EAST steady-state long pulse H-mode with core-edge integration for CFETR

Recent EAST experiment has successfully demonstrated long pulse steady-state high plasma performance scenario and core-edge integration since the last IAEA in 2018. A discharge with a duration over 60s with βP ~2.0, βN ~1.6, H98y2~1.3 and internal transport barrier on electron temperature channel is obtained with multi-RF power heating and current drive. A higher βN (βN~1.8, βp~2.0, H98y2~1.3, ne/nGW~0.75) with a duration of 20s is achieved by using the modulated neutral beam and multi-RF power, where several normalized parameters are close or even higher than the phase III 1GW scenario of CFETR steady-state. High-Z impurity accumulation in the plasma core is well controlled in a low level by using the on-axis ECH. Modelling shows that the strong diffusion of TEM turbulence in the central region prevents tungsten impurity to accumulate. More recently, EAST has demonstrated compatible core-edge integration discharges in the high βp scenario: high confinement H98y2>1.2 with high βP~2.5/βN~2.0 and fbs~50% is sustained with reduced divertor heat flux at high density ne/nGW~0.7 and moderate q95~6.7. By combining active impurity seeding through radiative divertor feedback control and strike point splitting induced by resonant perturbation coil, the peak heat flux is reduced by 20-30% on the ITER-like tungsten divertor, here a mixture of 50% neon and 50% D2 is applied.

The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System

We develop a comprehensive framework in which the existence of solutions to the semiclassical Einstein equation (SCE) in cosmological spacetimes is shown. Different from previous work on this subject, we do not restrict to the conformally coupled scalar field and we admit the full renormalization freedom. Based on a regularization procedure, which utilizes homogeneous distributions and is equivalent to Hadamard point splitting, we obtain a reformulation of the evolution of the quantum state as an infinite-dimensional dynamical system with mathematical features that are distinct from the standard theory of infinite-dimensional dynamical systems (e.g., unbounded evolution operators). Nevertheless, applying methods closely related to Ovsyannikov’s method, we show existence of maximal/global solutions to the SCE for vacuum-like states and of local solutions for thermal-like states. Our equations do not show the instability of the Minkowski solution described by other authors.

Renormalization of local polynomials. Short-distance expansion (SDE)

This chapter discusses two related topics: the renormalization of local polynomials (or local operators) of the field, and the short-distance expansion (SDE) of the product of local operators, in space dimension 4 for simplicity. Both problems are related, since one can consider the insertion of a product of operators at different point as a regularization by point splitting of the product at the same points. Therefore, in the limit of coinciding points, one expects that the product is dominated by a linear combination of the local operators which appear in the renormalization of the product, with singular coefficients, functions of the separation, replacing the usual cut-off dependent renormalization constants. We first discuss the renormalization of local polynomials is first discussed from the viewpoint of power counting. Callan–Symanzik (CS) equations are derived for the insertion of operators of dimension 4 in the φ4 quantum field theory (QFT). Field equations are shown to imply linear relations between operators. The existence of a SDE for the product of two basic fields is established. A CS equation is derived for the Fourier transform of the coefficient of the expansion at leading order. The generalization of this analysis to the SDE beyond leading order, to the SDE of arbitrary operators and to the light-cone expansion (LCE), which appears in the study of the large momentum behaviour of real-time correlation function, are briefly discussed.

The constraint equation of the vertex function of quantum anomaly and Dyson–Schwinger equations in massless QED2 theory

In this paper, we calculate the quantum anomaly for the longitudinal and the transverse Ward–Takahashi (WT) identities for vector and axial-vector currents in QED2 theory by means of the point-splitting method. It is found that the longitudinal WT identity for vector current and transverse WT identity for axial-vector current have no anomaly while the longitudinal WT identity for axial-vector current and the transverse WT identity for vector current have anomaly in QED2 theory. Moreover, we study the four WT identities in massless QED2 theory and get the result that the four WT identities together give the constraint equation of the vertex function of quantum anomaly. At last, we discuss the Dyson–Schwinger equations in massless QED2 theory. It is found that the vertex function of the quantum anomaly has corrections for the fermion propagator and Schwinger model.

The Abraham–Lorentz force and electrodynamics at the classical electron radius

The Abraham–Lorentz force is a finite remnant of the UV singular structure of the self-interaction of a point charge with its own field. The satisfactory description of such an interaction needs a relativistic regulator. This turns out to be a problematic point because the energy of regulated relativistic cutoff theories is unbounded from below. However, one can construct point-splitting regulators which keep the Abraham–Lorentz force stable. The classical language can be reconciled with QED by pointing out that the effective quantum theory for the electric charge supports a saddle point producing the classical radiation reaction forces.

Boost invariant regulator for field theories

It is shown that by imposing the relativistic symmetries on the cutoff in field theories, one rules out all known nonperturbative regulators except the point splitting. The relativistic cutoff dynamics is nonlocal in time and thereby unstable, bringing the very existence of relativistic field theory into question. A stable, relativistic regulator is proposed for a scalar field theory model and its semiclassical stability is shown numerically.