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Electron beam for determining plasma potential and charge density as function of radius of inertially confined tenuous plasma cylinder
One of the main approaches to thermonuclear fusion relies on confining high temperature plasmas with properly shaped magnetic fields. The determination of the magnetic topology is, therefore, essential for controlling the experiments and for achieving the required performance. In Tokamaks, the reconstruction of the fields is typically formulated as a free boundary equilibrium problem, described by the Grad-Shafranov equation in toroidal geometry and axisymmetric configurations. Unfortunately, this results in mathematically very ill posed problems and, therefore, the quality of the equilibrium reconstructions depends sensitively on the measurements used as inputs and on the imposed constraints. In this paper, it is shown how the different diagnostics (Magnetics Measurements, Polarimetry and Motional Stark Effect), together with the edge current density and plasma pressure constraints, can have a significant impact on the quality of the equilibrium on JET. Results show that both the Polarimetry and Motional Stark Effect internal diagnostics are crucial in order to obtain reasonable safety factor profiles. The impact of the edge current density constraint is significant when the plasma is in the H-mode of confinement. In this plasma scenario the strike point positions and the plasma last closed flux surface can change even by centimetres, depending on the edge constraints, with a significant impact on the remapping of the equilibrium-dependent diagnostics and of pedestal physics studies. On the other hand and quite counter intuitively, the pressure constraint can severely affect the quality of the magnetic reconstructions in the core. These trends have been verified with several JET discharges and consistent results have been found. An interpretation of these results, as interplay between degrees of freedom and available measurements, is provided. The systematic analysis described in the paper emphasizes the importance of having sufficient diagnostic inputs and of properly validating the results of the codes with independent measurements.
Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the equilibrium fluid toroidal velocity (and the velocity itself) vanishes. Previously [Waltz et al., Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)], we demonstrated with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] gyrokinetic simulations that TAM pinching from (ion pressure gradient supported or diamagnetic level) equilibrium ExB velocity shear could provide some of the residual stress needed to support spontaneous toroidal rotation against normal diffusive loss. Here we show that diamagnetic level shear in the intrinsic drift wave velocities (or ''profile shear'' in the ion and electron density and temperature gradients) provides a comparable residual stress. The individual signed contributions of these small (rho-star level) ExB and profile velocity shear rates to the turbulence level and (rho-star squared) ion energy transport stabilization are additive if the rates are of the same sign. However because of the additive stabilization effect, the contributions to the small (rho-star cubed) residual stress is not always simply additive. If the rates differ in sign, the residual stress from one can buck out that from the other (and in some cases reduce the stabilization.) The residual stress from these diamagnetic velocity shear rates is quantified by the ratio of TAM flow to ion energy (power) flow (M/P) in a global GYRO core simulation of a ''null'' toroidal rotation DIII-D [Mahdavi and Luxon, Fusion Sci. Technol. 48, 2 (2005)] discharge by matching M/P profiles within experimental uncertainty. Comparison of global GYRO (ion and electron energy as well as particle) transport flow balance simulations of TAM transport flow in a high-rotation DIII-D L-mode quantifies and isolates the ExB shear and parallel velocity (Coriolis force) pinching components from the larger ''diffusive'' parallel velocity shear driven component and the much smaller profile shear residual stress component.
An overview of recent results obtained at the tokamak ASDEX Upgrade (AUG) is given. A work flow for predictive profile modelling of AUG discharges was established which is able to reproduce experimental H-mode plasma profiles based on engineering parameters only. In the plasma center, theoretical predictions on plasma current redistribution by a dynamo effect were confirmed experimentally. For core transport, the stabilizing effect of fast ion distributions on turbulent transport is shown to be important to explain the core isotope effect and improves the description of hollow low-Z impurity profiles. The L–H power threshold of hydrogen plasmas is not affected by small helium admixtures and it increases continuously from the deuterium to the hydrogen level when the hydrogen concentration is raised from 0 to 100%. One focus of recent campaigns was the search for a fusion relevant integrated plasma scenario without large edge localised modes (ELMs). Results from six different ELM-free confinement regimes are compared with respect to reactor relevance: ELM suppression by magnetic perturbation coils could be attributed to toroidally asymmetric turbulent fluctuations in the vicinity of the separatrix. Stable improved confinement mode plasma phases with a detached inner divertor were obtained using a feedback control of the plasma β. The enhanced D α H-mode regime was extended to higher heating power by feedback controlled radiative cooling with argon. The quasi-coherent exhaust regime was developed into an integrated scenario at high heating power and energy confinement, with a detached divertor and without large ELMs. Small ELMs close to the separatrix lead to peeling-ballooning stability and quasi continuous power exhaust. Helium beam density fluctuation measurements confirm that transport close to the separatrix is important to achieve the different ELM-free regimes. Based on separatrix plasma parameters and interchange-drift-Alfvén turbulence, an analytic model was derived that reproduces the experimentally found important operational boundaries of the density limit and between L- and H-mode confinement. Feedback control for the X-point radiator (XPR) position was established as an important element for divertor detachment control. Stable and detached ELM-free phases with H-mode confinement quality were obtained when the XPR was moved 10 cm above the X-point. Investigations of the plasma in the future flexible snow-flake divertor of AUG by means of first SOLPS-ITER simulations with drifts activated predict beneficial detachment properties and the activation of an additional strike point by the drifts.
