Nonlocal effects in energy balance in an equilibrium plasma during its fast heating/cooling in tokamaks and stellarators

Abstract

The long-standing problem of nonlocal energy transfer observed in a number of fast heating/cooling experiments in tokamaks and stellarators is discussed. The most representative and still unexplained are the results from cold-pulse experiments that demonstrate a rapid transient increase in the electron temperature in the plasma core in response to an abrupt cooling of the edge. This occurs on a timescale much faster than the diffusive one, which is incompatible with conventional local transport models. This paper contains a review of the most enigmatical observations and theoretical efforts to describe them, and offers an alternative theoretical approach to the problem. Its essential element is the incorporation of the induction effects and fast energy exchange between the plasma and the magnetic field into the traditional transport model. This makes an emphasis on the magnetic field as the main carrier of the interaction, which naturally explains the fast and nonlocal character of the process. The approach uses the ideas recently applied to the analysis of a closely related problem of 'missing power'. Accordingly, the flux-conserving evolution of the plasma equilibrium and evaluation of the integral energy balance are parts of the analysis.

Alfvénic Propagation: A Key to Nonlocal Effects in Magnetized Plasmas

“…These requirements are exactly met by the magnetic field, which is tied to electron dynamics via Ohm's law. This point was recently put forward again by Pustovitov [22], regarding the magnetic field as a buffer able to absorb plasma energy and then quickly deliver it at a different location. In this Letter, we show that the force balance and the rule of frozen flux produce features (I) and (II) on Alfvénic time scales.…”

“…Points (I) and (II) have been defying any attempt of understanding for the past 20 years (see the earlier references alongside with the reviews [20][21][22]). As Callen and Kissick [21] stated, the challenge is to find some quantity which may act as a carrier of the perturbation, which (a) is physically coupled to the electron temperature, so as to trigger the variation of the latter, but its own perturbation from the equilibrium value must be so small to escape detection, too, and (b) is able to support fast signal propagation.…”

“…This explains the nonlocal, transient change of central plasma temperature in response to the peripheral perturbations. We tried successfully this scenario on a large data set: all the experiments reviewed by Pustovitov [22], except for those from tokamaks JIIP-TIIU, TCA, and HL-2A, because the necessary time traces were not available. Extensive results are given in the Supplemental Material [23], while this Letter provides the details for a few only.…”

Observation of non-local effects in ion transport channel in J-TEXT plasmas

“…Pustovitov pointed out in ref [37], the magnetic field surrounding the plasma can provide the necessary heating source to make NLT. There is energy transfer between the plasma and the magnetic field when plasma edge is cooling [37]. In other words, the magnetic field heats the plasma by radial compression during cold pulse injection.…”

A Model of Recovering the Parameters of Fast Nonlocal Heat Transport in Magnetic Fusion Plasmas

“…Одним из самых интересных примеров быстрого нелокального переноса является необычное направление теплового потока, а именно мгновенное в шкале диффузионного времени повышение тем-пературы в центре плазмы в случае быстрого охлаждения периферии плазмы (эксперименты cold pulse на токамаках и стеллараторах [5,6,7]) или обратный процесс -мгновенное понижение температуры в центре плазмы в случае быстрого нагрева периферии плазмы [8]. Наиболее подробный обзор экспери-ментальных данных был представлен в [7], где также предложено учесть работу сил давления (напри-мер, адиабатическое сжатие) для объяснения обсуждаемых экспериментов. Эта работа послужила сти-мулом для анализа другими авторами [9] роли возмущений магнитного поля в экспериментах cold pulse, -переноса тепла альфвеновскими волнами.…”