Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics
The electric potential plays a key role in the confinement properties of tokamak plasmas, with the subsequent impact on the performances of fusion reactors. Understanding its structure in the peripheral plasma -- interacting with solid materials -- is of crucial importance, since it governs the boundary conditions for the burning core plasma. This paper aims at highlighting the dedicated impact of the plasma-wall boundary layer on this peripheral region. Especially, the physics of plasma-wall interaction leads to non-linear constraints along the magnetic field. First, the authors present the physics and the equations governing the evolution of the electric potential of a turbulent plasma flow. They examine the specific conditions introduced by the contact to the wall material and their impact on the system of equations. The reduction of the 3D electrostatic potential equation to a 2D equation is analyzed as well as the linearization procedure that allows one to cast the problem in a variational framework. Further, the mathematical nonlinear evolution problem for the electric potential is summarized. The existence and uniqueness of the solution of the linearized problem is proven. Finally, the existence and uniqueness of the solution to the original nonlinear evolution equation is examined. The results are obtained under an appropriate smallness condition on the source term of the equation, as well as by requiring more regularity of the source term and the initial condition. The working model is two-dimensional in space and time evolving.
scientific article; zbMATH DE number 5522919