Radial Electric Field Profile Research Articles

Certain considerations concerning the nature of radial electric field and toroidal rotation velocity profile in tokamak plasma

A new and simple approach aimed at understanding the nature of the radial electric field in some types of tokamak plasmas is presented. It is shown that the radial electric field at some point on a magnetic surface in a tokamak plasma can be divided physically into two parts. The first part is related to a very small difference between densities of electrons and ions of two component plasmas on a magnetic surface in the corotating frame. The second part is related to toroidal rotations of current layers on magnetic surfaces. A new integral equation is calculated. The efficiency of this approach is shown by means of an illustrative example of a Tore-Supra experiment.

Experimental characteristics of a lower hybrid wave multi-junction coupler in the HT-7 tokamak

A phase-controlled lower hybrid wave (LHW) multi-junction (MJ) coupler (3(rows)×4(columns)×4 (subwaveguides)) has been developed in the HT-7 tokamak. Simulations show that it is more effective for driving plasma current than an ordinary phase-controlled LHW antenna (3(rows)× 12(columns)) (traditional coupler). The plasma–wave coupling experiments show that the reflection coefficient (RC) is below 10%, implying that the MJ grill can launch the wave into the plasma effectively. The effect of power spectrum launched by the MJ coupler on RC indicates that an optimal condition is requisite for a better coupling in the lower hybrid current drive (LHCD) experiments. Studies indicate that the drive efficiency of the MJ antenna is higher than that of the traditional one, which is mainly ascribed to the discrepancy in impurity concentration, plasma temperature, and spectrum directivity. An improved confinement with an electron internal transport barrier is obtained by LHCD. The analysis shows that the modified negative (low) magnetic shear and the change of radial electric field profile due to LHCD are possible factors responsible for the eITB formation.

Novel advanced Gundestrup-like probe for the measurements of flows and edge plasma parameters in TEXTOR

A novel advanced Gundestrup-like probe head for local measurements of equilibrium and fluctuating plasma parameters in the plasma edge of TEXTOR is described. This probe assembly enables us to simultaneously determine the toroidal and poloidal plasma flows, the ion saturation current, density, electron temperature, floating potential, as well as their fluctuating properties. An improved analytical probe model is used to correctly relate the ratio of the ion saturation currents measured at the upstream and downstream collecting surfaces to the plasma flow. The probe is mounted on a fast reciprocating manipulator resulting in a high radial resolution of the profiles. A unique feature of the fast probe is the electrical linear motor drive which allows predefining any wave form of the radial position. The high speed of the probe drive reduces the exposure time which enables us to measure several radial profiles within a single discharge deep inside the last closed flux surface. We describe the first experimental results of flow, radial electric field, ion density, and temperature profiles measured in the plasma edge of TEXTOR. In order to verify the accuracy of these measured quantities we compare the measured radial electric field with the one calculated from the single ion momentum balance equation.

Modelling of radial electric field profile for different divertor configurations**This was originally submitted to the special issue on H-mode Physics and Transport Barriers. This special issue may be accessed online at stacks.iop.org/PPCF/48/i=5A.

The impact of divertor configuration on the structure of the radial electric field has been simulated by the B2SOLPS5.0 transport fluid code. It is shown that the change in the parallel flows in the scrape-off layer, which are transported through the separatrix due to turbulent viscosity and diffusivity, should result in variation of the radial electric field and toroidal rotation in the separatrix vicinity. The modelling predictions are compared with the measurements of the radial electric field for the low field side equatorial mid-plane of ASDEX Upgrade in lower, upper and double-null (DN) divertor configurations. The parallel (toroidal) flows in the scrape-off layer and mechanisms for their formation are analysed for different geometries. It is demonstrated that a spike in the electric field exists at the high field side equatorial mid-plane in the connected DN divertor configuration. Its origin is connected with different potential drops between the separatrix vicinity and divertor plates in the two disconnected scrape-off layers, while the separatrix should be at almost the same potential. The spike might be important for additional turbulent suppression.

Investigation of edge pedestal structure in DIII-D

A calculation based on the requirements of particle, momentum and energy conservation, conductive heat transport, and atomic physics resulting from a recycling and fueling neutral influx was employed to investigate the experimental density, temperature, rotation velocities, and radial electric field profiles in the edge of three DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] high-confinement-mode plasmas. The calculation indicated that the cause of the pedestal structure in the density was a momentum balance requirement for a steep negative pressure gradient to balance the forces associated with an edge peaking in the inward pinch velocity (caused by the observed edge peaking in the radial electric field and rotation velocity profiles) and, to a lesser extent, in the outward radial particle flux (caused by the ionization of recycling neutrals). Thermal and angular momentum transport coefficients were inferred from experiment and compared with theoretical predictions, indicating that thermal transport coefficients were of the magnitude predicted by neoclassical and ion-temperature-gradient theories (ions) and electron-temperature-gradient theory (electrons), but that neoclassical gyroviscous theory plus atomic physics effects combined were not sufficient to explain the inferred angular momentum transfer rate throughout the edge region.

