This article presents a new method for estimating the electron temperature of the Proto-sphera's screw pinch. The temperature radial profile is obtained by a self-consistent modeling of a 1D MHD equilibrium along with a 0D power balance of the plasma column, given measurements and estimates of the axial pinch plasma current, of the plasma rotational frequency and, at the equatorial plane, of the electron density radial profile, of the edge poloidal magnetic field, of the edge electron temperature and of the neutrals pressure in the vacuum vessel. The plasma is considered in equilibrium with its neutral phase and in constant rotation. A MATLAB code has been developed with the aim of estimating the MHD radial equilibrium profiles, the thermodynamic plasma state and the neutrals profile. The numerical estimates are compared with available experimental data showing a good agreement.

The distribution of velocity and density of plasma and of neutral particles along the axis of a screw-pinch discharge is studied numerically and analytically. The considered pinch is a model for the central plasma column of the PROTO-SPHERA experiment, in which a toroidal plasma is formed around a center post discharge. The main result of the analysis is that the plasma is fully ionized along most of the plasma column already at temperatures of 2 eV, i.e., well below the first ionization energy of argon, the working gas.

Analytical solutions of the Grad–Shafranov equilibrium equation in simply connected plasma configurations, comprised of toroidal magnetic surfaces and open surfaces connected to electrodes, are reviewed and generalised. The Grad–Shafranov equation is linearised introducing assumptions on plasma current and pressure, which preserve regularity of solutions on the symmetry axis, as required for a simply connected geometry. Particular solutions are found by separation of variables both in cylindrical coordinates and in spherical ones. Equilibria that model local or global features of PROTO-SPHERA plasmas are constructed by combining a few particular solutions.

We analyze the temperature distribution on the vertical axis of an axisymmetrical plasma, the radial temperature being almost constant. We solve the equation for the temperature analytically. Further we investigate the bidimensional flow inside the plasma, showing the existence of a convective cell. The considered plasma is the central column of the PROTO-SPHERA configuration, which aims at forming a confined plasma torus around the central plasma discharge.

PROTO-SPHERA (Spherical Plasma for Helicity Relaxation Assessment) is a new concept of torus that aims to produce a spherical torus with closed flux surfaces and a force-free Screw Pinch with open flux surfaces, fed by electrodes. In order to verify the stability of the configuration and the technical components of the PROTO-SPHERA initial arc, the initial Phase-1 experiment was built, and its plasma, in the year 2108, has reached both the total current (10 kA) and total duration (1 s) targets. A two colour interferometer is one of the diagnostic system proposed to provide PROTO-SPHERA with the measurement of its electron density, which is currently of the order of similar to 10(20 )m(-3). It will allow to obtain line density, necessary to characterize this uncommon plasma, as integrate measurement along the equatorial plane. The design and the interferometer characteristics are described in this paper.

Fishbone is ubiquitous in tokamak plasmas with fast ions. A numerical study of nonlinear dynamics of fishbone has been carried out in this work. Realistic parameters of NSTX are used to understand linear instability and nonlinear frequency chirping in real tokamak plasmas. First, the effects of shear toroidal rotation are considered for fishbone instability. It is shown that with low qmin , toroidal rotation has small effects on the mode; while with high q min , a new unstable region with a strong ballooning feature in mode structure appears. Second, a systematic study of nonlinear frequency chirping and energetic particles' dynamics is carried out. It is found that, linearly, the mode is driven by both trapped particles and passing particles, with resonance condition ω! ≃ ω for trapped particles and ω! + ω! ≃ ω for passing particles, where ω! is trapped particles precession frequency, and ω!, ω! are passing particle transit frequency around toroidal and poloidal direction. As the mode grows, resonance particles oscillate and move outward in P! space, which reduces particles' frequency. We believe that this is the main reason for the mode frequency chirping down. Finally, as the mode frequency chirping down, particles with lower orbit frequencies, which are non-resonant linearly, can turn into resonant particles in the nonlinear regime. This effect can sustain a quasi-steady state mode amplitude observed in the simulation. Distinct turbulence sources and confinement features in spherical tokamak plasma regime W. X. Wang, S. Ethier, Y. Ren, S. Kaye, J. Chen, E. Startsev, and Z. Lu (UCSD) Princeton Plasma Physics Laboratory Highly distinct features of spherical tokamaks (ST) such as NSTX/U result in a different fusion plasma regime with unique physics properties compared to conventional tokamaks. Nonlinear global gyrokinetic simulations critical for addressing turbulence and transport physics in ST regime have led to new insights regarding non-traditional turbulence sources contributing to plasma transport and confinement in ST experiments. The drift wave Kelvin-Helmholtz (KH) instability characterized by intrinsic mode asymmetry is identified in strongly rotating NSTX L-mode plasmas. For the first time, the KH mode is shown as a driver of significant transport in realistic fusion experiments. Also for the first time, long wavelength, quasicoherent dissipative trapped electron modes are found to be excited over a wide range of NSTX parameter regime despite the presence of strong E × B shear, providing a robust turbulence source dominant over the traditional collisionless trapped electron modes in ST plasmas. Furthermore, DTEMdriven transport in NSTX parametric regime is shown to increase with electron collision frequency, offering one possible source for the confinement scaling observed in experiments. More interestingly, the existence of a minimum plasma transport regime that future advanced STs may access is predicted. This work was supported by U.S. DOE Contract DE-AC0209CH11466.

