Showing papers in "Plasma Physics and Controlled Fusion in 2009"

Relativistically correct hole-boring and ion acceleration by circularly polarized laser pulses

Abstract: The problem of the 'hole-boring' (HB)-type of radiation pressure acceleration of ions by circularly polarized laser pulses interacting with overdense plasmas is considered in the regime where the dimensionless scaling parameter I/ρc3 becomes large. In this regime a non-relativistic treatment of the 'HB' problem is no longer adequate. A new set of fully relativistic formulae for the mean ion energy and 'HB' velocity is derived and validated against one-dimensional particle-in-cell simulations. It is also found that the finite acceleration time of the ions results in large energy spreads in the accelerated ion beam even under the highly idealized conditions of constant laser intensity and uniform mass density.

Pair production in counter-propagating laser beams

Abstract: Based on an analysis of a specific electron trajectory in counter-propagating beams, Bell and Kirk (2008 Phys. Rev. Lett. 101 200403) recently suggested that laboratory lasers may shortly be able to produce significant numbers of electron–positron pairs. We confirm their results using an improved treatment of non-linear Compton scattering in the laser beams. Implementing an algorithm that integrates classical electron trajectories, we then examine a wide range of laser pulse shapes and polarizations. We find that counter-propagating, linearly polarized beams, with either aligned or crossed orientation, are likely to initiate a pair avalanche at intensities of approximately 1024 W cm−2 per beam. The same result is found by modelling one of the beams as a wave reflected at the surface of an overdense solid.

A review of experimental drift turbulence studies

Abstract: Experimental drift turbulence and zonal flow studies in magnetically confined plasma experiments are reviewed. The origins of drift waves, transition to drift turbulence and drift turbulence?zonal flow interactions in open field line and toroidal closed flux surface experiments are discussed and the free energy sources, dissipation mechanisms and nonlinear dynamics of drift turbulence in the core, edge and scrape-off layer plasma regions are examined. Evidence that turbulence across these regions is linked and that turbulence-driven zonal flows exist is presented, and evidence that these flows help regulate the turbulent scale lengths, amplitude and fluxes is summarized. Seemingly contradictory reports exist regarding the scale of turbulent transport events; gyro-Bohm behavior of turbulence correlation lengths as well as evidence for long-range transport phenomena both exist. Changes in turbulence during and after transport barrier formation are summarized and compared. The inferred turbulent particle and heat fluxes due to turbulent transport are usually consistent with global confinement, and edge plasma momentum transport appears to be linked to plasma flows at the last-closed flux surface and in the open field line region. However, inconsistencies between observed transport and turbulence have sometimes been reported and are pointed out here. Special attention is given to open issues, and suggestions for future experimental studies are given.

Particle transport in tokamak plasmas, theory and experiment

Abstract: The physical processes producing electron particle transport in the core of tokamak plasmas are described. Starting from the gyrokinetic equation, a simple analytical derivation is used as guidance to illustrate the main mechanisms driving turbulent particle convection. A review of the experimental observations on particle transport in tokamaks is presented and the consistency with the theoretical predictions is discussed. An overall qualitative agreement, and in some cases even a specific quantitative agreement, emerges between complex theoretical predictions and equally complex experimental observations, exhibiting different dependences on plasma parameters under different regimes. By these results, the direct connection between macroscopic transport properties and the character of microscopic turbulence is pointed out, and an important confirmation of the paradigm of microinstabilities and turbulence as the main cause of transport in the core of tokamaks is obtained. Finally, the impact of these results on the prediction of the peaking of the electron density profile in a fusion reactor is illustrated.

Non-linear MHD simulations of edge localized modes (ELMs)

Abstract: Non-linear MHD simulations of edge localized modes (ELMs) show features in qualitative agreement with the experimental observations such as the formation and speed of filaments, features in the radial profiles and the fine structure observed in the power deposition profiles at the divertor target. The density perturbation predominantly follows the ballooning mode convection cells leading to density filaments. The temperature perturbation, due to the large parallel conduction, follows the magnetic field perturbation. Simulations of pellets injected in the H-mode pedestal show that the high pressure in the high density plasmoid can become large enough to drive ballooning type modes forming a single helical structure located at the pellet (plasmoid) position.

