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The problem of power exhaust is one of the grand challenges of nuclear fusion research today. In order to understand the physics phenomena occurring in the scrape-off layer and the divertor regions of tokamaks, it is essential to correctly determine the divertor plasma parameters, which are often measured by swept Langmuir probes (LPs). While the construction and operation of this diagnostic can be straightforward, the data analysis using three- or four-parameter fits presents a challenge and can potentially lead to erroneous values of electron temperature and ion saturation current. In this work, we present modelling and experiments aimed at determination of conditions for proper analysis of swept LPs using these two fitting models. Particle-in-cell modelling was employed to evaluate the sheath-expansion effects for particular probe geometry and plasma conditions, yielding a semi-empirical rule capable of predicting its magnitude. Experiments with unusually wide range of swept voltage in the divertor of the COMPASS tokamak explored the magnitude of voltage range required for successful analysis with either three or four-parameter fitting. With the use of our new semi-empirical rule, it is possible to improve the four-parameter fit reliability in situations where the available voltage range is limited. In addition, we introduce the tangent method—an independent and fast method of electron temperature estimation, which allows to reliably determine the available voltage range and as such assist more complex methods of probe analysis.

Two identical neutral beam injectors (NBIs) have been installed on the COMPASS tokamak. Each of them is capable of producing a deuterium (or hydrogen, helium) neutral beam with nominal power of up to 400 kW at 40 keV. Since the COMPASS tokamak is a compact machine, the design of the neutral beams was carefully optimized to fit the neutral beam through the narrow ports of the tokamak. However, once the neutral beams are operated out of the scope of their optimal parameters, additional power losses occur due to neutral beam scraping. This article investigates the amount of power loss due to neutral beam scraping. The losses are calculated using the neutral beam models and measured neutral beam parameters. The calculated results are compared with the measured power delivered into the plasma. Two different neutral beam models are employed. One describes the neutral beam as a sum of small beamlets, which are Gaussian-like. The second one describes the neutral beam as a single Gaussian beam. The amount of the power lost to scraping is determined by both models and compared. Neutral beam parameters, the input parameters for both models, are derived from the Doppler-shifted spectra emitted by fast neutral atoms. It is shown that when operating NBIs at nominal parameters, the scraping losses are negligible ( < 5% ). If the NBIs are operated too far from the nominal parameters, the scraping losses can reach up to ∼60% of the NBI output power. As the highest fractional losses occur with low power NBI, the beam duct is capable of withstanding the corresponding power loads. The expected auxiliary heating power P A U X , the power entering the tokamak chamber carried by fast neutrals, is benchmarked against the additional plasma input power observed in the measured plasma parameters P N B I . The additional plasma input power P N B I is derived from the plasma power balance. The power balance terms are independent of the neutral beam model used for the auxiliary heating power calculation P A U X . The results of the power balance evaluation reveal a difference between two NBIs installed on COMPASS. One of the injectors systematically delivers 17% less power than the other into the plasma given the same beam parameters. It is concluded that the additional losses occur before the beam enters the tokamak chamber.

COMPASS addressed several physical processes that may explain the behaviour of important phenomena. This paper presents results related to the main fields of COMPASS research obtained in the recent two years, including studies of turbulence, L–H transition, plasma material interaction, runaway electron, and disruption physics: Tomographic reconstruction of the edge/SOL turbulence observed by a fast visible camera allowed to visualize turbulent structures without perturbing the plasma. Dependence of the power threshold on the X-point height was studied and related role of radial electric field in the edge/SOL plasma was identified. The effect of high-field-side error fields on the L–H transition was investigated in order to assess the influence of the central solenoid misalignment and the possibility to compensate these error fields by low-field-side coils. Results of fast measurements of electron temperature during ELMs show the ELM peak values at the divertor are around 80% of the initial temperature at the pedestal. Liquid metals were used for the first time as plasma facing material in ELMy H-mode in the tokamak divertor. Good power handling capability was observed for heat fluxes up to 12 MW m−2 and no direct droplet ejection was observed. Partial detachment regime was achieved by impurity seeding in the divertor. The evolution of the heat flux footprint at the outer target was studied. Runaway electrons were studied using new unique systems—impact calorimetry, carbon pellet injection technique, wide variety of magnetic perturbations. Radial feedback control was imposed on the beam. Forces during plasma disruptions were monitored by a number of new diagnostics for vacuum vessel (VV) motion in order to contribute to the scaling laws of sideways disruption forces for ITER. Current flows towards the divertor tiles, incl. possible short-circuiting through PFCs, were investigated during the VDE experiments. The results support ATEC model and improve understanding of disruption loads.