The Fusion Advanced Studies Torus (FAST) conceptual study has been proposed as possible European ITER Satellite [1]. This facility is aimed at exploring and preparing ITER operation scenarios as well as helping DEMO design and R&D. One challenging operational point is that the power exhaust handling and plasma wall interaction must be mastered to a level compatible with wall materials (for instance actively cooled W) and, at the same time, to address possible solutions for DEMO. Different solutions [2-4] have been proposed to reduce the plasma-wall interaction optimizing the divertor region by acting on the magnetic field topology. Among these, one is the so-called snowflake (SF) divertor configuration [2, 3]. Starting from a standard single null X-point configuration, a second order null divertor (snowflake) has been preliminary studied on the present geometry of FAST proposal, by means of MAXFEA and FIXFREE codes [5, 6], with the constrains of using exactly the present poloidal system (i.e. coils and power supplies). At the moment a SF configuration of at least 4MA has been obtained. The poloidal field coils system is able to sustain this SF configuration for ~ 50s with all the coil currents compatible with the present circuits current limits. The second-order null strongly modifies the magnetic topology in the full X point region and, consequently, it is expected to affect the edge plasma properties. In the paper the magnetic properties of this innovative configuration have been analyzed and compared with the FAST standard X-point configuration.

In this paper we present the fusion advanced studies torus (FAST) equilibrium configurations, designed by means of the ITM FIXFREE code version for reproducing those of ITER (with scaled plasma current) and suitable to fulfil plasma conditions for integrated studies of plasma–wall interaction, burning plasma physics, ITER relevant operation problems and steady state scenarios. FIXFREE is a toroidal multipolar expansions equilibrium code, recently ported to the Integrated Tokamak Modelling (ITM) Gateway platform. The European ITM Task Force opted for the open source workflow system Kepler to link various codes and coordinate the data flow among them. A description of the development of the FIXFREE code under the Kepler environment will be given in this paper.

The PROTO-SPHERA experiment (under construction in Frascati inside the START vacuum vessel) aims to study the properties of a spherical torus (ST), where a hydrogen force-free screw pinch (SP, with open field lines and fed by electrodes) replaces the central rod of the standard spherical tokamak experiments: PROTO-SPHERA, with a central screw pinch current Ie = 60 kA, aims at producing a spherical torus (with closed field lines) of diameter 2Rsph = 70 cm, and aspect ratio R/a = A = 1.2–1.3, carrying a toroidal current Ip = 120–240 kA. Such a configuration is an evolution of the flux core spheromak (FCS) concept, first proposed by Taylor. The formation mechanism of the configuration will be the one successfully developed by the TS-3 team at the University of Tokyo. The spherical torus toroidal current should be sustained by helicity injection from the screw pinch, therefore some level of resistive instability with toroidal mode numbers n = 1 and/or n = 2 is requested after the formation and during the sustainment phase; nevertheless, the configuration should be operated such as to maintain it stable from an ideal MHD point of view. The ideal MHD stability limits of PROTO-SPHERA have been analysed by a numerical code able to handle magnetic configurations endowed with both closed and open magnetic field lines. The results of such an analysis are presented in terms of the main parameter, which is the ratio between the currents in the spherical torus and in the central screw pinch, Ip/Ie, and of other relevant parameters of the ST (elongation, aspect ratio, total beta and the toroidal plasma current profile). A comparison with the TS-3 results is also shown.