Plasma response to lithium-coated plasma-facing components in the National Spherical Torus Experiment

Abstract: Experiments in the National Spherical Torus Experiment (NSTX) have shown beneficial effects on the performance of divertor plasmas as a result of applying lithium coatings on the graphite and carbon-fiber-composite plasma-facing components These coatings have mostly been applied by a pair of lithium evaporators mounted at the top of the vacuum vessel which inject collimated streams of lithium vapor toward the lower divertor In neutral beam injection (NBI)-heated deuterium H-mode plasmas run immediately after the application of lithium, performance modifications included decreases in the plasma density, particularly in the edge, and inductive flux consumption, and increases in the electron and ion temperatures and the energy confinement time Reductions in the number and amplitude of edge-localized modes (ELMs) were observed, including complete ELM suppression for periods of up to 12 s, apparently as a result of altering the stability of the edge However, in the plasmas where ELMs were suppressed, there was a significant secular increase in the effective ion charge Zeff and the radiated power as a result of increases in the carbon and medium-Z metallic impurities, although not of lithium itself which remained at a very low level in the plasma core, <01% The impurity buildup could be inhibited by repetitively triggering ELMs with the application of brief pulses of an n = 3 radial field perturbation The reduction in the edge density by lithium also inhibited parasitic losses through the scrape-off-layer of ICRF power coupled to the plasma, enabling the waves to heat electrons in the core of H-mode plasmas produced by NBI Lithium has also been introduced by injecting a stream of chemically stabilized, fine lithium powder directly into the scrape-off-layer of NBI-heated plasmas The lithium was ionized in the SOL and appeared to flow along the magnetic field to the divertor plates This method of coating produced similar effects to the evaporated lithium but at lower amounts

Sheared flows and transition to improved confinement regime in the TJ-II stellarator

Abstract: Sheared flows have been experimentally studied in TJ-II plasmas. In lowdensity ECH plasmas, sheared flows can be easily controlled by changing the plasma density, thereby allowing the radial origin and evolution of the edge velocity shear layer to be studied. In high density NBI heated plasmas a negative radial electric field is observed that is dominated by the diamagnetic component. The shear of the negative radial electric field increases at the L‐H transition by an amount that depends on the magnetic configuration and heating power. Magnetic configurations with and without a low order rational surface close to the plasma edge show differences that may be interpreted in terms of local changes in the radial electric field induced by the rational surface that could facilitate the L‐H transition. Fluctuation measurements show a reduction in the turbulence level that is strongest at the position of maximum Er shear. High temporal and spatial resolution measurements indicate that turbulence reduction precedes the increase in the mean sheared flow, but is simultaneous with the increase in the low frequency oscillating sheared flow. These observations may be interpreted in terms of turbulence suppression by oscillating flows, the so-called zonal flows. (Some figures in this article are in colour only in the electronic version)

Shock ignition: an alternative scheme for HiPER

Abstract: Two main paths are now under investigation that aim at thermonuclear ignition of hydrogen isotopes using lasers: central hot spot self-ignition and externally driven fast ignition of preassembled fuel. A third, intermediate, scheme is shock ignition, which combines the simplicity of self-ignition capsules to the hydrodynamic robustness of the fast ignition fuel assembly. This study addresses the potential of shock ignition for the HiPER project and provides a preliminary assessment of possible detrimental effects. Monodimensional simulations are performed to study the robustness of the ignition scheme in terms of shock launching time and laser power. Bidimensional simulations address the sensitivity of shock ignition to irradiation nonuniformity and to low mode asymmetries of the fuel assembly.

Gyrokinetic simulations of spherical tokamaks

Abstract: This paper reviews transport and confinement in spherical tokamaks (STs) and our current physics understanding of this that is partly based on gyrokinetic simulations. Equilibrium flow shear plays an important role, and we show how this is consistently included in the gyrokinetic framework for flows that greatly exceed the diamagnetic velocity. The key geometry factors that influence the effectiveness of turbulence suppression by flow shear are discussed, and we show that toroidal equilibrium flow shear can sometimes entirely suppress ion scale turbulence in today's STs. Advanced nonlinear simulations of electron temperature gradient (ETG) driven turbulence, including kinetic ion physics, collisions and equilibrium flow shear, support the model that ETG turbulence can explain electron heat transport in many ST discharges.

