S. V. Cherkasov

Self-consistency of pressure profiles in tokamaks

Plasma pressure profiles from various tokamaks are analysed. It is shown that in the gradient zone the pressure profiles are conserved under variation of the plasma density and deposited power. Usually these profiles are close to the canonical ones. Conservation of pressure profiles means that the density and temperature profiles are consistently correlated under different external actions on the plasma. A simple transport model for the plasma density based on the self-consistency of the pressure profiles is proposed.

Canonical profiles and transport model for the toroidal rotation in tokamaks

The equilibrium equation for a rotating plasma is constructed supposing the thermal Mach number is much less than unity. The canonical profile of angular rotation velocity is defined as the profile which minimizes the total plasma energy while conserving toroidal current and obeying the equilibrium condition. The transport model based on this canonical profile, with stiffness calibrated by JET ELMy H-mode and hybrid mode data, reasonably describes the velocity of the forced toroidal rotation. The RMS deviations of the calculated rotation profiles from the experimental ones do not exceed 10?15%. The developed model is also applied to the modeling of MAST rotation.

Simulation of START shots with the canonical profile transport model

The canonical profile transport model, which has been benchmarked previously for tokamaks with a conventional aspect ratio, is applied to simulations of the spherical tokamak START. A set of Ohmic shots is used to modify the model so that it is appropriate for the specific conditions of the spherical tokamak plasma. The application of the model as a tool to analyze neutral beam-heated START shots allows the estimation of the neutral beam-injection power absorbed by the plasma, PNBabs, which is experimentally uncertain. The modeling shows that both PNBabs and the energy confinement time increase with increasing the average density. Finally, the modified model is used to simulate the performance of the new megaampere spherical tokamak MAST at Culham.

Non-local plasma response within the canonical profiles transport model

The experiments on some tokamaks are simulated, where a fast response near the plasma centre was observed after cooling (by impurity ablation) or heating (by current rampup) at the edge. The canonical profiles transport model (CPTM) is modified for the simulations. The existing equations describing a slow relaxation of the real profile to the canonical profile are complemented by equations describing a fast evolution of the canonical profile. The problem of the canonical profile determination is linked to the transport set through the boundary conditions. Ohms law and one of the Maxwell equations at the edge are used as boundary conditions for the canonical profile of μc (μ = 1/q, q is the safety factor). Therefore, a change of Te(r) profile near the edge leads to a redistribution of the μc(r) profile and to a jump in the electron and ion heat diffusivities over the whole plasma cross-section. The sign of the response (heating or cooling) is very sensitive to details of Te(r) and the evolution of its gradient at the edge. The model reasonably describes both the core heating in TFTR and TEXT, and the core cooling in JET.

OPERATIONAL REGIMES OF THE MODIFIED T-15 TOKAMAK

Transport calculations of the operational regimes for the constructed modified T-15 device are presented. The Canonical Profiles Transport Model (CPTM), verified with JET and MAST tokamaks, is used in the simplified version: Te, Ti and current density diffusion equations are solved with the fixed plasma density n profile. L- and H- modes are described by the appropriate modeling of the boundary conditions for the temperatures and plasma density, confirmed by JET experiment. The absorbed power density profile is determined by the simple formulas. The results are presented as graphics and tables, which can be easily used in order to cre ate the scientific device programs, to develop diagnostics or to define the position of the device in modern tokamak experiments.

Application of the Canonical Profile Theory to the Problems of Heat Transport in Tokamaks

AbstracA transport model for describing electron and ion plasmatemperatures is developed on the basis of the canonical profile theory for a tokamak with an arbitrary cross section. A comparison with the data from experiments on eight different tokamaks shows that the model is capable of adequately simulating plasma discharges. A scaling for the behavior of the relative temperature gradient at half the plasma minor radius is constructed based on both an analysis of the experimental data and the results of numerical calculations.

Canonical Profiles in Tokamak Plasmas with an Arbitrary Cross Section

Two principles are used to determine a canonical profile: the principle of the minimum of free plasma energy with the constraint that the total current is conserved and the principle of profile consistency. A second-order differential equation for the canonical profile of the function μ=1/q is deduced in the natural coordinate system. Soft and hard boundary conditions are proposed to find an unambiguous solution to this equation. The range of their applicability is discussed. Numerical calculations show that the half-width of the canonical profile increases with decreasing aspect ratio, increasing plasma elongation, and decreasing qa value. The canonical profiles obtained make it possible to determine the critical gradients for the heat and particle fluxes in transport models.

Variational problems for the canonical profiles

A noncontradictory formulation of the variational problem for a canonical profile is proposed that refines the problem posed by B.B. Kadomtsev for a circular plasma cylinder. The results are generalized to a toroidal plasma with an arbitrary cross section. For the problem in toroidal geometry, boundary conditions are proposed with which to single out the Kadomtsev-like solution (the canonical profile) from the solutions to the Euler equation. Canonical profiles for the L-and H-modes are constructed. For a number of interesting examples, it is numerically shown that the second variation of the magnetic energy functional is positive. The canonical profile transport model is outlined, and the relationship between the canonical, numerical, and experimental profiles in tokamaks is briefly discussed.

Simulation of internal transport barriers by means of the canonical profile transport model

Models with critical gradients are widely used to describe energy balance in L-mode discharges. The so-called first critical gradient can be found from the canonical temperature profile. Here, it is suggested that discharge regimes with transport barriers can be described based on the idea of the second critical gradient. If, in a certain plasma region, the pressure gradient exceeds the second critical gradient, then the plasma bifurcates into a new state and a transport barrier forms in this region. This idea was implemented in a modified canonical profile transport model that makes it possible to describe the energy and particle balance in tokamak plasmas with arbitrary cross sections and aspect ratios. The magnitude of the second critical gradient was chosen by comparing the results calculated for several tokamak discharges with the experimental data. It is found that the second critical gradient is related to the magnetic shear s. The criterion of the transport barrier formation has the form (a2/r)d/drln(p/pc) > z0(r), where r is the radial coordinate, a is the plasma minor radius, p is the plasma pressure, pc is the canonical pressure profile, and the dimensionless function zO(r) = CO + C1s (with C0i ∼1, C0e ∼3, and C1i,e ∼2) describes the difference between the first and second critical gradients. Simulations show that this criterion is close to that obtained experimentally in JET. The model constructed here is used to simulate internal transport barriers in the JET, TFTR, DIII-D, and MAST tokamaks. The possible dependence of the second critical gradient on the plasma parameters is discussed.

Simulation of plasma density evolution in the T-10 tokamak

Analysis of the experimental profiles of the plasma density and pressure in the T-10 tokamak shows that in the plasma core they are close to the corresponding canonical profiles. This allows one to construct an expression for the particle flux in terms of the canonical profile model. T-10 experiments performed with ohmic discharges have revealed transitions from improved to low particle confinement, similar to the effect of the density pump-out from the central part of the plasma upon switching-on of the electron cyclotron resonance heating (ECRH). It is shown that such a change in the particle confinement is associated with the deviation of the radial pressure profile from the canonical one. A nonlinear model of particle transport in discharges with density variations that allows for the transition effects is proposed. The plasma density evolution is numerically simulated for a number of ohmic and ECRH T-10 discharges.