The filament state of a magnetic field is the usual way for plasmas to avoid magnetic inhibition of convective overturning. However, it requires dynamo conversion of kinetic into magnetic energy and is therefore often associated with a plasma velocity shear layer. In the sun, isolated current carrying magnetic filaments (twisted flux tubes) are produced by the solar dynamo from a continuous strong toroidal field, sitting just below the radiative–convective transition, on the Sun rotation shear layer (tachocline, rTach ∼ 2 · R⊙/3 in terms of the solar radius, R⊙). The twisted flux tubes, become buoyant; some of them fall back into the tachocline adding up to the continuous toroidal field; some emerge from the photosphere kinked and twisted, reconnect and produce flares. In the mode of high magnetic confinement (H-mode), when a magnetic separatrix bounds the axisymmetric tokamak discharge and a sheared plasma rotation is present, magnetic filaments with concentrated internal currents (edge localized modes) are produced near the velocity shear layer (pressure pedestal, at rPed ⩾ 0.94aSep in terms of the minor radius of the plasma boundary, aSep): again a dynamo conversion of kinetic into magnetic energy is required in order to filament the current density at the pedestal. The current carrying filaments break the unperturbed axisymmetric tokamak equilibrium, producing ergodicity in the edge plasma. The faster loss of energy from the ergodic plasma makes the rotating magnetic filaments outboards anti-buoyant: therefore they convect outboards from the pedestal. The anti-buoyancy and motion model for the tokamak case is compared with the buoyancy model for the Sun.

Substantial advances have been made on the Mega Ampere Spherical Tokamak (MAST). The parameter range of the MAST confinement database has been extended and it now also includes pellet-fuelled discharges. Good pellet retention has been observed in H-mode discharges without triggering an ELM or an H/L transition during peripheral ablation of low speed pellets. Co-ordinated studies on MAST and DIII-D demonstrate a strong link between the aspect ratio and the beta scaling of H-mode energy confinement, consistent with that obtained when MAST data were merged with a subset of the ITPA database. Electron and ion ITBs are readily formed and their evolution has been investigated. Electron and ion thermal diffusivities have been reduced to values close to the ion neoclassical level. Error field correction coils have been used to determine the locked mode threshold scaling which is comparable to that in conventional aspect ratio tokamaks. The impact of plasma rotation on sawteeth has been investigated and the results have been well-modelled using the MISHKA-F code. Alfven cascades have been observed in discharges with reversed magnetic shear. Measurements during off-axis NBCD and heating are consistent with classical fast ion modelling and indicate efficient heating and significant driven current. Central electron Bernstein wave heating has been observed via the O-X-B mode conversion process in special magnetically compressed plasmas. Plasmas with low pedestal collisionality have been established and further insight has been gained into the characteristics of filamentary structures at the plasma edge. Complex behaviour of the divertor power loading during plasma disruptions has been revealed by high resolution infra-red measurements.

In the calculation of the ideal magnetohydrodynamic free-boundary stability of magnetoplasma equilibria, the integration of the perturbed magnetic energy in the vacuum region that can exist between the plasma edge and nearby conducting shells is extended to axisymmetric configurations composed in part by closed and in part by open field lines. Examples of such equilibria are flux-core-spheromaks and spherical tori with a plasma central column, where a magnetic separatrix divides a spherical torus—with closed field lines—from a central screw pinch discharge—with open field lines that end on the sustaining electrodes. These configurations pose two problems: their plasma-vacuum interface is composed of multiple flux surfaces (i.e., they enclose different values of toroidal and poloidal flux) and their plasma extends up to the symmetry axis. A Green’s function method based on two-dimensional finite elements is used to solve both problems, and an application to the experimental results of the Tokyo University Spherical Torus No. 3 flux-core-spheromak experiment [N. Amemiya, A. Morita, and M. Katsurai, J. Phys. Soc. Jpn. 63, 1552 (1993)] is illustrated.