Snowflake divertor plasmas on TCV

Abstract: Starting from a standard single null X-point configuration, a second order null divertor (snowflake (SF)) has been successfully created on the Tokamak a Configuration Variable (TCV) tokamak. The magnetic properties of this innovative configuration have been analysed and compared with a standard X-point configuration. For the SF divertor, the connection length and the flux expansion close to the separatrix exceed those of the standard X-point by more than a factor of 2. The magnetic shear in the plasma edge is also larger for the SF configuration.

Inter-ELM filaments and turbulent transport in the Mega-Amp Spherical Tokamak

Abstract: Results on edge turbulence in periods separating edge localised modes (ELMs), i.e. inter-ELM periods, in Mega-Amp Spherical Tokamak (MAST) are presented. It is shown through combined measurements of fast camera images and reciprocating Langmuir probes that filamentary structures contribute to transport during these periods. Analysis of Dα light emission reveals that inter-ELM filaments are the lowest amplitude fluctuations in the MAST scrape-off layer (SOL) relative to L-mode and ELM filaments. Physical properties such as size, density and mode numbers have also been characterized, along with measurements of the spatio-temporal evolution: inter-ELM filaments are found to rotate in the vicinity of the last closed flux surface and propagate radially outwards. Motion of these filaments is found to depend strongly on plasma density such that with increasing density, there is an enhancement of the radial transport manifested by an increased number of filaments which leave the edge and travel faster into the SOL. Camera images show that intermittent fluctuations in ion saturation current signals correspond to inter-ELM filaments passing the probe. Measured radial e-folding lengths indicate larger decay lengths at higher densities. Similar trends are also obtained in simulations of a filament propagating radially and losing particles on ion parallel loss timescales. Finally, a discussion is presented on how the radial velocity and Isat measurements reported in this paper are used to test the velocity scalings predicted by different theories.

Fast ignition of fusion targets by laser-driven electrons

Abstract: We present hybrid PIC simulations of fast electron transport and energy deposition in pre-compressed fusion targets, taking full account of collective magnetic effects and the hydrodynamic response of the background plasma. Results on actual ignition of an imploded fast ignition configuration are shown accounting for the increased beam divergence found in recent experiments (Green et al 2008 Phys. Rev. Lett. 100 015003) and the reduction in the electron kinetic energy due to profile steepening predicted by advanced PIC simulations (Chrisman et al 2008 Phys. Plasmas 15 056309). Target ignition is studied as a function of injected electron energy, distance of cone tip to dense core, initial divergence and kinetic energy of the relativistic electron beam. We found that beam collimation reduces substantially the ignition energies of the cone-guided fuel configuration assumed here.

Collisionless damping of short wavelength geodesic acoustic modes

Abstract: Collisionless damping of geodesic acoustic mode (GAM) excited in the large safety factor (q) region of a tokamak plasma is investigated taking into account the effects of finite ion Larmor radius and guiding-center drift orbit width as well as parallel electric field contributions. A corresponding analytical expression for the damping rate including higher-order harmonics of ion transit resonances is systematically derived and agrees well with numerical results in its validity regime.

Stopping and scattering of relativistic electron beams in dense plasmas and requirements for fast ignition

Abstract: The interaction of a relativistic electron with a dense plasma is studied in the context of inertial fusion fast ignition. Expressions for the electron stopping power and deflection are given and implemented in a three-dimensional (3D) Monte Carlo code. Electron range and penetration depth are computed as functions of the electron energy and plasma parameters; approximate expressions are also proposed. Conditions for fast ignition are studied by including the 3D Monte Carlo code in a 2D hydrodynamic code. The required beam energy is determined as a function of mean electron energy for monoenergetic and exponential energy distributions and a uniform initial deuterium?tritium plasma with a density of 300?g?cm?3. A simple model is shown to agree with the code.