This article introduces a concept based on flush-mounted probes embedded in the limiters of the COMPASS-Upgrade tokamak. Main issues related to flush probe geometry are taken into account and discussed. Calculations of heat fluxes and the incident angle of the field lines on the different limiters using the PFCflux code are performed to support in probe arrangement optimization. Model current-voltage characteristics for a flush probe are simulated using the SPICE2 code and their dependence on the angle of incidence is studied. The results are used to predict the current to be collected by the flush probes for different magnetic fields and to examine the reliability of the proposed diagnostics. A discussion is included on the capability of the electronic system considered for the measurements.

The presented experimental study realized in the COMPASS tokamak demonstrates, for the first time, that the current density that flows from the plasma into the vacuum vessel during disruptions is limited by the ion particle flux. Such a limitation shows that, at least in COMPASS, the sheath that forms between the plasma and the first wall dominates the halo current flow. This observation is achieved by measuring simultaneously the ion saturation current with negatively biased Langmuir probes and the halo current with grounded probes to the vacuum vessel. These comparative measurements, which were never performed during disruptions in other machines, directly confirm that the halo current density remains below the ion particle flux in COMPASS. The study also shows, using Mirnov coils measurement, that the total electric current entering the wall grows with the plasma current while the current density obtained by Langmuir probes remains unaffected. This, together with the current density limitation, leads to a novel finding that the halo current width increases with the pre-disruptive plasma current, which limits the local forces. The new findings reported here could also provide potential constraints on the modeling of disruption-induced loads on future reactor scale tokamaks and motivation for further experiments on existing devices.

This paper presents measurements of the plasma turbulence with an emphasis on the ion temperature fluctuations in comparison to the electron temperature and the ion saturation current fluctuations in the edge of the COMPASS tokamak. The ion temperature values are obtained by using a fast swept ball-pen probe, with temporal resolution up to 10 µs, accompanied by independent 1 µs measurements of the electron temperature and ion saturation current. The experimental results obtained for a wide range of line-averaged densities show that statistical properties of the fluctuations are in good agreement with a form of beta or gamma distribution function. In addition, the dependence of the averaged ion and electron temperatures on the line-averaged density is studied in the near and main scrape off layer region.

Objective The aim of the study was to quantify the differences in viscosity of over a range of commercial food-based formulas and home-prepared blenderized feeds used for enteral feeding in the clinical management of gastroesophageal reflux and gastroesophageal reflux-related aspiration in children with oropharyngeal dysphagia. Methods The viscosity of commercial and home blends was measured using digital rotational viscometer and International Dysphagia Diet Standardization Initiative Syringe Flow Test. Additional testing was performed to determine the impact of added cereal, water flushes, and freezing/thawing on formula viscosity. Results There were significant variations in viscosity between commercial blends with values ranging from extremely to mildly thick by Syringe Flow Test. The highest centipoise (cP) value was 13,847 and the lowest 330 and 438 cP. Dilution of 240 mL of commercial blend with 30, 60, and 90 mL of water resulted in a decrease in viscosity of 31%, 62%, and 85%, respectively. Exposure to 1 freeze/thaw cycle decreased viscosity by as much as 59% to 80% depending on the blend. Thickening conventional pediatric formulas with rice or oatmeal did not achieve consistency equivalent to most blenderized feeds. Conclusions Commercial food-based formulas and home prepared blends vary greatly in viscosity, ranging from thin to extremely thick liquids, with the majority achieving viscosity greater than thickened formula. Viscosity is reduced by addition of free water and with freezing and thawing. These data can inform the clinical choice of feeding regimen depending on the goals of nutritional therapy.