Wendelstein 7-X is the first comprehensively optimized stellarator aiming at good confinement with plasma parameters relevant to a future stellarator power plant. Plasma operation started in 2015 using a limiter configuration. After installing an uncooled magnetic island divertor, extending the energy limit from 4 to 80 MJ, operation continued in 2017. For this phase, the electron cyclotron resonance heating (ECRH) capability was extended to 7 MW, and hydrogen pellet injection was implemented. The enhancements resulted in the highest triple product (6.5 × 10 19 keV m ₋3 s) achieved in a stellarator until now. Plasma conditions [T e (0) ≈ T i (0) ≈ 3.8 keV, τ E > 200 ms] already were in the stellarator reactor-relevant ion-root plasma transport regime. Stable operation above the 2nd harmonic ECRH X-mode cutoff was demonstrated, which is instrumental for achieving high plasma densities in Wendelstein 7-X. Further important developments include the confirmation of low intrinsic error fields, the observation of current-drive induced instabilities, and first fast ion heating and confinement experiments. The efficacy of the magnetic island divertor was instrumental in achieving high performance in Wendelstein 7-X. Symmetrization of the heat loads between the ten divertor modules could be achieved by external resonant magnetic fields. Full divertor power detachment facilitated the extension of high power plasmas significantly beyond the energy limit of 80 MJ.
The thermal equilibrium correlation properties of a magnetically confined pure electron plasma (McPEP) are related to those of a one-component plasma (OCP). The N-particle spatial distribution rho sub s and the Helmholtz free energy F are evaluated for the McPEP to O(lambda sub d-squared/a-squared), where lambda sub d is the thermal de Broglie wavelength and is an interparticle spacing. The electron gyromotion is allowed to be fully quantized while the guiding center motion is quasi-classical. The distribution rho sub s is shown to be identical to that of a classical OCP with a slightly modified potential. To O(lambda sub d-squared/a-squared) this modification does not affect that part of F that is caused by correlations, as long as certain requirements concerning the size of the plasma are met. This theory is motivated by a current series of experiments that involve the cooling of a magnetically confined pure electron plasma to the cryogenic temperature range.
Penning-Malmberg traps confining electron plasmas usually rely on external sources like thermo- and photocathodes. It has been already demonstrated that electron plasmas of comparable densities can be produced by applying a radio-frequency (RF) power to any inner electrode of the trap. Such excitation may result in significant electron heating and ionization of the residual gas with the formation of a plasma column when the RF frequency is of the order or larger than the typical axial bounce frequencies of few-eV electrons, even at RF amplitude of few volts. While discharges are common in plasma generation at higher pressures and RF power, this mechanism is not yet well explored in our working conditions, namely ultra-high vacuum and very low RF power. This plasma production mechanism is very sensitive to the experimental conditions. Interesting phenomena can be observed: transition from a diffuse to a narrow-section, denser plasma column; presence of low-order diocotron modes in transient and steady-state plasmas; modulation of the m=1 diocotron mode and suppression of its instability despite the presence of positive ions and resistive loads. These observations are reported here, and possible explanations are discussed. In addition, a possible electron heating mechanism is investigated with a single-particle, one-dimensional model described by an area-preserving map where an electron bounces within a square potential well and the RF excitation is modelled by a time-oscillating square barrier. The low-energy part of the Poincaré plot includes both quasi-periodic and chaotic regions, where heating up to ionization energies is achievable. Results of a systematic analysis of the map extracting its chaotic properties and scaling laws as a function of the control parameters are reported.