Tokamak rotation sources, transport and sinks

Abstract: Toroidal rotation has become a topic of wide interest experimentally and theoretically because of the recognition that it is important for confinement, stability and even access to the H-mode confinement regime. The inception of ITER has generated a focus upon developing a prediction for rotation in burning plasmas where auxiliary injected torque will be relatively small. We will describe experimental results and cite theory, organized by sources of toroidal momentum, transport of this momentum and sinks for momentum, including the effects of some loss of toroidal axisymmetry (AS). We will also describe the so-called 'intrinsic rotation' where rotation under AS conditions is observed in the absence of any auxiliary momentum source, presumably due to effects such as off-diagonal transport elements or turbulent stresses and others. We describe how rotation is measured, and specific areas where the importance of rotation has been established. The predominant source of rotation generation in present devices is the toroidal torque from neutral beam injection. Experiments verify the accuracy of neoclassical (NC) models to describe the torque deposition process in AS conditions. Applied electromagnetic wave power is also found to generate rotation. The radial transport of momentum is found to be much larger than predicted by standard NC theory, having transport rates similar to that of ion thermal energy. Experiments have also verified the existence of a pinch term in the momentum transport, which could generate the interior rotation gradient often observed with intrinsic rotation. The ambient or purposely imposed non-axisymmetric magnetic fields can provide an interior sink for momentum, and that may also drag the rotation to a nonzero offset value. The rotation itself tends to shield out resonant perturbations. Nonresonant (NR) perturbations from toroidal field ripple have long been considered, and the area of NR perturbations has taken on new import for the fields generated by perturbation coils for mitigation of edge localized modes. We consider some of these effects in relation to what might be extrapolated to ITER, but continued experimental and theoretical efforts are required.

Thomson scattering system on the TEXTOR tokamak using a multi-pass laser beam configuration

Abstract: The main challenge for the Thomson scattering (TS) diagnostic on the TEXTOR tokamak is the detailed study of fast plasma events at a high spatial resolution and a high repetition rate of the measurements. The diagnostic uses intra-cavity probing of the plasma with a repetitively pulsed ruby laser and a fast CMOS camera as detectors. Since 2004, the TS system on TEXTOR has been gradually and systematically enhanced for the measurements of fast plasma events. For that it has recently been upgraded to obtain a multi-pass configuration. Two spherical mirrors have been installed that force the laser beam to probe the plasma a specified number of times before it is directed back into the laser medium. The diagnostics with the upgraded probing system have achieved the measurement accuracy of 3% for the electron temperature and 1.5% for the electron density at <1 cm spatial resolution and 3 × 1019 m−3 plasma density and can measure at 5 kHz during an interval up to 8 ms. This makes it possible to detect, amongst others, fine structures of magnetic islands and variations of the edge pedestal in the ELMy limiter H-mode.

Laser acceleration of monoenergetic protons in a self-organized double layer from thin foil

Abstract: We present a theory for the acceleration of monoenergetic protons, trapped in a self-organized double layer, by short pulse laser irradiation on a thin foil with the specific thickness suggested by the simulation study of Yan et al (2008 Phys. Rev. Lett. 100 135003). The laser ponderomotive force pushes the electrons forward, leaving the ions behind until the space charge electric field balances the ponderomotive force at a distance Δ. For the optimal target thickness D = Δ > c/ωp, the electron sheath is piled up at the rear surface and the sheath electric field accelerates the protons until they are reflected by the inertial force in the accelerated frame. These protons are therefore trapped by the combined forces of the electrostatic field of the electron sheath and the inertial force of the accelerating target. Together with the electron layer, they form a double layer and are collectively accelerated by the laser ponderomotive force, leading to monoenergetic ion production.

Kinetic Alfvén eigenmodes at ASDEX Upgrade

Abstract: On the way to a comprehensive understanding of the properties of a burning plasma the physics of super-thermal particles due to external heating and fusion reactions plays a key role. In particular, Alfven and Alfven-acoustic type instabilities are predicted to strongly interact with the fast particle population and to contribute critically to the radial redistribution of the energetic ions.This paper focuses on the comparison of the kinetic dispersion relation for BAEs/GAMs (Zonca et al 1996 Plasma Phys. Control. Fusion 38 2011) with numerical results obtained by the gyrokinetic eigenvalue code LIGKA (Lauber et al 2007 J. Comput. Phys. 226/1 447–65) and experimental findings at ASDEX Upgrade. It is shown that thermal ions with a finite perpendicular energy (circulating and trapped) modify the dispersion relation significantly for low frequencies. The resulting frequency downshift together with shaping and diamagnetic effects is crucial to explain the mode frequency as measured at ASDEX Upgrade stressing the importance of a kinetic description for frequencies comparable to the thermal ion transit frequency.In the second part the BAE-frequency behaviour during a sawtooth cycle is investigated and the possibility of an accurate q-profile determination via kinetic Alfven spectroscopy is discussed.