Scintillation detectors are widely used for hard X-ray spectroscopy and allow us to investigate the dynamics of runaway electrons in tokamaks. This diagnostic tool proved to be able to provide information about the energy or the number of runaway electrons. Presently it has been used for runaway studies at the GOLEM and the COMPASS tokamaks. The set of scintillation detectors used at both tokamaks was significantly extended and improved. Besides NaI(Tl) (2 × 2 inch) scintillation detectors, YAP(Ce) and CeBr3 were employed. The data acquisition system was accordingly improved and the data from scintillation detectors is collected with appropriate sampling rate (≈300 MHz) and sufficient bandwidth (≈100 MHz) to allow a pulse analysis. Up to five detectors can currently simultaneously monitor hard X-ray radiation at the GOLEM. The same scintillation detectors were also installed during the runaway electron campaign at the COMPASS tokamak. The aim of this contribution is to report progress in diagnostics of HXR radiation induced by runaway electrons at the GOLEM and the COMPASS tokamaks. The data collected during the 12th runaway electron campaign (2020) at COMPASS shows that count rates during typical low-density runaway electron discharges are in a range of hundreds of kHz and detected photon energies go up to 10 MeV (measured outside the tokamak hall). Acquired data from experimental campaigns from both machines will be discussed.

Background While many people with overweight or obesity can lose weight temporarily, most have difficulty maintaining weight loss over the long term. Studies of dietary composition typically focus on weight loss, rather than weight-loss maintenance, and rely on nutrition education and dietary counseling, rather than controlled feeding protocols. Variation in initial weight loss and insufficient differentiation among treatments confound interpretation of results and compromise conclusions regarding the weight-independent effects of dietary composition. The aim of the present study was to evaluate three test diets differing in carbohydrate-to-fat ratio during weight-loss maintenance. Design and dietary interventions Following weight loss corresponding to 12 ± 2% of baseline body weight on a standard run-in diet, 164 participants aged 18 to 65 years were randomly assigned to one of three test diets for weight-loss maintenance through 20 weeks (test phase). We fed them high-carbohydrate (60% of energy from carbohydrate, 20% fat), moderate-carbohydrate (40% carbohydrate, 40% fat), and low-carbohydrate (20% carbohydrate, 60% fat) diets, controlled for protein content (20% of energy). During a 2-week ad libitum feeding phase following the test phase, we assessed the effect of the test diets on body weight. Outcomes The primary outcome was total energy expenditure, assessed by doubly-labeled water methodology. Secondary outcomes included resting energy expenditure and physical activity, chronic disease risk factors, and variables to inform an understanding of physiological mechanisms by which dietary carbohydrate-to-fat ratio might influence metabolism. Weight change during the ad libitum feeding phase was conceptualized as a proxy measure of hunger.

A python package, called Tomotok, focused on performing tomographic inversion of tokamak plasma radiation is being developed at the Institute of Plasma Physics of the Czech Academy of Sciences. It aims at providing multiple inversion algorithms with an user friendly interface. In order to enable and ease performing tomographic inversion on different devices worldwide, it is planned to publish this software as open source in the near future. In this contribution, the package structure allowing an easy implementation of various tokamak and diagnostic geometries is described and an overview of the package contents is given. Apart from inversion methods, overview of Tomotok auxiliary content is given. The package provides tools for creating simple synthetic diagnostic system. These can be used for testing and benchmarking the code. This includes tools for building geometry matrices that describe the view of detectors using single line of sight approximation and artificial data generators capable of creating simple or hollow Gaussian profiles. The implemented inversion methods cover the minimum Fisher regularisation, biorthogonal decomposition and linear algebraic methods. The implementation of each method is explained, example results obtained by inverting phantom models are presented and discussed. The computation speed of implemented algorithms is benchmarked and compared.

