Pfirsch-Schluter Regime Research Articles

Bounds on edge shear layer persistence while approaching the density limit

This paper details the theory of edge shear layer collapse as the density approaches the Greenwald density limit. It significantly extends earlier work, which was restricted in applicability. The zonal shear flow screening length is calculated for banana, plateau and Pfirsch–Schluter regimes. Poloidal field scaling persists in the plateau regime. Neoclassical screening and drift wave–zonal flow dynamics are combined in a theory, which is then reduced to a predator–prey model. Zonal noise, due to incoherent mode coupling, is retained. The threshold condition for edge shear layer collapse is computed, and linked to a critical value of the dimensionless parameter . Here is the ion sound radius, is the zonal flow screening length and is the equilibrium density scale length. The limiting initial edge density for shear layer collapse is derived and shown to scale favorably with the plasma current. The results are discussed in light of the density limit and Ohmic phenomenology.

Extended Numerical Modeling of Impurity Neoclassical Transport in Tokamak Edge Plasmas

AbstractUnderstanding of impurity transport in tokamaks is an important issue in order to reduce the impurity contamination in fusion core plasmas. Recently, a new kinetic numerical scheme of impurity classical/neoclassical transport has been developed. This numerical scheme makes it possible to include classical self‐diffusion (CL SD), classical inward pinch (CL IWP), and classical temperature screening effect (CL TSE) of impurity ions. However, impurity neoclassical transport has been modeled only in the case where background plasmas are in the Pfirsch‐Schluter (PS) regime. The purpose of this study is to extend our previous model to wider range of collisionality regimes, i.e., not only the PS regime, but also the plateau regime. As in the previous study, a kinetic model with Binary Collision Monte‐Carlo Model (BMC) has been adopted. We focus on the modeling of the neoclassical self‐diffusion (NC SD) and the neoclassical inward pinch (NC IWP). In order to simulate the neoclassical transport with the BCM, velocity distribution of background plasma ions has been modeled as a deformed Maxwell distribution which includes plasma density gradient. Some test simulations have been done. As for NC SD of impurity ions, our scheme reproduces the dependence on the collisionality parameter in wide range of collisionality regime. As for NC IWP, in cases where test impurity ions and background ions are in the PS and plateau regimes, parameter dependences have been reproduced. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Eulerian approach to bounce–transit and drift resonance and neoclassical toroidal plasma viscosity in tokamaks

An Eulerian approach to treat the bounce–transit and precession drift resonance in tokamaks is developed by expanding the poloidal angle dependence in terms of a Jacobian elliptic function in the low collisionality regime instead of integrating along the unperturbed particle trajectories. One of the advantages is that a complex Coulomb collision operator can be adopted in the approach. The full thermodynamic forces are kept to conserve momentum in the collision processes. To illustrate the method, the approach is applied to calculate the neoclassical toroidal plasma viscosity in both the resonant plateau regime and the Pfirsch–Schluter regime. Both trapped particles and circulating particles contribute to the resonant plateau regime through the bounce and drift resonance and the transit and drift resonance, respectively. The dependences on plasma parameters for both regimes are found to be the same as that of the nonlinear plasma viscosity. The resonant plateau regime naturally connects to the Pfirsch–Schluter regime in the collisional limit.

Transport processes in magnetically confined plasmas in the nonlinear regime

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

A possible way to reverse the impurity influx by alfvén heating in a tokamak plasma

A study is made of the effect of local heating on impurity fluxes in the Pfirsch-Schluter regime. When the effect of the thermoforce on impurity ions is taken into consideration, the impurity flux can be reversed by heating the impurities. This concept may be implemented in experiments on Alfven heating of plasmas in tokamaks. The RF heating power required to reverse the impurity influx is estimated.

Neoclassical Radial Electric Field and Ion Heat Flux in the Presence of the Transport Barrier

The ambipolar radial electric field and ion heat flux in the presence of this field are studied using Monte Carlo guiding centre orbit following code ASCOT. These are studied as a function of temperature gradient in different collisionality regimes. Good agreement with the analytic theory is found for heat fluxes in plateau and banana regimes but in Pfirsch-Schluter regime sub-neoclassical heat flux is found for steep temperature gradients. For radial electric field, deviations from analytic theory are significant.

A Note for Neoclassical Transport in the Pfirsch-Schlueter Regime of Ultra-Low-Aspect-Ratio Tokamak.

In the ultra-low-aspect-ratio tokamak, neoclassical viscosity plays a role to enhance the neoclassical transport such as bootstrap current and ion thermal conductivity in the Pfirsch-Schluter regime. The geometrical factor for calculating the viscosity [K.C. Shaing et al., Phys. Plasmas 3, 965 (1996)] shows divergent tendency for assumed sequences of numerical MHD equilibria when the aspect ratio is reduced to 1.05, where n=B/B and B is the equilibrium magnetic field.

