A. V. Danilov

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.

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 canonical profiles transport model to the H-mode shots in tokamaks

The linear and nonlinear versions of the Canonical Profiles Transport Model (CPTM), which includes both heat and particle transport equations, are used to simulate core and pedestal plasma for JET, and MAST H-mode shots. Simulations by the nonlinear version show reasonable agreement with experiment for both ELMy and ELM-free shots. RMS deviations of calculated results from the experimental ones are on the level 10–12% in main. The calculated ion and electron temperature profiles are very insensitive to the change of the deposited peaked power profiles. The calculated pedestal temperature rapidly increases with plasma current; density profile peaking increases at low collisionalities.

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 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.

Physical meaning of one-machine and multimachine tokamak scalings

Specific features of energy confinement scalings constructed using different experimental databases for tokamak plasmas are considered. In the multimachine database, some pairs of engineering variables are collinear; e.g., the current I and the input power P both increase with increasing minor radius a. As a result, scalings derived from this database are reliable only for discharges in which such ratios as I/a2 or P/a2 are close to their values averaged over the database. The collinearity of variables allows one to exclude the normalized Debye radius d* from the scaling expressed in a nondimensional form. In one-machine databases, the dimensionless variables are functionally dependent, which allow one to cast a scaling without d*. In a database combined from two devices, the collinearity may be absent, so the Debye radius cannot generally be excluded from the scaling. It is shown that the experiments performed in support of the absence of d* in the two-machine scaling are unconvincing. Transformation expressions are given that allow one to compare experiments for the determination of scaling in any set of independent variables.

Simulation of the Plasma Density Evolution during Electron Cyclotron Resonance Heating at the T-10 Tokamak

In ohmically heated (OH) plasma with low recycling, an improved particle confinement (IPC) mode is established during gas puffing. However, after gas puffing is switched off, this mode is retained only for about 100 ms, after which an abrupt phase transition into the low particle confinement (LPC) mode occurs in the entire plasma cross section. During such a transition, energy transport due to heat conduction does not change. The phase transition in OH plasma is similar to the effect of density pump-out from the plasma core, which occurs after electron cyclotron heating (ECH) is switched on. Analysis of the measured plasma pressure profiles in the T-10 tokamak shows that, after gas puffing in the OH mode is switched off, the plasma pressure profile in the IPC stage becomes more peaked and, after the peakedness exceeds a certain critical value, the IPC-LPC transition occurs. Similar processes are also observed during ECH. If the pressure profile is insufficiently peaked during ECH, then the density pump-out effect comes into play only after the critical peakedness of the pressure profile is reached. In the plasma core, the density and pressure profiles are close to the corresponding canonical profiles. This allows one to derive an expression for the particle flux within the canonical profile model and formulate a criterion for the IPC-LPC transition. The time evolution of the plasma density profile during phase transitions was simulated for a number of T-10 shots with ECH and high recycling. The particle transport coefficients in the IPC and LPC phases, as well as the dependences of these coefficients on the ECH power, are determined.

Modification of the canonical profile transport model on the basis of new DIII-D experiments

Recent DIII-D experiments have shown that the stiffness of the ion temperature profile κiPC in the region 0.4 < ρ < 0.7 increases by one order of magnitude with increasing radius. At ρ < 0.4, the stiffness is low and the ion temperature profile is “soft.” The stiffness of the temperature profile also increases with decreasing the toroidal rotation velocity. The approximation of the experimental stiffness profiles allows one to modify the canonical profile transport model. The heat conductivity κi0 in the plasma core is determined by minimizing the r.m.s. deviations of the calculated ion temperature from the measured one. This procedure also makes it possible to determine how κi0 depends on the central ion temperature.