The tokamak scrape-off (the region between the vacuum vessel wall and the magnetically confined fusion plasma edge), represents a source/sink for the hot fusion plasma. The electron densities and temperatures are in the ranges 10 to the 11th - 10 to the 13th/cu cm and 1-40 eV, respectively (depending on the size, magnetic field intensity and configuration, plasma current, etc). In the work reported, the electron temperature and density have been estimated in a Penning ionization discharge by comparing its spectroscopic emission in the VUV with that predicted by a collisional radiative model. An attempt to directly compare this emission with that of the tokamak edge is briefly described.
A study of the effects of drifts on the particle flow pattern and in–out divertor plasma density asymmetry for L-mode and H-mode plasmas is carried out for EAST discharges by the edge plasma transport codes SOLPS and BOUT++. The simulation of L-mode plasmas is done by SOLPS while the simulation of H-mode plasmas is done by BOUT++. The toroidal magnetic field direction for the simulated discharge is artificially reversed in the codes to study the effects of different drift directions on the divertor particle flow pattern and the in–out asymmetry of divertor plasma density. The divertor particle flows induced by diamagnetic and E × B drifts are found to have similar directions in the divertor region for the same discharge. The directions of the flows induced by drifts would be reversed with the reverse of toroidal magnetic field direction. The diamagnetic drift seems to have no effect on the in–out asymmetry of divertor plasma density due to its divergence-free nature. However, the E × B drift could result in a pronounced asymmetry of plasma density between the inner and outer divertor targets. The density in–out asymmetry caused by E × B drift is reversed with the reverse of E × B drift flow direction. Detailed analysis shows that the radial component of the E × B drift flow is the main cause of density asymmetry. The results from the simulation of H-mode plasmas with BOUT++ are similar to those of the L-mode plasmas with SOLPS except that the drift effects seem to be slightly larger in the H-mode plasmas compared to the L-mode plasmas.
The coupling between the transport and magnetic topology is an important issue because the structure of magnetic islands, embedded in a toroidal equilibrium field, depends on the nature of the transport at the edge of the islands. Measurements of modulated heat pulse propagation in the DIII-D tokamak have revealed the existence of self-regulated oscillations in the radial energy transport into magnetic islands that are indicative of bifurcations in the island structure and transport near the q = 2 surface. Large amplitude heat pulses are seen in one state followed by small amplitude pulses later in the discharge resulting in a repeating cycle of island states. These two states are interpreted as a bifurcation of magnetic island with high and low heat pulse accessibility. In conclusion, this report describes the discovery of a bifurcation in the coupled dynamics between the transport and topology of magnetic islands in tokamak plasmas.
Plasma relaxation inside a highly conducting cylindrical boundary is studied both experimentally and computationally. Dynamics are initiated by the introduction of two equal helicity spheromaks at either end of the cylinder. In the experiment, dense, high-magnetic-flux spheromaks are injected into the flux conserving volume with magnetized plasma guns. In the simulation, identical spheromaks initially occupy both halves of the cylinder and a perturbation is introduced. Merging commences with a single three-dimensional null-point that moves radially out of the flux conserving volume at velocities up to 0.2 of the reconnection outflow velocity. Relaxation to the minimum energy state occurs in about ten Alfven times. An important conclusion is that even though the dynamical activity is limited to a few modes, this activity is sufficient to promote relaxation to the final, minimum energy state. The dynamical activity appears to conserve magnetic helicity while magnetic energy is converted to flow and heat. The final state arrived at dynamically is identical to that described by C. D. Cothran et al. [Phys. Rev. Lett. 103, 215002 (2009)] using static, eigenvalue analysis.
Indirectly driven inertial confinement fusion (ICF) rests on the setting up of a radiation temperature within a laser cavity and on the optimization of the capsule implosion ablated by this radiation. In both circumstances, the ablation of an optically thick medium is at work. The nonlinear radiation conduction equations that describe this phenomenon admit different kinds of solutions called generically Marshak waves. In this paper, a completely analytic model is proposed to describe the ablation in the subsonic regime relevant to ICF experiments. This model approximates the flow by a deflagrationlike structure where Hugoniot relations are used in the stationary part from the ablation front up to the isothermal sonic Chapman-Jouguet point and where the unstationary expansion from the sonic point up to the external boundary is assumed quasi-isothermal. It uses power law matter properties. It can also accommodate arbitrary boundary conditions provided the ablation wave stays very subsonic and the surface temperature does not vary too quickly. These requirements are often met in realistic situations. Interestingly, the ablated mass rate, the ablation pressure, and the absorbed radiative energy depend on the time history of the surface temperature, not only on the instantaneous temperature values. The results compare very well with self-similar solutions and with numerical simulations obtained by hydrodynamic code. This analytic model gives insight into the physical processes involved in the ablation and is helpful for optimization and sensitivity studies in many situations of interest: radiation temperature within a laser cavity, acceleration of finite size medium, and ICF capsule implosion, for instance.
