF Power in a Spatially Bounded Inductive Plasma Source

The measured dependences of the equivalent plasma resistance on the external magnetic field (0–50 G) in a 46-cm-diameter RF inductive plasma source operating at frequencies of 2, 4, and 13.56 MHz and a power of 100–500 W are presented. The experiments were carried out in argon at pressures of 0.1–30 mTorr. The presence of the external magnetic field leads to the appearance of resonance domains of efficient RF power absorption corresponding to the conditions of resonance excitation of helicons coupled with Trivelpiece–Gould modes. It is shown that RF power absorption at frequencies of 2 MHz can be optimized by applying an external magnetic field corresponding to the domains of resonance absorption. The effect is enhanced with increasing operating frequency.     

Electrostatic electron vortex structure in a plasma in an external magnetic field

A previously developed method for describing vortex structures is used to construct electrostatic vortices in a plasma in an external magnetic field. An equation for the radial electric field that gives rise to azimuthal electron drift in crossed electric (E _r ) and magnetic (B _z ) fields is derived without allowance for the magnetic field of the electron currents. Two types of the resulting electrostatic vortex structures with a positive and a negative electric potential at the axis are analyzed. The results obtained are compared with experimental data on vortex structures.     

Estimation of the electron density and radiative energy losses in a calcium plasma source based on an electron cyclotron resonance discharge

The parameters of a calcium plasma source based on an electron cyclotron resonance (ECR) discharge were calculated. The analysis was performed as applied to an ion cyclotron resonance system designed for separation of calcium isotopes. The plasma electrons in the source were heated by gyrotron microwave radiation in the zone of the inhomogeneous magnetic field. It was assumed that, in such a combined trap, the energy of the extraordinary microwave propagating from the high-field side was initially transferred to a small group of resonance electrons. As a result, two electron components with different transverse temperatures—the hot resonance component and the cold nonresonance component—were created in the plasma. The longitudinal temperatures of both components were assumed to be equal. The entire discharge space was divided into a narrow ECR zone, where resonance electrons acquired transverse energy, and the region of the discharge itself, where the gas was ionized. The transverse energy of resonance electrons was calculated by solving the equations for electron motion in an inhomogeneous magnetic field. Using the law of energy conservation and the balance condition for the number of hot electrons entering the discharge zone and cooled due to ionization and elastic collisions, the density of hot electrons was estimated and the dependence of the longitudinal temperature T _e∥ of the main (cold) electron component on the energy fraction β lost for radiation was obtained.     

Effect of electron-cyclotron resonance heating conditions on the local parameters of short-wavelength plasma turbulence in the L-2M stellarator

Changes in the energy spectra of short-wavelength (k _s ≈ 35 cm^?1) plasma density fluctuations in the local region of the plasma column (r/a = 0.5–0.6) of the L-2M stellarator were studied by the method of collective scattering of 150-GHz radiation. The plasma was heated at the second harmonic of the electron gyrofrequency, the microwave heating power being in the range of 90–170 kW. A sector limiter was introduced in the peripheral plasma (r/a ≥ 0.8), and the Shafranov shift of the magnetic axis was varied by varying the vertical magnetic field. The results of measurements were averaged over 9–16 discharges. It is found that an increase in the heating power and/or the introduction of the sector limiter in the plasma lead to an increase in the energy of density fluctuations, which correlates with a decrease in the plasma energy lifetime. In the spectra of fluctuations, a broad spectral band in the range of 3–50 kHz was observed in which the spectral density was one order of magnitude higher than in the rest of the spectrum. Analysis of the Fourier spectra showed that the introduction of the sector limiter in the plasma resulted in an increase in both the spectral density of fluctuations in the range of 3–50 kHz and the fraction of quasi-coherent structures in turbulent density fluctuations.     

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.     

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.     