The paper describes the conceptual design of the COMPASS Upgrade (COMPASS-U) tokamak which represents a compact, medium-size, high-magnetic-field and high-density device with a flexible set of poloidal field coils for generation of single, double null and snowflake configurations. In addition, COMPASS-U will be equipped with a closed divertor, which will be operated at high plasma and neutral density and with high optical opacity similar to future reactors. COMPASS-U is capable of addressing some of the key challenges in the field of the plasma exhaust physics, reactor-relevant edge plasma physics, advanced confinement regimes, advanced magnetic configurations and materials for next-step devices. The conceptual design of the individual COMPASS-U systems is presented with emphasis on magnets, support structure and power supply system enhancement.

Objective To determine whether clinical and patient-reported outcomes differ in children receiving blenderized diets compared with conventional formula. Study design We conducted a prospective cohort study of 70 children aged 1-18 years receiving blenderized diets vs conventional formula via feeding tube. We assessed rates of hospitalization and visits to the emergency department (ED) at Boston Children's Hospital in 2017 and Likert scale addressing satisfaction with feeding regimen; Pediatric Gastroesophageal Reflux Disease Symptom and Quality of Life Questionnaire; Pediatric Quality of Life Inventory; and Pediatric Quality of Life Inventory Gastrointestinal Symptoms Scale. Results Participants receiving blenderized diets (n = 42, 60%) did not differ in demographics or comorbid diagnoses from those receiving conventional formula (n = 28, 40%). Rates of total visits to the ED (0.8 ± 1.5 vs 1.4 ± 2.7, P = .05), total admissions (0.8 ± 1.2 vs 1.7 ± 2.3, P = .01), and respiratory-related admissions (0.2 ± 0.5 vs 0.6 ± 0.8, P = .04) per year were significantly lower in participants receiving blenderized diets, and respiratory-related visits to the ED trended toward significance (0.1 ± 0.4 vs 0.4 ± 0.8, P = .08). Compared with those receiving conventional formula, participants on blenderized diets reported greater satisfaction ratings (Likert scale 4.3 ± 1.0 vs 3.3 ± 1.2, P = .001), lower symptom (0.7 ± 0.8 vs 1.2 ± 1.1, P = .03), and total (0.8 ± 0.8 vs 1.2 ± 1.0, P = .02) scores on Pediatric Gastroesophageal Reflux Disease Symptom and Quality of Life Questionnaire and greater scores on the Pediatric Quality of Life Inventory Gastrointestinal Symptoms Scale, indicating less nausea and vomiting (64.0 ± 22.6 vs 49.0 ± 37.9, P = .02), abdominal pain (65.0 ± 26.8 vs 56.4 ± 33.9, P = .04), diarrhea (87.9 ± 15.5 vs 73.6 ± 26.3, P = .004), and fewer total symptoms (70.2 ± 16.3 vs 62.3 ± 19.6, P = .03). Conclusions Blenderized diets are associated with decreased healthcare use, improved symptom scores, and increased patient satisfaction compared with conventional formulas.

Objective To examine associations of baseline insulin dynamics with changes in body composition and resting energy expenditure (REE) following weight loss.

We sought to characterize the effects of dietary macronutrient composition on various hormones implicated in the regulation of insulin sensitivity (IS) and energy expenditure (EE). Following 10–15% weight loss, 21 overweight subjects consumed 3 weight-loss maintenance diets [low fat (LF), low glycemic index (LGI) and very low carbohydrate (VLC)] in random order, each for 4 weeks. At baseline and at the end of each treatment period, fasting samples for fibroblast growth factor (FGF)-21, heme-oxygenase-1 (HO-1), chemerin, irisin, secreted frizzle-related protein (SFRP-4), total bile acids, ghrelin, gastrin inhibitory peptide (GIP), peptide-Y, and amylin; hepatic and peripheral IS; and EE were obtained. Analyses were controlled for age, gender, baseline body mass index, and diet sequence. FGF-21 decreased (P