MHD stability analysis of small ELM regimes in JET

Abstract: We have analysed the edge stability of JET discharges with small edge localized modes (ELMs) using the high resolution Thomson scattering system for accurate edge profiles in the equilibrium reconstruction. For the reference plasmas with large Type I ELMs we confirm the results from earlier analyses that the edge stability is limited by intermediate-n peeling–ballooning modes with a relatively large radial extent. The double null configuration needed to replace Type I ELMs by smaller Type II ELMs considerably increases the stability against these modes while the stability against n = ∞ ballooning modes is not affected. When this is combined with high collisionality (which is the other requirement for Type II ELMs), we find that the plasma cannot reach the Type I ELM triggering peeling–ballooning mode stability boundary before it is destabilized by high-n ballooning modes resulting in more benign ELMs. The ELM mitigation by magnetic perturbation causes the edge stability to be limited by pure peeling modes with a narrow radial extent. This explains the smaller ELM size and also why the ELMs are not fully suppressed. The transition from Type I ELMs to Type III ELMs by increasing the edge radiation fully stabilizes the edge plasma against ideal MHD modes. Therefore, the Type III ELMs are due to be triggered by some other mechanism than an ideal MHD instability.

Disruption studies in ASDEX Upgrade in view of ITER

Abstract: Experiments on ASDEX Upgrade and other tokamaks have shown that the magnitude of mechanical forces and thermal loads during disruptions can be significantly reduced by raising the plasma density with massive injection of noble gases. This method should be applicable to ITER too. Nevertheless, the suppression of the runaway electron (RE) avalanche requires a much larger (two order of magnitude) density rise. This paper reports on recent experiments aimed at increasing the plasma density towards the critical value, needed for the collisional suppression of REs. An effective electron density equal to 24% of the critical density has been reached after injection of 3.3?bar?l of neon. However, the resultant large plasma density is very poloidally and toroidally asymmetric; this implies that several valves distributed around the plasma periphery become necessary at this level of massive gas injection to ensure a homogeneous density distribution.

A unified method for operator evaluation in local Grad–Shafranov plasma equilibria

Abstract: This work describes a unified method to treat model and general flux-surface shape in gyrokinetic and neoclassical transport calculations. In both cases the associated equilibria are constructed to be solutions of the Grad–Shafranov equation on each flux surface. Included is a systematic calculation and cataloging of the set of functions required to implement the method numerically. In the case where model equilibria (defined by shape parameters such as elongation and triangularity) are considered, we provide a modest extension of the original method usually attributed to Miller, whereas for general equilibria, a Fourier method is developed. The unified formulation makes use of and extends the intuitively appealing concepts of a midplane minor radius and effective field, originally introduced by Waltz (Waltz and Miller 1999 Phys. Plasmas 6 4265). In the limit that the model and general flux-surface shapes approach one another, the two methods give identical results. Although the Miller model approach has been widely implemented over the past decade, variations or errors in the implementations can vary to the extent that code–code comparisons are difficult or ambiguous. This work should serve to standardize such implementations. Finally, it is shown that for N = 12 Fourier harmonics in the general expansion, the accuracy of the present approach likely exceeds that of, and is thus limited by, the original equilibrium data.

