Scaling Of Confinement Time Research Articles

Nondimensional transport scaling in DIII-D: Bohm versus gyro-Bohm resolved

The scaling of cross-field heat transport with relative gyroradius ρ* was measured in low (L) and high (H) mode tokamak plasmas using the technique of dimensionally similar discharges. The relative gyroradius scalings of the electron and ion thermal diffusivities were determined separately using a two-fluid transport analysis. For L-mode plasmas, the electron diffusivity scaled as χe∝χBρ1.1±0.3* (gyro-Bohm-like) while the ion diffusivity scaled as χi∝χBρ−0.5±0.3* (worse than Bohm-like). The results were independent of the method of auxiliary heating (radio frequency or neutral beam). Since the electron and ion fluids had different gyroradius scalings, the effective diffusivity and global confinement time scalings were found to vary from gyro-Bohm-like to Bohm-like depending upon whether the electron or ion channel dominated the heat flux. This last property can explain the previously disparate results with dimensionally similar discharges on different fusion experiments that have been published. Experiments in H mode were also done with the expected values of beta, collisionality, safety factor, and plasma shape for thermonuclear ignition experiments. For these dimensionally similar discharges, both the electron and ion diffusivities scaled gyro-Bohm-like, χe, χi∝χBρ*, as did the global thermal confinement time. This leads to a very favorable prediction for the confinement time of future ignition devices.

Recent transport experiments in W7-AS on the stellarator-tokamak comparison

Parameter scans in density, heating power and isotope mass have been carried out in W7-AS. ECRH at a frequency of 140 GHz has allowed to study the density scaling of the energy confinement time of ECRH plasmas up to densities of 1020 m−3. In power scans it has been tried to relate the power degradation of the energy confinement to a local plasma parameter. Transport analyses using power balance an heat wave techniques indicate that the transport coefficient does not depend on the electron temperature or related parameters. This observation can be reconciled with power degradation if the transport coefficient is formally allowed to vary with changes in the heating power on a faster than the diffusive time scale. Such a transport process describes also the observations in the dynamic phases following large changes in the heating power.

Recent Transport Experiments in W7-AS

Parameter scans in density, heating power and isotope mass have been carried out in W7-AS. ECRH at a frequency of 140 GHz has allowed one to study the density scaling of the energy confinement time of ECRH plasmas up to densities of 10{sup 20}m{sup -3}. In power scans it has been tried to relate the power degradation of the energy confinement to a local plasma parameter. Transport analyses using power balance and heat wave techniques indicate that the transport coefficient does not depend on the electron temperature or related parameters. This observation can be reconciled with power degradation if the transport coefficient is formally allowed to vary with changes in the heating power on a faster than the diffusive time scale. Such a transport process describes also the observations in the dynamic phases following large changes in the heating power. 7 refs., 18 figs.

Gyroradius scaling of electron and ion transport.

The scaling of heat diffusion with relative gyroradius ${\ensuremath{\rho}}_{*}$ is measured on the DIII-D tokamak using dimensionally similar discharges. For the first time, a two-fluid transport analysis allows the ${\ensuremath{\rho}}_{*}$ scaling of the electron and ion fluids to be determined separately. The electron diffusivity is found to scale like ${\ensuremath{\chi}}_{e}\ensuremath{\propto}{\ensuremath{\chi}}_{B}{\ensuremath{\rho}}_{*}^{1.1\ifmmode\pm\else\textpm\fi{}0.3}$ (gyro-Bohm-like) while the ion diffusivity is found to scale like ${\ensuremath{\chi}}_{i}\ensuremath{\propto}{\ensuremath{\chi}}_{B}{\ensuremath{\rho}}_{*}^{\ensuremath{-}0.5\ifmmode\pm\else\textpm\fi{}0.3}$ (Goldston-like). The scaling of the global confinement time and the effective diffusivity can vary from gyro-Bohm-like to Bohm-like depending upon whether the electrons or ions dominate the heat transport.

Neoclassical kinetic theory near an X point: Plateau regime

Traditionally, neoclassical transport calculations ignore poloidal variation of the poloidal magnetic field. Near an X point of the confining field of a diverted plasma, the poloidal field is small, causing guiding centers to linger at that poloidal position. A study of how neoclassical transport is affected by this differential shaping is presented. The problem is solved in general in the plateau regime, and a model poloidal flux function with an X point is utilized as an analytic example to show that the plateau diffusion coefficient can change considerably (factor of 2 reduction). Ion poloidal rotation is proportional to the local value of Bpol but otherwise it is not strongly affected by shaping. The usual favorable scaling of neoclassical confinement time with plasma current is unaffected by the X point.