The development of the plasma diagnostic and control (D&C) system for a future tokamak demonstration fusion reactor (DEMO) is facing unprecedented challenges. The DEMO D&C system has to operate with very high reliability, since any loss of plasma control may result in machine damage. On the same time, high accuracy of the D&C system is needed in order to allow for plasma operation near operational limits, where the fusion power is maximized. The implementation and performance of diagnostic components is however limited by space restrictions (optimization of the tritium breeding rate; integrity of the first wall and divertor against loads), and by adverse effects acting on the front-end components (neutron and gamma radiation, heat loads, erosion and deposition). Finally, the capabilities of the available actuators (poloidal field coils, external heating and fueling) are limited as well. As part of the European DEMO conceptual design studies, the development of the D&C system has recently been launched [1]. A preliminary suite of candidate diagnostics for DEMO have been selected, aiming to cover all the main plasma control quantities with some redundancy, and choosing types and locations for diagnostic front-end components such that long-term durability with minimum need for maintenance can be expected under typical loads (e.g. neutron radiation, particle fluxes and fluencies). Specifically, only robust metallic or ceramics diagnostic components shall be used inside the vacuum vessel, while the more sensitive components shall be located at more remote (protected) positions. This initial plasma diagnostic suite comprises microwave diagnostics, magnetic coil based and Hall sensors, passive spectroscopy and radiation power measurements, divertor thermo-current measurement, infrared interferometry/polarimetry and neutron-gamma measurements. In the first R&D phase the possibilities and conditions for integration of diagnostic sightlines and front-end components into the machine have been investigated, and an understanding of the required number of channels and components has been obtained. The conditions for controllability of the DEMO plasma are being analyzed by numerical simulations. To this purpose, the transport modelling code ASTRA, coupled to a radiation module, has been connected to the Simulink simulation framework, and the performance properties of diagnostics and actuators are being added [2]. Similarly, the existing CREATE equilibrium code is being amended to include limitations of diagnostics and actuators, such that the controllability e.g. of fast VDEs can be simulated under DEMO relevant settings. Furthermore, predictive control oriented models such as RAPTOR are being further developed as an alternative approach to analyze the controllability of DEMO. The common goal is to arrive at numerical simulations which closely mimic the control of the DEMO plasma such that the controllability based on the available diagnostics and actuators can be demonstrated quantitatively. Based on these R&D results, an initial version of the DEMO diagnostic and control concept has been elaborated and will be presented in this paper.

The Molten Salt Reactor (MSR) – SPHINX (SPent Hot fuel Incinerator by Neutron fluX) concept is dealing with the solution of a principle problem of sustainable development of nuclear power – current reactors spent fuel treatment by means of nuclear incineration. It means burning of fissionable part of its inventory and transmutation of other radionuclides by use of nuclear reactions with neutrons in an MSR – SPHINX system. In the SPHINX R&D program, there are besides computational analyses also experimental activities involved in the program, which serves for a verification of design inputs for designing of a demonstration unit of the MSR-type. The experimental program EROS will focus on a large-scale experimental verification of design inputs by use of MSR-type inserting zones into the existing light water moderated experimental reactor LR-0, which may allow to modify it to experimental zero power salt reactor SR-0. There will be a detail description of the proposed program given in the paper together with the so far performed experiments and their preliminary results.

To examine associations of baseline insulin dynamics with changes in body composition and resting energy expenditure (REE) following weight loss.Twenty-one participants with overweight or obesity achieved 10-15% weight loss and then received 3 weight loss maintenance diets (high-carbohydrate, moderate-carbohydrate, and low-carbohydrate) in random order, each for 4 weeks. Body composition was measured at baseline and after weight loss. Insulin 30 min after glucose consumption (insulin-30; insulin response), C-peptide deconvolution analysis, HOMA, hepatic insulin sensitivity (IS), and REE were assessed at baseline and after each maintenance diet.Insulin-30, but not maximal insulin secretion, hepatic IS, or HOMA, predicted changes in fat mass (standardized β = 0.385, 1.7 kg difference between 10th and 90th centile of insulin-30, P = 0.04) after weight loss. Insulin-30 (β = -0.341, -312 kcal day(-1) , P = 0.008), maximal insulin secretion (β = -0.216, -95 kcal day(-1) , P = 0.0002), HOMA (β = -0.394, -350 kcal day(-1) , P = 0.002), and hepatic IS (β = 0.217, 225 kcal day(-1) , P = 0.0003) predicted change in REE during weight loss maintenance, independent of changes in body composition. The inverse relationship between insulin-30 and REE was substantially attenuated when the low-carbohydrate diet was consumed first.These findings distinguish a novel phenotype, characterized by high insulin response, at risk for weight regain, and identify a dietary approach to ameliorate this risk.