Poloidal Rotation Dynamics, Radial Electric Field, and Neoclassical Theory in the Jet Internal-Transport-Barrier Region

Results from the first measurements of a core plasma poloidal rotation velocity (upsilontheta) across internal transport barriers (ITB) on JET are presented. The spatial and temporal evolution of the ITB can be followed along with the upsilontheta radial profiles, providing a very clear link between the location of the steepest region of the ion temperature gradient and localized spin-up of upsilontheta. The upsilontheta measurements are an order of magnitude higher than the neoclassical predictions for thermal particles in the ITB region, contrary to the close agreement found between the determined and predicted particle and heat transport coefficients [K.-D. Zastrow, Plasma Phys. Controlled Fusion 46, B255 (2004)]. These results have significant implications for the understanding of transport barrier dynamics due to their large impact on the measured radial electric field profile.

Two-Dimensional Structure and Particle Pinch in Tokamak H Mode

Two-dimensional structures of the electrostatic potential, density, and flow velocity near the edge of a tokamak plasma are investigated. The model includes the nonlinearity in bulk-ion viscosity and turbulence-driven shear viscosity. For the case with the strong radial electric field (H mode), a two-dimensional structure in a transport barrier is obtained, giving a poloidal shock with a solitary radial electric field profile. The inward particle pinch is induced from this poloidal asymmetric electric field, and increases as the radial electric field becomes stronger. The abrupt increase of this inward ion and electron flux at the onset of L- to H-mode transition explains the rapid establishment of the density pedestal, which is responsible for the observed spontaneous self-reorganization into an improved confinement regime.

Control of the radial electric field shear by modification of the magnetic field configuration in LHD

Control of the radial electric field, Er, is considered to be important in helical plasmas, because the radial electric field and its shear are expected to reduce neoclassical and anomalous transport, respectively. In general, the radial electric field can be controlled by changing the collisionality, and positive or negative electric fields have been obtained by decreasing or increasing the electron density, respectively. Although the sign of the radial electric field can be controlled by changing the collisionality, modification of the magnetic field is required to achieve further control of the radial electric field, especially to produce a strong radial electric field shear. In the Large Helical Device (LHD) the radial electric field profiles are shown to be controlled by the modification of the magnetic field by (1) changing the radial profile of the effective helical ripples, εh, (2) creating a magnetic island with an external perturbation field coil and (3) changing the local island divertor coil current.

Application of a particle, momentum, and energy balance model to calculate the structure of the edge pedestal in DIII-D

A calculation of edge density and temperature profiles based on “classical” physics—particle, momentum, and energy balances, heat conduction closure relations, and neutral particle transport—yielded a pedestal structure that is qualitatively and quantitatively similar to that found experimentally in five DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] discharges, when experimental radial electric field and rotation profiles and experimentally inferred heat transport coefficients were used. The principal cause of the density pedestal was a peaking of the inward pinch velocity just inside the separatrix caused by the negative well in the experimental electric field, and the secondary cause was a peaking of the radial particle flux caused by the ionization of incoming neutrals. There is some evidence that this peaking of the radial particle flux just inside the separatrix may also be responsible in part for the negative electric field in that location.

Multi-Dimensional Structure of the Electric Field in Tokamak H-Mode

In tokamak H-mode, a large poloidal flow exists in an edge transport barrier, and the electrostatic potential and density profiles can be steep both in the radial and poloidal direction. Two-dimensional structures of the potential, density and flow velocity near the edge of a tokamak plasma are investigated. The model includes the nonlinearity in bulk-ion viscosity and turbulence-driven shear viscosity. For the case with a strong radial electric field (H-mode), a two-dimensional structure in a transport barrier is obtained, giving a poloidal shock with a solitary radial electric field profile. The poloidal electric field induces convective transport in the radial direction, and poloidal asymmetry makes the flux-surface-averaged particle flux direct inward with a pinch velocity on the order of 1 [m/s]. A large poloidal flow with radial shear enhances the inward pinch velocity. The abrupt increase of this inward ion and electron flux at the onset of L-to-H-mode transition explains the rapid establishment of the density pedestal at the transition.