Physics and applications of atmospheric non-thermal air plasma with reference to environment

Abstract: Since air is a natural part of our environment, special attention is given to the study of plasmas in air at atmospheric pressure and their applications. This fact promoted the study of electrical conduction in air-like mixtures, i.e. mixtures containing an electronegative gas component. If the ionization growth is not limited its temporal evolution leads to spark formation, i.e. a thermal plasma of several thousand kelvins in a quasi-local thermodynamic equilibrium state. But before reaching such a thermal state, a plasma sets up where the electrons increase their energy characterized by an electron temperature Te much higher than that of heavy species T or T+ for the ions. Since the plasma is no longer characterized by only one temperature T , it is said to be in a nonthermal plasma (NTP) state. Practical ways are listed to prevent electron ionization from going beyond the NTP states. Much understanding of such NTP may be gathered from the study of the simple paradigmatic case of a discharge induced between a sharp positively stressed point electrode facing a grounded negative plane electrode. Some physical properties will be gathered from such configurations and links underlined between these properties and some associated applications, mostly environmental. Aerosol filtration and electrostatic precipitators, pollution control by removal of hazardous species contained in flue gas exhaust, sterilization applications for medical purposes and triggering fuel combustion in vehicle motors are among such applications nowadays.

Numerical experiments on plasma focus neutron yield versus pressure compared with laboratory experiments

Abstract: Published literature shows that the neutron yield of the plasma focus has been modeled in two papers using a thermonuclear mechanism. However, it is more widely held that plasma focus neutrons are produced mainly by non-thermalized mechanisms such as beam–target. Moreover these papers use several parameters which are adjusted for each machine until the computed neutron yield Yn data agree with measured Yn data. For this paper numerical experiments are carried out, using the Lee model code, incorporating a beam–target mechanism to compute the Yn versus pressure data of plasma focus devices PF-400 J and FN-II. The Lee model code is first configured for each of these two machines by fitting the computed current waveform against a measured current waveform. Thereafter all results are computed without adjusting any parameters. Computed results of Yn versus pressure for each device are compared with the measured Yn versus pressure data. The comparison shows degrees of agreement between the laboratory measurements and the computed results.

Two-point analysis of the numerical modelling of detached divertor plasmas

Abstract: A two-point model connecting plasma parameters at the divertor target and upstream is considered which is exact in the framework of the equations solved by the 2D multi-species plasma fluid code B2. The two-point formulae allow verification and quantitative analysis of the results of numerical modelling. The definition of the loss factors proposed here allows one to relate directly the free parameters of conventional two-point models with the simulation results. An example for the B2-EIRENE modelling of an ASDEX-Upgrade plasma with detached divertor is discussed. The new code analysis tool is applied to analyse the phenomenon of roll-over of the target incident particle flux as it appears in the simulations.

The effect of plasma triangularity on turbulent transport: modeling TCV experiments by linear and non-linear gyrokinetic simulations

Abstract: The effect of plasma shape on confinement has been experimentally explored in the TCV tokamak revealing that the core electron heat transport is significantly reduced by a negative triangularity configuration, which could indicate a (partial) stabilization of the microinstabilities at play in a conventional positive triangularity configuration.This work is a theoretical investigation of the effect exerted by triangularity on plasma turbulence. In particular, it compares the TCV experimental results with non-linear local gyrokinetic simulations performed on the basis of actual MHD equilibrium reconstructions.In both the linear and non-linear phases, negative triangularity is found to have a stabilizing influence on ion-scale instabilities, specifically on the so-called trapped electron mode (TEM) which is the dominant instability in the conditions of the TCV experiments considered; more specifically, the variation of the heat flux with triangularity calculated by the non-linear simulations is in fair agreement with the experimental results.The resulting stabilization is a result of a rather complex modification of the toroidal precessional drift of trapped particles exerted by negative triangularity.

Laser absorption by overdense plasmas in the relativistic regime

Abstract: Laser absorption is reviewed in the context of fast ignition inertial fusion. This leads us to consider laser absorption by overdense plasmas for values of intensity times wavelength squared (Iλ2) greater than 1010 W (1018 W cm−2 µm2), which corresponds to the onset of relativistic electron motion in the laser fields. A collection of published absorption values obtained in laser–solid experiments and in numerical modelling of laser–plasma interactions is presented.