The direct method of integration of the operator Heisenberg equations of motion is extended to the solution of quantum tunneling when the central potential is a sum of inverse powers of the radial distance. By obtaining the equation of motion for the Weyl-ordered basis set {l_brace}{ital S}{sub {ital m},{ital n}}({ital t}){r_brace} formed from {ital r}({ital t}) and {ital p}{sub {ital r}}({ital t}), one can express the time evolution of any member of the set as an infinite sum involving the operators {l_brace}{ital S}{sub {ital m},{ital n}}(0){r_brace}. The direct integration enables one to find the expectation values of the radial position operator and its conjugate momentum and higher moments of these operators as functions of time. {copyright} {ital 1996 The American Physical Society.}

Particles and heat transport in the scrape-off layer (SOL) of tokamaks is not yet fully understood. COMPASS is a small-size tokamakp where the edge plasma is well diagnosed in view of studying the competition between the parallel and the cross-field transport in the SOL. In order to better characterize SOL dynamics, in particular the poloidal asymmetry of the main parameters' radial profiles, two new in-situ magnetically driven reciprocating manipulators have been recently installed in COMPASS. These manipulators, the so-called pecker probes, are two additional poloidal measurement points to the existing two (vertical and horizontal) reciprocating manipulators. The pecker probes are located at the low field side of COMPASS at ±47.5o with respect to the outer mid-plane and are equipped with identical tunnel probe heads, providing simultaneous measurements of the ion saturation current density Jsat, the electron temperature Te and the parallel Mach number M// with high temporal resolution. In this paper, a detailed description of the pecker probe system in COMPASS is described and first measurements are presented.

A wave equation formulation of the problem of quantum tunneling in a dissipative medium is developed by considering a many-body system in which the central particle is subject to an arbitrary force law, and at the same time is coupled to a bath of noninteracting harmonic oscillators. For the motion of the central particle it is possible to obtain an effective Lagrangian and Hamiltonian by eliminating the degrees of freedom of the oscillators. However both of these operators are nonlocal, and it is difficult to derive a wave equation for this motion. As an alternative method one can write a many-body Schrödinger equation for the whole system, and then eliminate the wave functions of all of the oscillators. This result is a many-channel Schrödinger equation for the motion of the central particle. By truncating this set of coupled equations, one can solve the problem for different force laws. In particular, in this work, the cases of dissipative tunneling, hopping, and quantum coherence are studied in detail. It is also shown how this approach can be generalized to multidimensional dissipative systems.

Small tokamaks may significantly contribute to the better understanding of phenomena in a wide range of fields such as plasma confiement and energy transport; plasma stability in different magnetic configurations; plasma turbulence and its impact on local and global plasma parameters; processes at the plasma edge and plasma‐wall interaction; scenarios of additional heating and non‐inductive current drive; new methods of plasma profile and parameter control; development of novel plasma diagnostics; benchmarking of new numerical codes and so on. Furthermore, due to the compactness, flexibility, low operation costs and high skill of their personnel small tokamaks are very convenient to develop and test new materials and technologies. Small tokamaks are suitable and important for broad international cooperation, providing the necessary environment and manpower to conduct dedicated joint research programmes. In addition, the experimental work on small tokamaks is very appropriate for the education of students,...

Localised ion temperature measurements can only be performed with special electric probes where the electron component of the current is kept off from the collector. In a strong magnetic field the effect can be utilised that the electron gyro-radius is much smaller than that of the ions. This method was developed by Katsumata and Okazaki (Japan J. Appl. Phys. 6, 123 (1967)). We have used a so-called tunnel probe (which consists of a conductive tunnel, terminated by an isolated back plate) by adding a diaphragm in front. Thereby the tunnel is prevented from incident electrons at any potential of both electrodes. By sweeping the potential across the tunnel, the perpendicular ion temperature can be inferred. By segmenting the tunnel axially in two parts also the parallel ion temperature can be determined. When the electrodes are biased to ion saturation, the ratio between the ion currents, which reach the first and the second segment, respectively, is a measure for the parallel ion temperature. The dependence of the ratio of the currents has to be determined by a PIC simulation.