Edge pedestal structure

The hypothesis is advanced and it is investigated that, in between or in the absence of edge-localized modes, the structure of the edge pedestal is determined by the transport requirements of plasma particle, momentum and energy balance, and by recycling neutral atoms. A set of “pedestal equations” following from this hypothesis are presented and applied to calculate the edge density, temperature, rotation velocity, and radial electric field profiles in a DIII-D H (high)-mode plasma. It is found that a pedestal structure in the density profile and sharp negative peaks in the radial electric field and poloidal velocity just inside the separatrix are predicted as natural consequences of the conservation of particle and momentum, in qualitative and quantitative agreement with measured values. Detailed examination of the calculation reveals a sequence of mechanisms by which the ionization of recycling neutrals affect the structure of the density profile in the edge pedestal.

Structure of the edge density pedestal in tokamaks

A “first-principles” model for the structure of the edge density pedestal in tokamaks between or in the absence of edge localized magnetohydrodynamic instabilities is derived from ion momentum and particle conservation and from the transport theory of recycling neutral atoms. A calculation for (high) H-mode tokamak discharge parameters indicates that the equations have a self-consistent solution which has an edge pedestal in the ion density profile and sharp negative spikes in the poloidal velocity and radial electric field profiles in the edge pedestal, features characteristic of H-mode edge profiles. These sharp negative spikes in radial electric field and poloidal rotation produce a peak in the inward ion pinch velocity in the sharp gradient (pedestal) region which produces an edge particle transport barrier. The calculated magnitude of the density at the top of the pedestal and the density gradient scale length and radial electric field in the pedestal region are comparable to measured values.

Diagnostics for current density and radial electric field measurements: overview and recent trends

The measurements of the current density and the radial electric field profiles in tokamaks have considerably gained importance since advanced operational scenarios have come into play. A detailed knowledge of these profiles is desirable for operational scenarios involving reversed magnetic shear and/or the active control of internal and edge transport barriers. Unfortunately, the current density as well as the radial electric field are among the plasma parameters that are most difficult to diagnose. Routine methods to measure the current density profile are based on the Faraday effect (i.e. polarimetry) and the motional Stark effect (MSE). The most advanced diagnostics for the measurement of the radial electric field in the plasma core are the heavy ion beam probe and again the MSE. This paper will briefly explain the need for detailed measurements of the current density and radial electric field profile. Subsequently, the various diagnostics to measure these parameters will be reviewed. The emphasis will be especially put on recent trends, rather than on an exhaustive overview.

Theoretical interpretation of the toroidal rotation velocityobserved in Alcator C-Mod Ohmic H-mode discharges

It is shown that neoclassical theory explains quite well the origin of the co-current toroidal rotation velocity measured in the core of stationary Alcator C-Mod edge localized mode (ELM)-free Ohmic high confinement (H)-mode discharges. Both edge and core toroidal rotation velocity profiles are determined to a good approximation by the edge ion temperature and density pedestals, where the gradients are large and the plasma is in the high collisionality regime. Under these conditions, the predicted radial electric field profile is similar to those measured in the DIII-D tokamak whereas the usual expression for the poloidal velocity is modified by finite Larmor radius (FLR) effects. Over the entire plasma cross section, the expression of the toroidal velocity can approximately be cast as the product of a dimensionless non-local functional of the pedestal normalized profiles Ti(r)/Ti(rinf) and Ni(r)/Ni(rinf) with powers of the plasma density, temperature, safety factor and magnetic field at the pedestal inflexion point rinf provided the FLR related corrections are independent of the latter parameters. The collapse of the core toroidal rotation velocity when either an internal transport barrier forms (that leads to impurity accumulation), or the plasma experiences a transition from the H- to the low confinement (L)-mode, or ELMs appear, and the spin up at the L-H transition are also explained. In the edge region, power balance is consistent with the prediction from sub-neoclassical ion energy transport theory at high collisionality. The role of charge exchange neutrals is discussed and the critical density above which they are expected to noticeably slow down the rotation is estimated. The toroidal velocity gradient predicted by theory at the edge of the ELM-free Ohmic H-mode discharge mainly under study (qs = 3.4) is near the onset value for the Kelvin-Helmholtz (K-H) parallel velocity shear (PVS) instability; this result is very interesting since a transition from ELM-free to enhanced Dα (EDA) H-modes occurs at q≅3.5-4; the PVS K-H instability appears to have the characteristics of the `quasi-coherent' mode that is present in all EDA plasmas, but not in ELM-free H-modes.

Role of parallel flow in the improved mode on the STOR-M tokamak.

