Determination of the Dynamic ITER Energy Confinement Time Scalings

TL;DR

This paper derives a differential equation for the dynamic ITER energy confinement time scalings, linking scaling parameters to the second derivative of power loss, and compares solutions with numerical models for tokamak plasmas.

Contribution

It introduces a differential equation approach to determine dynamic energy confinement time scalings for ITER, connecting parameters to power loss derivatives.

Findings

Derived a differential equation for ITER energy confinement time.

Linked scaling parameters to the second derivative of power loss.

Validated the differential equation solution against numerical plasma models.

Abstract

We derive the differential equation, which is satisfied by the ITER scalings for the dynamic energy confinement time. We show that this differential equation can also be obtained from the differential equation for the energy confinement time, derived from the energy balance equation, when the plasma is near the steady state. We find that the values of the scaling parameters are linked to the second derivative of the power loss, estimated at the steady state. As an example of an application, the solution of the differential equation for the energy confinement time is compared with the profile obtained by solving numerically the balance equations (closed by a transport model) for a concrete Tokamak-plasma.