Experiments in the tokamaks TEXTOR, CASTOR, T-10 and ISTTOK, as well as in the reversed field pinch RFX have provided new and complementary evidence on the physics of the universal mechanism of E×B velocity shear stabilization of turbulence, concomitant transport barrier formation and radial conductivity by using various edge biasing techniques. In TEXTOR the causality between transport reduction and induced electric fields in the edge has been for the first time clearly demonstrated. The high electric field gradients have been identified as the cause for the quenching of turbulent cells. A quantitative analysis of the measured transport reduction is in good agreement with theoretical predictions. The scaling of plasma turbulence suppression with velocity shear has been established, revealing the density-potential cross-phase as a key element. Reduction in poloidal electric field, temperature, and density fluctuations across the shear layer lead to a reduction of the anomalous conducted and convected heat fluxes resulting in an energy transport barrier that is measured directly. In CASTOR the biasing electrode is placed at the separatrix in a non-intrusive configuration which has demonstrated strongly sheared electric fields and consequent improvement of the global particle confinement, as predicted by theory. The impact of sheared E×B flow on edge turbulent structures has been measured directly using a comprehensive set of electrostatic probe arrays as well as emissive probes. Measurements with a full poloidal Langmuir probe array have revealed quasi-coherent electrostatic waves in the SOL with a dominant mode number equal to the edge safety factor. In T-10 edge biasing is clearly improving the global performance of ECR heated discharges. Reflectometry and heavy ion beam probe measurements show the existence of a narrow plasma layer with strong suppression of turbulence. On ISTTOK, the influence of alternating positive and negative electrode and (non-intrusive) limiter biasing has been compared. Electrode biasing is found to be more efficient in modifying the radial electric field Er and confinement, limiter biasing acting mainly on the SOL. In the RFX reversed field pinch it has been demonstrated that also in RFPs biasing can increase the local E×B velocity shear in the edge region, and hence substantially reduce the local turbulence driven particle flux mainly due to a change in the relative phase between potential and density fluctuations.

A direct integration of the Heisenberg equations of motion yields expansions of the position and momentum operators x(t) and p(t), each as an infinite series in terms of the initial Weyl-ordered basis set {${\mathit{S}}_{\mathit{m},}$n} formed from x(0) and p(0), with c-number time-dependent coefficients. This method is applied to the problem of tunneling in a symmetric and an asymmetric quartic potential. The expectation values of the position and momentum operators with minimum uncertainty wave packet 〈0\ensuremath{\Vert}x(t)\ensuremath{\Vert}0〉 and 〈0\ensuremath{\Vert}p(t)\ensuremath{\Vert}0〉 can be calculated accurately for a maximum time that is short compared to the period of oscillation of the wave packet. From the result of this calculation, with the help of Prony's method one can determine the level spacings for the low-lying states. In addition, in this formulation the wave packet retains its shape; therefore, one can study the trajectory 〈0\ensuremath{\Vert}x(t)\ensuremath{\Vert}0〉 and 〈0\ensuremath{\Vert}p(t)\ensuremath{\Vert}0〉 as the quantal analogue of the motion of the system in phase space.