A novel feature of the H-mode induced by compact torus injection on the STOR-M tokamak is observed. There is almost no change in the radial electric field profiles during and after the L-H transition. The usual hypothesis of the E x B shear stabilization mechanism is therefore unlikely to play a role in this transition. A new mechanism of the stabilization of microinstabilities by parallel flow is suggested as the plausible cause for the transition to this improved regime.

Diagnostics for Radial Electric Field Measurements in Hot Magnetized Plasmas

Measurements of the radial electric field profile in magnetically confined plasmas have yielded important new insights in the physics of L-H transitions, edge biasing and/or the active control of Internal and Edge Transport Barriers. The radial electric field is not an easy plasma parameter to diagnose. Techniques to measure the radial electric field in the plasma core are the Heavy Ion Beam Probe and the Motional Stark Effect. An indirect method that is quite often applied is to derive the electric field from measurements of the poloidal and toroidal rotation velocities via the radial ion force balance. This paper will first briefly explain the need for detailed measurements of the radial electric field profile. Subsequently, the various diagnostics to measure this parameter will be reviewed. The emphasis will be especially put on recent trends, rather than on an exhaustive overview.

Particle Beam Application. Present Status and Future Prospective. Neutral Particle Beams for Plasma Heating in Magnetic Confinement System. Diagnostics for the Fusion Plasma by using the Neutral Beams.

Motional Stark effect (MSE) polarimetry is described as a diagnostic system utilizing neutral beam injection. MSE systems measure magnetic field profiles and (radial) electric field profiles in plasmas. When the electric field is much smaller than the motional Stark electric field (vb × B),an MSE system can measure the magnetic field profile, that is, the safety factor profile q(r). The design of the MSE system for the ITER (International Thermonuclear Experimental Reactor) is briefly described.

Diagnostics for advanced tokamak research (invited)

Advanced tokamak research seeks to find the ultimate potential of the tokamak as a magnetic confinement system. Achieving this potential involves optimizing the plasma cross-sectional shape, current density, and pressure profiles for stability to magnetohydrodynamic (MHD) modes while simultaneously controlling the current density, pressure, and radial electric field profiles to minimize the cross field transport of plasma energy. In its ultimate, steady-state incarnation, the advanced tokamak also requires pressure profiles that have been adjusted to achieve the maximum possible bootstrap current, subject to the constraints of MHD stability. This simultaneous, nonlinear optimization of shape, current, pressure, and electric field profiles to meet multiple goals is a grand challenge to plasma physics. To keep the plasma at peak performance, active feedback control will almost certainly be required. Diagnostic measurements play a crucial role in advanced tokamak research both for developing the scientific understanding underlying the optimization and for serving as sensors for real time feedback control. One outstanding example of this is the way motional Stark effect (MSE) measurements of the internal magnetic field revolutionized work on current profile shaping. Improved diagnostic measurements are essential in testing theories which must be validated in order to apply advanced tokamak results to next step devices.

Experimental Study of a Ka-Band Cylindrical Open Resonator

A study of the electrodynamical properties of a Ka-band gyrotron open resonator was experimentally conducted. Experiments were accomplished to measure resonant frequencies and their respective loaded quality factors for TE modes in the frequency range from 26 to 40 GHz. In particular, a perturbation technique was used to determine the axial, radial and azimuthal electric field profiles, as an identification method of the TE021 mode operating around 35 GHz. In any experimental event, good agreement with the values predicted by theory was found.

Two-dimensional electric fields and drifts near the magnetic separatrix in divertor tokamaks

A two-dimensional calculation is presented for the transport of plasma in the edge region of a divertor tokamak solving continuity, momentum, and energy balance fluid equations. The model uses classical processes of parallel transport along the magnetic field and cross-field drifts together with anomalous radial diffusion, including perpendicular ion viscosity. The self-consistent electrostatic potential is calculated on both sides of the magnetic separatrix via quasineutrality and current continuity. Outside the separatrix, the model extends to material divertor plates where the incident plasma is recycled as neutral gas and where the plate sheath and parallel currents dominate the potential structure. Inside the separatrix, various radial current terms—from anomalous viscosity, collisional damping, inertia, and ∇B drifts—contribute to determining the potential. The model rigorously enforces cancellation of gyroviscous and magnetization terms from the transport equations. The results emphasize the importance of E×B particle flow under the X-point which depends on the sign of the toroidal magnetic field. Radial electric field profiles at the outer midplane show strong variation with the magnitude of the anomalous diffusion coefficients and the core toroidal rotation velocity, indicating that shear stabilization of edge turbulence can likewise be sensitive to these parameters.