An Eulerian method for the solution of the multi-species drift-kinetic equation

Abstract: An Eulerian numerical discretization scheme for the solution of the first-order drift-kinetic equation is presented in detail. The approach is valid for multi-species plasmas, including complete impurity and electron physics, and thus ambipolarity is properly maintained. The code, NEO, provides a complete description of the second-order neoclassical transport fluxes and first-order flows, including the effects of strong (finite Mach number) toroidal rotation. Corrections to the weak rotation limit are demonstrated for multi-species plasmas over a wide range of collisionality.

Numerical experiments on plasma focus neon soft x-ray scaling

Abstract: Numerical experiments are carried out systematically to determine the neon soft x-ray yield Ysxr for optimized neon plasma focus with storage energy E0 from 0.2 kJ to 1 MJ. The ratio c = b/a, of outer to inner electrode radii, and the operating voltage V0 are kept constant. E0 is varied by changing the capacitance C0. Parametric variation at each E0 follows the order operating pressure P0, anode length z0 and anode radius a until all realistic combinations of P0, z0 and a are investigated. At each E0, the optimum combination of P0, z0 and a is found that produces the biggest Ysxr. At low energies the soft x-ray yield scales as whilst towards 1 MJ it becomes . The Ysxr scaling laws are found to be (0.1–2.4 MA) and (0.07–1.3 MA) throughout the range investigated. When numerical experimental points with other c values and mixed parameters are included, there is evidence that the Ysxr versus Ipinch scaling is more robust and universal, remaining unchanged whilst the Ysxr versus Ipeak scaling changes slightly, with more scatter becoming evident.

Comparison of measured poloidal rotation in MAST spherical tokamak plasmas with neo-classical predictions

Abstract: Neo-classical tokamak plasma theory predicts poloidal rotation driven by the temperature gradient of a few km?s?1. In conventional aspect-ratio tokamak plasmas, e.g. on JET and DIII-D, apparent poloidal velocities considerably in excess of the neo-classical values have been measured, particularly in the presence of internal transport barriers, by means of charge-exchange recombination spectroscopy (CXRS) on the fully ionized C6+ impurity ions. Comparison between such measurements and theoretical predictions requires careful corrections to be made for apparent 'pseudo' velocities, which can arise from the finite lifetime of the excited atoms in the magnetized plasma and the energy dependence of the charge-exchange excitation process. In present day spherical tokamak plasmas this correction is an order of magnitude smaller than on large conventional tokamaks, which operate at higher temperature and magnetic field, hence reducing any associated systematic uncertainties. On MAST measurements of toroidal and poloidal flows of the C6+ impurities are available from high-resolution Doppler CXRS measurements, including appropriate corrections for the pseudo-velocities. Comparison of the measured C6+ velocities with neo-classical theory requires calculation of the impurity flow, which differs from that of the bulk ions due to the respective diamagnetic contributions for each species and inter-species friction forces. Comparisons are made with the predictions of a recent neo-classical theory (Newton 2007 Collisional transport in a low collisionality plasma with strong rotation PhD Thesis University of Bristol, Newton and Helander 2006 Phys. Plasmas 13 102505), which calculates the full neo-classical transport matrix for bulk ions and a single impurity species for a strongly rotating plasma, as well as those of a simpler neo-classical theory (Kim et al 1991 Phys. Fluids B 3 2050?9) for an impure plasma and the NCLASS code (Houlberg et al 1997 Phys. Plasmas 4 3230?42). Initial results for both L- and H-mode plasmas show that, within the measurement uncertainties, the measured poloidal rotation of the core plasma is consistent with the neo-classical predictions.

Bootstrap current and neoclassical transport in quasi-isodynamic stellarators

Abstract: It is shown that the problem of neoclassical transport at low collisionality in a perfectly quasi-isodynamic (or omnigeneous) stellarator can be reduced to the corresponding problem in a tokamak. In fact, the distribution function consists of two parts: one that can be calculated exactly (for any collision operator) and does not carry any net parallel current and one that is proportional to the total toroidal current and is determined by an equation that is identical to that solved in tokamak theory. Results from the latter can therefore be carried over to the corresponding stellarator situation. Specifically, if the total toroidal current enclosed by a flux surface vanishes, then the net bootstrap current on that surface also vanishes. It is therefore consistent to optimize a stellarator in such a way that the bootstrap current and neoclassical transport are simultaneously minimized.