The ideal magnetohydrodynamic (MHD) stability analysis of axisymmetric plasma equilibria is simplified if magnetic coordinates, such as Boozer coordinates (ψT radial, i.e., toroidal flux divided by 2π, θ poloidal angle, ϕ toroidal angle, with Jacobian g∝1∕B2), are used. The perturbed plasma displacement ξ⃗ is Fourier expanded in the poloidal angle, and the normal-mode equation δWp(ξ⃗*,ξ⃗)=ω2δWk(ξ⃗*,ξ⃗) (where δWp and δWk are the perturbed potential and kinetic plasma energies and ω2 is the eigenvalue) is solved through a 1D radial finite-element method. All magnetic coordinates are however plagued by divergent metric coefficients, if magnetic separatrices exist within (or at the boundary of) the plasma. The ideal MHD stability of plasma equilibria in the presence of magnetic separatrices is therefore a disputed problem. We consider the most general case of a simply connected axisymmetric plasma, which embeds an internal magnetic separatrix—ψT=ψTX, with rotational transform ι̷(ψTX)=0 and regular X-points (B⃗≠0)—and is bounded by a second magnetic separatrix at the edge—ψT=ψTmax, with ι̷(ψTmax)≠0—that includes a part of the symmetry axis (R=0) and is limited by two singular X-points (B⃗=0). At the embedded separatrix, the ideal MHD stability analysis requires the continuity of the normal plasma perturbed displacement variable, ξψ=ξ⃗∙∇⃗ψT; the other displacement variables, the binormal ηψ=ξ⃗∙(∇⃗θ−ι̷∇⃗ϕ) and the parallel μ=−gξ⃗∙∇⃗ϕ, can instead be discontinuous everywhere. The permissible asymptotic limits of (ξψ,ηψ,μ) are calculated for the unstable (ω2<0) eigenvectors, imposing the regularity of δWp, δWk, and ξ⃗ at the embedded separatrix and at the edge separatrix. An intensified numerical radial mesh following Boozer magnetic coordinates is set up; it requires a logarithmic fit to the rotational transform near the embedded magnetic separatrix, a minimum distance between the radial mesh and both separatrices, and finally an extended spectrum of poloidal mode numbers in the Boozer angle. The numerical results are compared “a posteriori” with the permissible asymptotic limits for the perturbed displacement: the radial displacement variable ξψ is found to be always near its most unstable asymptotic limit, while the full range of permissible asymptotic behaviors can be obtained for the binormal and the parallel displacement variables.

Spherical Tokamak (ST) based Component Test Facility (CTF) or ST Power Plant requires high values of plasma current I p : nevertheless the I p start-up and ramp-up have to be obtained without a central solenoid, due to the high neutron flux (there being no space for an effective shield). The use of the poloidal field coils (PF) is one of the most promising techniques to achieve this goal. In fact, the peculiar characteristics of the ST equilibria allow for using the PF coil magnetic flux alone in order to obtain an initial current and for ramping it up to the flat-top value. Among the present large ST devices, MAST is particularly suitable to test those new techniques, due to the large space inside its vacuum vessel that contains all the PF coils. Two different methods has been investigated on MAST: Merging Compression (M/C) and Double Null Merging (DNM).

A scanning interferometer has been developed and installed on the FTU tokamak for plasma density profile measurements. A scanning system is equivalent to a multi-chord system while keeping the optical scheme as simple as a single-chord interferometer. This new diagnostic has achieved a spatial resolution of similar to 1 cm and a time resolution of 62 mu s. In this paper, we present the first measurements carried out with this interferometer showing its peculiar capabilities. Particular care has been paid to the analysis of pellet fuelled discharges, where the fast and large density change (10(21) m(-3) in 100 mu s) is a great challenge for the system. Results and problems with the inversion are reported. Comparison with other FTU diagnostics is also presented.

The design study of PROTO-SPHERA, a novel compact torus configuration, has been completed. It is composed of a spherical torus (ST) (with closed flux surfaces) and a force-free screw pinch (SP) (with open flux surfaces and fed by electrodes). PROTO-SPHERA is formed at spherical-tokamak-like densities (similar to 10(19) M-3) with low voltage (similar to 200 V) between the electrodes. The idea of replacing the metal centrepost current (I-tf) of the spherical tokamaks with the SP plasma electrode current (I-e) is aimed mainly at getting rid of the rod at the centre of the plasma configuration, which is the most critical component of spherical tokamak design. As a consequence it should be possible to decrease the aspect ratio A = R/a (R = ST major radius, a = ST minor radius) in the course of experiment and to increase the ratio between the toroidal plasma current (I-ST) and the plasma electrode current, I-ST/I-e >> 1. Matching two plasma configurations, i.e. an open flux-surface SP and a closed flux-surface ST, brings to life several radically new issues. The purpose of this paper is to analyse the equilibrium, the ideal MHD stability and the formations and modelling issues of such a combined magnetic confinement system. The MULTI-PINCH experimental setup, which is being assembled inside the START vacuum vessel (now in Frascati), will represent the first phase of PROTO-SPHERA: its goal is to prove the feasibility of a stable disc-shaped SP around the electrodes.

