Fast heat pulse propagation in hot plasmas
Enzo Lazzaro · Hans Wilhelmsson
Abstract and summary · read the original at the source
In one page
Heat spreads through a hot plasma the way it spreads through a metal bar — slowly, by diffusion — and the rate is set by a transport coefficient that experimenters measure from the steady-state power balance. Then tokamak teams did something simple: they gave the plasma a sudden kick, a hot pulse from a sawtooth crash at the centre or a cold pulse from the edge, and watched the front move. It arrived far sooner than the measured diffusion rate said it should. Lazzaro and Wilhelmsson answer with mathematics rather than a new mechanism. They show that the diffusion equation itself admits travelling-wave solutions whose crossing time depends on the sharpness, the scale length, of the disturbance — and that this time can be a great deal shorter than the plasma’s characteristic diffusion time. A sharp front, in other words, gets across quickly without anything exotic being added. That gives the fast-pulse experiments a candidate explanation from inside ordinary transport theory.
Why it matters hereChapter 9 needs the plasma physics of how a disturbance actually travels through a hot, magnetised medium, and this paper is a clean statement that the speed of a front and the rate of bulk diffusion are two different quantities. Chapter 12’s energy substrate depends on the same distinction: how quickly heat leaves a confined plasma is what decides whether a fusion device holds together.
What it claims
01Travelling-wave solutions of the diffusion equation can have propagation times, related to the scale length of the perturbation, which are considerably less than the characteristic diffusion times of the same system.Abstract, first sentence
Published and peer-reviewed02The controlling quantity for how fast a disturbance crosses the plasma is therefore the scale length of the perturbation itself, not the bulk transport coefficient — so a sharp, short-scale front and a slow, broad relaxation can coexist in one and the same medium without contradiction.Abstract, first sentence, read with the paper’s title
Published and peer-reviewed03This provides a possible model for the interpretation of the experiments on fast hot and cold pulses in magnetically confined plasmas that were current when the paper was written.Abstract, second sentence
Published and peer-reviewed04The argument is analytical rather than simulational: it works from particular solutions of a nonlinear reaction-diffusion equation in one dimension, the technique Wilhelmsson had developed in earlier work on particular solutions and relaxation, applied here to the plasma energy balance.Bibliographic record and reference list, including the 1992 Physica D paper on reaction-diffusion equations in one dimension
Published and peer-reviewed05The open question the paper speaks into is whether the fast-pulse observations require a genuinely non-local transport mechanism at all — its reference list is assembled from exactly that debate, including non-local diffusivity in transient transport studies, a model of non-local effects in tokamaks, and the evidence for inhomogeneous thermal transport in the RTP tokamak. The measurement that settles it is a pulse experiment that separates front speed from bulk diffusivity.Reference list, the transient- and non-local-transport entries
What to watch
Read it · abstract
Abstract
It is found that traveling wave solutions of the diffusion equation can have propagation times, related to the scale length of the perturbation, which can be considerably less than the characteristic diffusion times. This provides a possible model for the interpretation of recent experiments of fast “hot” and “cold” pulses in magnetically confined plasmas.
Enzo Lazzaro and Hans Wilhelmsson, Istituto di Fisica del Plasma del Consiglio Nazionale delle Ricerche, Euratom-ENEA-CNR Association, Milan. Physics of Plasmas 5, issue 8, pages 2830 to 2835, August 1998.
(Abstract only — no open full text of this article was reachable; see the rights note above for what was and was not read. On this site, the companion tokamak sheets are the rotating nonlinear magnetic islands paper at /library/stm-c728aa7225, the modelling of macroscopic magnetic islands in tokamaks at /library/stm-1990916bc3, and nonlinear flow generation by electrostatic turbulence at /library/stm-ea244957db.)
The way in
https://doi.org/10.1063/1.873002PUBLICATION. Physics of Plasmas, volume 5, issue 8, pages 2830 to 2835, August 1998, published by the American Institute of Physics. Copyright AIP Publishing, with no Creative Commons statement recorded in Crossref and none found on the article, so the sheet is abstract-only. WHAT WAS READ. No open full text of this article was reachable. Unpaywall records the article as closed with no open location; INSPIRE-HEP holds no record of it; the publisher’s own article page at pubs.aip.org answers HTTP 403 to automated retrieval. The abstract reproduced below is the article’s own abstract as deposited with Crossref by AIP Publishing, cross-checked against the identical text carried by OpenAlex. The summary and claims on this page were therefore written from that abstract together with the article’s bibliographic record and its reference list, and each claim’s locator says so; nothing here is drawn from the body of the paper, which the editorial rail did not see. AUTHOR AFFILIATION as deposited: both authors, Istituto di Fisica del Plasma del Consiglio Nazionale delle Ricerche, Euratom-ENEA-CNR Association, Via Cozzi 53, 20125 Milan, Italy. Hans Wilhelmsson was a professor at Chalmers University of Technology in Gothenburg working with the Milan group in this period. RELATED PAGES on this site: the tokamak magnetic-island and transport sheets at /library/stm-c728aa7225, /library/stm-1990916bc3 and /library/stm-ea244957db.
How to cite it
Enzo Lazzaro, Hans Wilhelmsson (1998) Fast heat pulse propagation in hot plasmas. doi:10.1063/1.873002
Where it sits in the curriculum
Plasmoids, charge clusters and the orbsLattice confinement fusion