Investigation of the H-mode during ECRH in the T-10 tokamak

An improved confinement regime with an external transport barrier (H-mode) is obtained during electron-cyclotron resonance heating of a plasma in the T-10 tokamak. A characteristic feature of this regime is a spontaneous density growth accompanied by a drop in the intensity of D_α line and an increase in β_p by a factor of ～1.6. The threshold power for the L-H transition is close to that predicted by the ITER scaling. The best characteristics of the H-mode are achieved with decreasing q _L to 2.2. It is shown that the external transport barrier arises for electrons, whereas the heat transport barrier insignificantly contributes to improved confinement.     

Raising the efficiency of a plasma opening switch by applying an external magnetic field

The influence of an external magnetic field on the performance of a high-impedance plasma opening switch is studied experimentally. A 1.5-fold increase in the output voltage of a plasma opening switch operating in the erosion mode is achieved by applying an external magnetic field. The magnetic field strength and the parameters of the plasma opening switch at which the maximum output voltage is attained are determined. It is shown experimentally that the predicted dependence of the maximum output voltage on the Marx generator voltage, U _POS [MV]=3.6 (U _MG [MV])^4/7, is confirmed experimentally.     

Steady-state vortex structure in a plasma with a strong magnetic field

A study is made of nonquasineutral vortex structures in a plasma with a magnetic field B _z in which the charges separate on a spatial scale equal to the magnetic Debye radius r _B=B _z/4πen _e. The electric field arising due to charge separation leads to radial expansion of the ions, thereby destroying the initial electron vortex. It is shown that the ion pressure gradient stops ion expansion in a nonquasineutral electron vortex and gives rise to a steady structure with a characteristic scale on the order of r _B. With the electron inertia taken into account in the hydrodynamic approximation, the magnetic vortex structure in a hot plas mamanifests itself in the appearance of a “hole” in the plasma density.     

Single minimum-<Emphasis Type="Italic">B</Emphasis> ambipolar trap

A new type of ambipolar trap is proposed, where a minimum-B magnetic field is used to confine the particles radially and to provide plasma macroscopic stability. The particles are confined axially by creating the plug potentials at both end-mirror cells of the ambipolar trap. The plug potential is produced by only electron cyclotron resonance heating, the mechanism of which is proposed.     

Conformational homogeneity and excited-state isomerization dynamics of the bilin chromophore in phytochrome Cph1 from resonance Raman intensities

The ground-state structure and excited-state isomerization dynamics of the P_r and P_fr forms of phytochrome Cph1 are investigated using resonance Raman intensity analysis. Electronic absorption and stimulated resonance Raman spectra of P_r and P_fr are presented; vibronic analysis of the Raman intensities and absorption spectra reveals that both conformers exist as a single, homogeneous population of molecules in the ground state. The homogeneous and inhomogeneous contributions to the overall electronic broadening are determined, and it is found that the broadening is largely homogeneous in nature, pointing to fast excited-state decay. Franck-Condon displacements derived from the Raman intensity analysis reveal the initial atomic motions in the excited state, including the highly displaced, nontotally symmetric torsional and C₁₅–H HOOP modes that appear because of symmetry-reducing distortions about the C₁₄–C₁₅ and C₁₅=C₁₆ bonds. P_fr is especially well primed for ultrafast isomerization and torsional Franck-Condon analysis predicts a <200 fs P_fr → P_r isomerization. This time is significantly faster than the observed 700 fs reaction time, indicating that the P_fr S₁ surface has a D-ring rotational barrier caused by steric interactions with the protein.     

Splitting of the spectra of MHD waves and the structure of a satellite alfvén resonance in a cold plasma in a strong axial magnetic field and a weak helical field

The possibility is demonstrated of splitting the eigenfrequencies of MHD plasma waves in a stellarator with a weakly rippled helical confining magnetic field. The distribution of the fields of an Alfvén wave in the satellite Alfvén resonance region is investigated when the influence of the helical ripple in a confining magnetic field on the resonance structure is comparable with the effects of the finite ion Larmor radius, electron inertia, and collisions between plasma particles.