RFP confinement physics studied on the Extrap-T1 device

Experiments have been performed on the high aspect ratio, high current density Extrap-T1 reversed field pinch to study the response in confinement properties to variations in plasma current and pinch parameter. The study includes measurements of energy and particle confinement times as well as radiated power, impurity concentrations and magnetic fluctuations. The ratio of Spitzer to total input power in these experiments is varied over the wide range 0.4 to 0.8. The operational β0 value is found to be primarily a function of plasma current and pinch parameter and scales only weakly with density since an increase in density is found to be accompanied by a decrease in temperature. Changes in Te/ne, however, directly affect the dynamo activity. At high Te/ne, the scaling of the energy confinement time is governed by the enhancement of the dynamo activity, which offsets the decrease in Spitzer input power with temperature. On the other hand, the particle confinement time is not deteriorated by enhanced dynamo activity. Instead, particle confinement is degraded at a high fraction of Spitzer input power. In this limit, convection of thermal particles can account for a major part of the total energy loss

Experimental relation between particle and energy confinement in reversed-field pinches.

Confinement studies have been performed on the high-aspect-ratio, high-current-density Extrap-T1 reversed-field pinch. Experimental evidence is presented that the scaling of the particle confinement time is not dominated by the dynamo activity. This results in an anticorrelation between particle confinement time and energy confinement time, which becomes apparent in this experiment, as the ratio of Spitzer to total input power is varied over the wide range 0.4--0.8.

An emerging understanding of H-mode discharges in tokamaks*

A remarkable degree of consistency of experimental results from tokamaks throughout the world has developed with regard to the phenomenology of the transition from L-mode to H-mode confinement in tokamaks. The transition is initiated in a narrow layer at the plasma periphery where density fluctuations are suppressed and steep gradients of temperature and density form in a region with large first and second radial derivatives in the vE=(E×B)/B2 flow velocity. These results are qualitatively consistent with theories which predict suppression of fluctuations by shear or curvature in vE. The required vE flow is generated very rapidly when the magnitude of the heating power or of an externally imposed radial current exceed threshold values and several theoretical models have been developed to explain the observed changes in the vE flow. After the transition occurs, the altered boundary conditions enable the development of improved confinement in the plasma interior on a confinement time scale. The resulting H-mode discharge has typically twice the confinement of L-mode discharges and regimes of further improved confinement have been obtained in some H-mode scenarios.

The role of edge physics and confinement issues in the fusion reactor

The compatibility of the power exhaust to the walls and target plates with an adequate survival time of these structures and a sufficiently low impurity concentration in the bulk plasma, on the one hand, and the scaling of the energy confinement time with the tokamak parameters, on the other, are presently seen as two of the most critical issues determining the viability and minimum size of a fusion reactor. Statistical analysis of the world-wide data base of divertor tokamaks and experimental progress in superposing different forms of confinement improvements instil confidence that tokamak devices with the dimensions of ITER can meet the energy confinement requirements for ignition when operating in the H-regime. The critical problem consists, however, in simultaneously satisfying both the impurity and energy confinement related requirements. Regimes of improved confinement also tend to show a reduced rate of outward flow of impurities, thus increasing (for a given production rate at the walls or - in the case of helium - in the interior) their expected concentration. The confinement improvement in the H-regime also extends beyond the separatrix, leading to a thinner scrape-off layer with enhanced power concentration at the target plate and an enhanced penetration of impurities into the bulk plasma. These issues have therefore become the focal point of divertor and H-regime studies. Experiments on ASDEX, DIII-D and JET have successfully demonstrated that the impurity concentration in the H-regime can be effectively limited by the spontaneous cyclic destruction of the transport barrier at the edge (through the so-called ELMs) with only partial sacrifice of the energy confinement improvement. Expectations of handling the power load issues hinge on the capability of the divertor solution to decouple plasma properties in the edge of the bulk plasma from those near the target plates and the possibility of converting the energy flux arriving in the divertor into radiation and spreading it out through charge exchange processes. The status of experiments and model calculations regarding this issue are described

L-mode global energy confinement scaling for ion cyclotron heated tokamak plasmas