The effect of energetic electrons on dust charging for different types of dust is studied in hydrogen plasma. The hydrogen plasma is produced by hot cathode filament discharge method in a dusty plasma device. A full line cusped magnetic field cage is used to confine the plasma elements. To study the plasma parameters for various discharge conditions, a cylindrical Langmuir probe having 0.15 mm diameter and 10.0 mm length is used. An electronically controlled dust dropper is used to drop the dust particles into the plasma. For different discharge conditions, the dust current is measured using a Faraday cup connected to an electrometer. The effect of secondary emission as well as discharge voltage on charging of dust grains in hydrogen plasma is studied with different dust.
No abstract prepared.
Particle balance is investigated using a Mach probe at the top of the scrape-off layer of circular ohmically heated L-mode plasmas in the Tore Supra tokamak [G. Giruzzi etal., Nucl. Fusion 49, 104010 (2009)]. Contributions from both poloidal EXB flows and ionization sources are found to be small. As a result the local parallel flow is a response of the radial flux distribution between the two strike points of open field lines, and the density profile is determined by the field-line-integrated radial flux. By scanning the poloidal position of the strike point on a secondary limiter situated at the outboard midplane, an indirect poloidal mapping of the radial flux distribution is obtained. The radial flux is centered at the outboard midplane and is relatively well described by a Gaussian distribution of half poloidal width of about 50 Degree-Sign at the last closed flux surface, decaying to about 30 Degree-Sign in the far scrape-off layer. The turbulent radial flux measured locally with a rake probe shows a reasonable agreement with the poloidal mapping obtained by the Mach probe. It is shown than the radial convective velocity decays along radius at the plasma top but should increase with radius at the outboard midplane.
Magnetohydrodynamic instabilities of high-mode (H-mode) pedestal are investigated in this paper with the inclusion of bootstrap current for equilibrium and rotation for stability. The jointed European torus-like equilibria of H-mode discharges are generated numerically using the VMEC code. It is found that, when the bootstrap current is taken into account, a safety-factor reversal or plateau can be generated near plasma edge. This confirms previous results of numerical equilibrium reconstructions using other types of codes. The n = 1 magnetohydrodynamic instabilities, where n is toroidal mode number, are investigated numerically in this type of equilibria using the AEGIS code. It is found that the infernal type harmonic can prevail at safety-factor reversal or plateau region. The toroidal plasma rotation effect with low Mach number is investigated. The numerical results show that the mode frequency is close to the rotation frequency at pedestal top, when the value of safety factor at plateau is slightly above a rational number. This mode frequency range seems to coincide with the experimentally observed frequencies of n = 1 edge harmonic oscillations (or outer modes) at the quiescent H-mode discharges.
The spherical torus edge region is among the most challenging regimes for plasma turbulence simulations. Here, we measure the spatial and temporal properties of ion-scale turbulence in the steep gradient region of H-mode pedestals during edge localized mode-free, MHD quiescent periods in the National Spherical Torus Experiment. Poloidal correlation lengths are about 10 ρ{sub i}, and decorrelation times are about 5 a/c{sub s}. Next, we introduce a model aggregation technique to identify parametric dependencies among turbulence quantities and transport-relevant plasma parameters. The parametric dependencies show the most agreement with transport driven by trapped-electron mode, kinetic ballooning mode, and microtearing mode turbulence, and the least agreement with ion temperature gradient turbulence. In addition, the parametric dependencies are consistent with turbulence regulation by flow shear and the empirical relationship between wider pedestals and larger turbulent structures.
Fluid Reynolds stress from turbulence has usually been considered to be responsible for the anomalous toroidal momentum transport in tokamak plasma. Experiment by Müller et al. [Phys. Rev. Lett. 106, 115001 (2011)], however, reported that neither the observed edge rotation profile nor the inward momentum transport phenomenon at the edge region of an H-mode plasma could be explained by the fluid Reynolds stress measured with reciprocating Langmuir-probe. The full-function gyrokinetic code XGC1 is used to explain, for the first time, Müller et al.'s experimental observations. It is discovered that, unlike in the plasma core, the fluid Reynolds stress from turbulence is not sufficient for momentum transport physics in plasma edge. The “turbulent neoclassical” physics arising from the interaction between kinetic neoclassical orbit dynamics and plasma turbulence is key in the tokamak edge region across the plasma pedestal into core.