Neoclassical transport analysis for a class of high- beta tokamak equilibria

Balescu's neoclassical transport theory is extended to the case of non-circular flux-surface geometries. Modified classical and neoclassical transport equations, governing particle and heat fluxes in the short- and long-mean-free-path regimes, are derived. These equations are shown to coincide to leading order with the corresponding equations given by Hirshman and Sigmar. They are then applied to an ideal MHD equilibrium, suitable as a simplified but analytically tractable model of a high- beta tokamak. Numerical results for the radial profiles of the global (i.e. flux-surface integrated) particle and heat fluxes in the classical, Pfirsch-Schluter and banana regimes are presented for geometry and plasma parameters realized in some tokamaks, like the divertor and injection tokamak experiment (DITE). This spatial representation provides direct insight into the overall collisional transport behaviour of a given equilibrium, whereas the anomalous transport problem is not addressed here. Our results demonstrate that for a given pressure profile the global neoclassical fluxes may depend very sensitively on the temperature profiles and that, in particular, the global classical and neoclassical ion heat fluxes exhibit a characteristic non-monotonic behaviour.

Effect of collisionality and radial electric field on bootstrap current in the Large Helical Device

The bootstrap current decreases in a more highly collisional regime, and in stellarator/heliotron it is predicted that a neoclassical current component proportional to the radial electric field exists when electrons and ions belong to different regimes of collisionality. To evaluate the bootstrap current in stellarator/heliotron in the whole range of collisionality from the collisionless 1/ν to the Pfirsch-Schluter regime, a new connection formula has been proposed. This connection formula has been applied to Large Helical Device (LHD) plasmas in which ions and electrons belong to different collisionality regimes, and finite beta MHD equilibria including the bootstrap current have been obtained. For LHD plasmas such as ECRH (T1 << Te) in electron root, the bootstrap current with an electric potential twice as high as the electron temperature reduces to about 1/5 to 2/3 of that with zero electric potential. Then, the MHD equilibrium configuration changes significantly, depending on collisionality and radial electric field, even for the same beta value of the LHD plasmas

Bootstrap current and ion thermal conductivity in an ultralow-aspect-ratio tokamak

The bootstrap current Jb=−IcP′B/〈B2〉 and χi= √2NνiMiTi(Ic/e)2〈1/B2〉/‖∇ψ ‖2 are valid for both the banana and the Pfirsch–Schlüter regimes for any finite value of the collision frequency at a radius where the local aspect ratio A approaches unity. Here, I=RBt with R the major radius, Bt the toroidal magnetic field strength, and the prime denoting the derivative with respect to the poloidal flux ψ. Thus, the bootstrap current does not vanish, even in the collisional regime, when A approaches unity. The physical reason for this dramatic result is that the magnitudes of the electron and ion parallel viscosity approach infinity as A approaches unity. This also indicates that the conventional theory underestimates the magnitude of bootstrap current in an ultralow-aspect-ratio tokamak.

Non-linear incompressible poloidal viscosity and its implications for H mode in stellarator/heliotron plasmas

Non-linear incompressible poloidal viscosity is an important ingredient in understanding the L-H transition in both tokamaks and stellarators. Usually two or more local maxima in poloidal viscosity corresponding to this transition may appear in stellarator/heliotron devices. Depending on the relative magnitudes of the toroidal and helical components of the magnetic spectrum, the local maxima can occur at a poloidal E*B Mach number Mp somewhat larger than mod m-nq mod /m, where E (B) is the electric (magnetic) field strength, m(n) is the poloidal (toroidal) mode number of the components of the mod B mod spectrum and q is the safety factor. Non-linear incompressible viscosities for the plateau Pfirsch-Schluter regime are calculated for present and next generation stellarator/heliotron devices (Heliotron-E, CHS, LHD, W7-AS and W7-X) by using a magnetic spectrum near the edge region under the assumption of negligibly small parallel flow. The possibility of the occurrence of the L-H transition and the limitation due to the effect of the charge exchange momentum loss are discussed. When the ion-ion collision frequency and neutrals are reduced sufficiently, all these devices show a local maximum of poloidal viscosity at Mp approximately 1. However, the reduction of the poloidal viscosity in the region beyond this maximum is not large compared with the tokamak case

Impurity poloidal rotation velocity in tokamaks

The impurity poloidal flow velocity, vθz, was measured for Ohmic discharges in banana, plateau, and Pfirsch–Schluter regimes in the Texas Experimental Tokamak (TEXT) [K. W. Gentle, Nucl. Tech./Fusion 1, 479 (1981)]. The velocities were measured spectroscopically using the Doppler shift of a C+4 emission line, and then compared with neoclassical predictions that were evaluated with sets of measured plasma profiles that included the radial electric field. Specifically, neoclassical theory was used to relate vθz to measured radial profiles, but it was not used to predict any profiles other than vθz(r). On that basis, neoclassical theory adequately describes vθz. The prediction is dominated by the impurity and ion density scale lengths. Contributions proportional to the parallel viscosity ratio do not contribute significantly to the prediction in this experiment, and thus are not tested. Similarly, though charge exchange momentum loss may significantly retard the toroidal flow velocity and introduces an unusual electric field dependence into the poloidal flow velocity, the charge exchange contribution to vθz is too small to be detected.