PROTO-SPHERA is a proposed spherical torus where a hydrogen plasma arc, in a form of a screw pinch field fed by electrodes, replaces the central conductor. This simply connected magnetic configuration, if fusion relevant, might strongly simplify the design of a fusion reactor. The machine design philosophy, basic geometry and operating conditions together with the major components like the vacuum vessel, coils, electrodes, protection components, divertor, etc. are analyzed. The thermal and electromagnetic behavior as well as the predicted and permitted key stresses will be discussed in order to demonstrate that the design, construction and reliable operation of the machine are feasible. Reference is also made to the proposed Multi-Pinch experiment using the START vacuum vessel to demonstrate the feasibility and stability of the PROTO-SPHERA configuration.

A. Sykes, F. Alladio, P. Costa , N. Conway, G. Cunningham, A.Dnestrovskij , M. Gryaznevich, J. Hicks, M. Hood, A.Mancuso , G. McArdle, P. Micozzi , M. Price, F. Volpe, M J Walsh, M. Wisse EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, United Kingdom. EURATOM-ENEA C.P. 65 I-00044 Frascati (Roma) Italy Kurchatov Institute, Institute of Nuclear Fusion, Moscow, Russia

Magnetic coordinates (ψT=radial label of flux surfaces, θ=poloidal, and ϕ=toroidal angle) are introduced in toroidal magnetoplasma equilibria in order to straighten the field lines [described by: θ−ι̷(ψT)ϕ=constant on any flux surface, ι̷(ψT) being the rotational transform]. The simplest method for analyzing the ideal magnetohydrodynamic (MHD) stability expands the perturbed plasma displacement ξ⃗ in magnetic coordinates and solves the normal mode equation through one-dimensional (1D) radial finite elements. This paper extends the calculation of (Boozer) magnetic coordinates to simply connected equilibria that embed a magnetic separatrix, with regular X-points (B⃗≠0), and reach the symmetry axis, with singular magnetic X-points (B⃗=0). These configurations include multiple plasma regions, whose outermost one (surrounding plasma) is not composed by toroidal surfaces closed around a single magnetic axis. Two examples are chosen: (i) flux-core-spheromak (FCS) configurations, where the surrounding plasma is a screw pinch, with open flux surfaces; (ii) Chandrasekhar–Kendall–Furth (CKF) configurations, where it is a toroidal shell, carved by multiple toroidal plasma regions. This paper shows that a proper ordering of the radial coordinate ψT, the requirement of continuity for θ and ϕ and an ι̷ matching condition (between neighboring mesh points on opposite sides of the connecting separatrix) resolve the ambiguities in the definition of magnetic coordinates in both CKF and FCS cases. However, a few metric coefficients diverge at the separatrices; therefore, often numerical MHD stability codes do not use magnetic coordinates there, but adopt local two-dimensional (2D) finite elements. This paper instead investigates all the divergences, in order to allow for the asymptotic analysis of ξ⃗ near the separatrices, with the purpose of maintaining the magnetic coordinate method and the 1D radial finite elements in the ideal MHD stability analysis.

Introduction. In order to improve the diagnostic performances in the Frascati Tokamak Upgrade (FTU) for the advanced scenario experiments, a new scanning interferometer was installed. More than 30 chords through the observation port have been obtained, with a substantial increase of the spatial resolution for density profiles. The scanning time was 12 kHz (density profiles every 42μs) in the 2004 campaign. Now a more reliable oscillator is used that provides a density profile every 62.5 μs (scanning frequency 8 kHz). The diagnostic has been developed by the “Consorzio RFX” [1] and was implemented during the first FTU shut down in 2004. In the following, we will present some measurements made during the 2004 and first part of 2005 experimental campaigns, to show the diagnostic capability of the instrument. The scanning interferometer. A “two colours” interferometer uses two different lasers to compensate the mechanical vibration contribution to the phase. The density is obtained by the phase difference of two interferometers (n e~ λ1φ1−λ2φ2). In this case CO 2 laser (10 W, λ = 10.6μm) is used for the measurement, while a CO laser (1 W, λ = 5.5μm) is used to compensate vibrations. The wavelength choice was dictated by the attainment of very high densities (> of 10 21 m-3) with multiple pellet injection. Due to an obstruction in the middle of the port, two Scanner Mirror Focusing Mirror Beam splitter そ Selection filter Bragg cell CO CO2 detector