The paper presents a study of the parametric scaling of L-mode global energy confinement times in tokamaks with plasma heating by ion cyclotron resonance frequency (ICRF) waves. A total of 292 observations from PLT, JET, ASDEX, TEXTOR, JET-2M and JIPP T-IIU, have been analysed by the multiple linear regression method. The proposed scaling of the global energy confinement time is τE ∝ a-0.2R1.3Ip1.0BT0.1κ0.2-0.1nePtot-0.5. Inspection of the residuals indicates that the ICRE discharges used in the study are well described by this scaling law. A comparison with other τE scalings based on different heating regimes was made. It appears that there is some similarity in the dependence of τE on the plasma current Ip and the absorbed total power Ptot between ICRF and NBI heating schemes. Within the experimental uncertainty, the empirical scaling law satisfies the constraints imposed by the collisionless high β model (Connor, J.W., Taylor, J.B., Nucl. Fusion 17 (1977) 1047), and it is qualitatively well linked with the mode conversion theory. In the L-mode, there is a continuous degradation of the energy confinement time with total heating power and, therefore, improvements are needed, which can be achieved by modification of either the experimental techniques or the tokamak configurations

Transport and turbulence due to itg and dissipative trapped electron modes

The anomalous transport and turbulence driven by a combination of the toroidal ion temperature gradient (ITG) mode and dissipative trapped electron (DTE) mode are studied for a plasma in the dissipative regime. The results from numerical mode coupling simulations show a good agreement with the results from quasilinear theory. A transition from the neo-Alcator scaling of the energy confinement time with density to a saturated state is obtained. It is shown that ion heat pinch effects (inward transport) may exist in the process of thermodynamic relaxation of the system.

Transport and turbulence due to ITG and dissipative trapped electron modes

The anomalous transport and turbulence driven by a combination of the toroidal ion temperature gradient (ITG) mode and dissipative trapped electron (DTE) mode are studied for a plasma in the dissipative regime. The results from numerical mode coupling simulations show a good agreement with the results from quasilinear theory. A transition from the neo-Alcator scaling of the energy confinement time with density to a saturated state is obtained. It is shown that ion heat pinch effects (inward transport) may exist in the process of thermodynamic relaxation of the system.

Isotope scaling in the drift wave model

Impurity ion dynamics are incorporated into a numerical stability analysis of electrostatic drift waves in a sheared slab model. Using a simple iδ model for the electron branch, it is shown that a significant increase in growth rate, proportional to the primary ion mass at moderate Zeff, results for Te ≫ Ti. For the ion branch, the ion temperature gradient (ITG) mode, it is found that in hydrogen and deuterium plasmas the growth rates are inversely proportional to the primary ion mass when Zeff < 2; for Zeff ≥ 2, the ITG mode is generally stable. Using quasilinear theory, it is also shown that for ITG mode turbulence in hydrogen and deuterium plasmas in the low Zeff range (typical of high density Ohmic plasmas) the energy confinement time scaling with atomic mass number A of the primary ion species is τE ∝ Aβ, with β ≃ 0.6. Conversely, the present analysis indicates that confinement in helium plasmas is similar to that obtained for hydrogen. It is suggested that a similar result obtains for electron drift wave turbulence in low density Ohmic plasmas where Tc ≫ Ti when Zeff ≫ 1.

Experimental study on beam acceleration with combined NBI heating and second-harmonic ICRF heating in JT-60

Beam acceleration by heating in the second-harmonic ion cyclotron range of frequency (ICRF) in combination with heating by hydrogen neutral beam injection (NBI) was investigated in the JT-60 tokamak. The energy spectra of the accelerated fast ions were measured by a charge exchange neutral energy analyser whose line of sight was intersected by specific beam lines in the plasma core in order to obtain the required information. The dependences of the tail ion temperature on various parameters (electron density, NBI power and the toroidal phasing of the antenna) were examined. Optimized conditions for beam acceleration were evaluated. For combined ICRF heating and NBI heating, an incremental energy confinement time of 210 ms was achieved, which was three times higher than that obtained with NBI heating alone or with ICRF heating alone. This improvement of the energy confinement during combined NBI and ICRF heating can be explained by a build-up of the fast ions accelerated by the ICRF wave. The scaling of the incremental energy confinement time during combined ICRF+NBI heating was obtained.