Spectral amplitudes and theoretical seismograms in the vicinity of caustic and critical points are evaluated numerically for acoustic waves propagating in Epstein media. The amplitude decay into the region beyond the caustic is compared with the asymptotic results and good agreement is found at high frequency. At low frequencies the partial reflection enhances the amplitudes at sub-critical angles and the amplitude increases with decreasing thickness of the transition zone. For a thin transition and low frequencies a head wave exists whose amplitude is inversely proportional to frequency. The study of amplitudes near caustics and critical point is of significant theoretical and experimental interest to seismologists. Improved coverage by stations of the USCGS worldwide network has provided better data and their interpretation has lead to more accurate estimates of elastic wave velocities within the Earth (Johnson 1967). In regions of high velocity gradient in the upper mantle caustics are formed and triplications occur on the travel-time curves. In this paper the amplitude properties near caustics and critical point are studied for the Epstein velocity transitions (Epstein 1930). Epstein profiles represent a group of models with transition zones for which solutions of the wave equation exist in terms of familiar tabulated functions. Wave propagation has also been studied analytically for linear transition layers (Nakamura 1964; Gupta 1966; Hirasawa & Berry 1971; Ward 1973) and exponential and parabolic layers (Merzer 1971 ; Rydbeck 1943). Linear layers have discontinuities in velocity gradient which may not be realistic. Merzer’s study is concerned only with head waves and their amplitude dependence on frequency, layer thickness and shape of the transition. Using Epstein models the caustics, head waves and shadow can be studied. Epstein (1930), Rawer (1939) and Phinney (1970) studied the modulus of the reflection coefficient in order to estimate the partial reflection. The modulus of the reflection coefficient itself, however, cannot give a full description of the energy propagation when the waves interact with the strong velocity gradient. That can only be studied when the spectral amplitudes and theoretical seismograms are evaluated. In this paper the exact spectral amplitudes are computed by contour integration using the method of Phinney & Cathles (1969). For evaluation of the theoretical seismograms the technique of Chapman & Phinney (1972) is employed. The amplitude curves are evaluated in the neighbourhood of both ends of the triplication. At high frequencies the results agree with the asymptotic results. At low

The Gel'fand–Levitan theory is applied to obtain the exact potential function for an atomic or a molecular system when the solution of the Schrodinger equation with a reference potential which is close to the actual potential is known. With this method one can construct bound state equivalent local potentials, or potentials which, for large quantum numbers, have spectra similar to that of the reference potential. In one-dimensional problems the resulting potentials are not generally symmetric about the origin, even if one starts with symmetric reference potentials. This lack of symmetry is due to the presence of additional terms in the Hamiltonian which are of purely quantal origin, and therefore in any semiclassical treatment become negligible. This observation leads one to investigate the relationship between the spectrum of a given system and the symmetry of the underlying Hamiltonian. Examples are given to show that the dynamical symmetries usually associated with the spectral properties do not necessarily follow from the Gel'fand–Levitan inverse theory, but can be imposed as constraints on the solution. Additional constraints on the form of the two-body wave function also arise from the observable transition rates for atom–molecule collisions and for the interaction of the charged particles in the system with an external electromagnetic field.

In the derivation of the Lippmann–Schwinger integral equation for scattering of a wave ψ(r) by the potential ν(r), one constructs the Green's function for the operator [Formula: see text], and treats νψ as the inhomogeneous term. However, in certain cases, it is desirable to formulate the scattering problem in terms of an integral equation by obtaining the Green's function for the operator [Formula: see text], and by considering (−k2ψ) as the inhomogeneous term. An important aspect of this formulation is that the resulting integral equation can be used to generate a low energy expansion of the wave function for some separable and nonseparable systems. For two-dimensional scattering, if the geometry of the scatterers is simple enough, the Laplace equation with the prescribed boundary conditions on the surface of the scatterers is separable in a certain coordinate system, then one can write the solution of the wave equation as an inhomogeneous integral equation. In this way the problems of scattering by two cylinders, an array of cylinders, and a grating can be formulated in terms of integral equations. For three-dimensional scattering, one can consider either the spherically symmetric cases or nonseparable problems. In the former case, for certain types of force laws, a Volterra integral equation in one variable can be found for the wave function. In the latter case, integral equations in two or three variables can be obtained for scattering by two spheres or by a torus.

From a given solvable Fokker-Planck equation one can construct a number of other solvable models for diffusion in a stable or bistable potential fields using the Gel'fand-Levitan method of the inverse scattering theory. The simplest way of achieving this is to change the lowest eigenvalue and/or the normalization of the lowest eigenfunction of the ordinary differential equation obtained by separating the time-dependent part. For these cases it is shown that the new probability distribution is expressible in terms of integrals involving the original probability distribution and the Gel'fand-Levitan kernel. The possibility of changing the lowest eigenvalue enables one to find bistable potential fields which would correspond to a well-defined long time relaxation rate for the probability current.