Calculation of transport processes in the Pfirsch-Schluter regime in stellarators

The author discusses a method of calculating particle and heat fluxes (including impurity ions) in the Pfirsch-Schluter regime in stellarators by integrating along the magnetic field lines. A computer is used to calculate the diffusion fluxes through the magnetic surfaces; these are determined by numerical methods, and full account is taken of the influence of three-dimensional inhomogeneity in a known confining magnetic field

Short scale radiative condensation instabilities in tokamak edge plasma

The linear evolution of radiative condensation driven short scale fluctuations has been studied using the ballooning mode formalism. A non-uniform plasma is considered with ion transport in the Pfirsch-Schluter regime and electrons in the anomalous regime. The perpendicular thermal conductivities are taken to be poloidally asymmetric, i.e. χ⊥0 (1 + Δcos θ), where θ is the poloidal angle. For typical values of Δ ⩾ 0.5, the fluctuations are found to be localized on the inboard side of tokamaks. In the collisional limit (me/mi) νei >> ω, the curvature does not affect the growth rate. Anomalous diffusion is found to reduce the critical poloidal mode number

Transport induced by ion-impurity friction in strongly rotating, collisional tokamak plasma

A moment approach to the transport theory of impure Tokamak plasmas with strong rotation velocity Vphi in the Pfirsch-Schluter regime with constant temperature is presented. Using the moment approach, the general form of friction and viscosity with effects of large rotation and arbitrary impurity concentration is obtained. In particular, corrections to Braginskii's viscous tensor due to the large rotation are found. When Vphi <or approximately= upsilon thi, strong in/out and up/down poloidal variations of the impurity density in the flux surface, the first-order poloidal flows, the radial particle flux, and the radial flux of toroidal angular momentum are evaluated. Most importantly, a strong ordering parameter Delta identical to delta piZ( nu ii)2- square root 2/ omega ti is introduced and found to be essentially a measure of up/down density variation; and a large enough Delta may lead to a bifurcation of the equilibrium poloidal flows.

Impurity transport in detached plasmas

Transport of metallic impurities in the plasma edge was compared for normal and detached Tokamak plasmas. A neo-classical model, valid for a dirty plasma in the Pfirsch-Schluter regime, was used to calculate the impurity flux terms. Changes in the edge density and temperature profiles, characteristic of detached discharges, were seen to greatly influence the impurity transport. In particular, the inward convective velocity increased significantly because of the detachment. A one-dimensional transport code was used to evaluate the influence of the edge transport modifications on the global impurity confinement time. Code predictions are in qualitative agreement with experimental measurements made on TEXTOR.

Neoclassical transport properties of a deuterium-tritium Tokamak plasma

The collisional transport theory for a multispecies Tokamak plasma is applied to discuss the properties of a deuterium-tritium mixture. It is shown that in the Pfirsch-Schluter regime tritium and deuterium tend to separate, tritium accumulating in the colder regions. This effect, which is small in the other transport regimes, is not appreciably affected by the presence of a reasonable amount of impurities.

Ballooning limit of collisional drift waves driven by temperature gradients

It is shown that in the ballooning limit collisional drift waves are unstable for temperature and density gradients of opposite signs, whereas they are stable if both gradients have the same sign. If shear damping persists (e.g. in cylindrical systems) both situations are stable. Instabilities are thus expected in such configurations as occur during the initial current rise in Tokamaks, possibly while fueling the system by cold neutral injection, and also in the case of a cold plasma mantle. The ballooning limit is consistent with the requirement on collisionality only in the Pfirsch-Schluter regime.

Effect of impurities on dissipative trapped ion modes

The stability of dissipative trapped ion modes in the presence of impurity ions is investigated and compared with previous theories of these modes in pure plasma. The impurities are assumed to be either in the plateau or Pfirsch–Schluter regime as is typical of either present day or the next generation of toroidal plasmas. The important effects of the impurities are found to be different depending on whether the parallel wave phase velocity is above or below the impurity thermal velocity. However, it can, in general, be stated that when the impurity density gradients are in the same direction as the electron and hydrogen ion density gradients, the impurity ions exert stabilizing effects on the modes. The critical density for stabilization of the modes is found to be significantly reduced, even at rather small impurity concentrations. On the other hand, cases of inverse impurity gradients are likely to be unstable. Numerical applications of the theory to nominal parameters of the PLT tokamak are given.

Impurity Transport in Pfirsch-Schluter Regime for Non-Circular Cross-Section Toroid

The impurity transport for a non-circular cross-section toroid is calculated. The transport rate in the Pfirsch-Schluter regime is found to be smaller than that of a circular cross-section torus by the square of the aspect ratio.