The multiple facets of Ohmic confinement in ASDEX

The scaling of the energy confinement time with plasma density and current has been investigated for ohmically heated tokamak discharges in ASDEX. The linear dependence τE ∽ n̄e is maintained in the high density improved Ohmic confinement (IOC) regime with peaked density profiles. The peaking of the radial density profile can be brought about by reducing the net power flow through the plasma surface, thereby leading to a reduction of the edge density. Tailoring of the radiation profile with the addition of low-Z impurities, for example neon, gives access to the IOC regime under conditions where otherwise the degraded saturated Ohmic confinement (SOC) behaviour prevails. The energy confinement time τE increases with current and decreases with heating power also in Ohmic discharges, as is shown by a statistical analysis. However, with the intrinsic coupling between power and current, the two relationships cancel and τE becomes independent of POH and Ip. The two most prominent features of Ohmic confinement can therefore be explained on the basis of simple physical models.

The significance of medium-sized and small devices in fusion research

The significance of medium-sized and small devices is reviewed and discussed taking the case of ITER Physics R&D. It is pointed out that the heat flux density expected in a fusioning plasma will reach an unexperienced high level and it is not self-evident that one could extend the present energy confinement time scaling to predict ITER performances. The confinement of a fusion plasma is considered to be related to heat, momentum and mass transport problems in a nonlinear non-equilibrium system with a finite source and dissipation. Therefore the recent progress of basic experiments and theories in fluid dynamics may greatly be referred, where series of basic experiments are unveiling various modes of heat and mass transport in the nonlinear non-equilibrium system including the scenario and conditions of transition to turbulence. In the field of plasma confinement, a more complex scenario would be expected. Therefore, a systematic and basic research along the same line is highly desired on medium-sized and small devices in order to get insight into the physics of plasma confinement which will provide us the methodology for confinement improvement.

The significance of medium- or small-size devices in fusion research.

The significance of medium-and small-size devices is reviewed and discussed taking the case of ITER Physics R&D. It is pointed out that the heat flux density expected in a fusioning plasma will become as large as an unexperienced high level and it is not self-evident that one could extend the present energy confinement time scaling to predict ITER performances. Systematic research is highly desired on medium-and small-size devices in order to get insight into the physics of plasma confinement which will provide us the methodology for confinement improvement.

Experimental scaling of particle confinement in tokamaks

Experimental measurements on particle confinement in tokamaks are reviewed. The global particle confinement is mainly determined by recycling of the particle flux at the edge, which can be evaluated from Hα emission. The global particle confinement time scales with the line-averaged electron density in small tokamaks, while it decreases with rising electron density in large tokamaks because particle recycling is more localized at the edge. The particle confinement appears to be degraded as heating power increases, like the energy confinement. Other parameter dependences, for example on the ion species, have not been clarified. The database for particle confinement is too limited for designing tokamak reactors.

Scaling laws for trace impurity confinement: a variational approach

A variational approach is outlined for the deduction of impurity confinement scaling laws. Given the forms of the diffusive and convective components to the impurity particle flux, we present a variational principle for the impurity confinement time in terms of the diffusion time scale and the convection parameter, which is a non-dimensional measure of the size of the convective flux relative to the diffusive flux. These results are very general and apply irrespective of whether the transport fluxes are of theoretical or empirical origin. The impurity confinement time scales exponentially with the convection parameter in cases of practical interest.

Scalings of energy confinement and density limit in stellarator/heliotron devices

The paper presents a study of empirical scaling of energy confinement observed experimentally in stellarator/heliotron devices (Heliotron E, Wendelstein VII-A, L2, Heliotron DR) for plasmas heated by electron cyclotron heating and/or neutral beam injection. The proposed scaling of the gross energy confinement time is: , where P is the absorbed power (MW), n is the line average electron density (1020 m−3), B is the magnetic field strength on the plasma axis (T), a is the average minor radius (m) and R is the major radius (m). The empirical scaling of the density limit obtainable under the optimum condition is proposed to be: . These scalings for helical systems are compared with those in tokamaks. The energy confinement scaling has a similar power dependence as the L-mode scaling of tokamaks. The density limit scaling for helical systems seems to indicate an upper limit of the achievable density similar to that in many tokamaks. From the energy confinement time and the density limit , a beta limit can be derived: , which can be lower than the stability/equilibrium beta limit. Thus, from the viewpoint of designing a machine, the values of B, a and R should be selected with care because the dependence of the confinement time (or nτET) and of the above beta limit on these values is different.