A Burning Plasma is Needed to Test the Standard Model of Tokamak Transport

by Dr. Gary Staebler (gary.staeblergat.com)
General Atomics

10 April 2002

Several contributors to this forum have observed that a burning plasma experiment should have a clear scientific mission. A scientific mission cannot replace the technology mission of developing a fusion energy power plant, but it should be part of the integrated goal. It has been argued by Dr. Heeter that plasma physics lacks a "standard model" like high energy physics and that we do not use the standard scientific process of testing theory with experiment because we lack a "comprehensive theoretical foundation". I would like to respond to these perceptions and in the process give support to a scientific mission for a burning plasma experiment. It is my opinion that plasma physics has a standard model and that quantitative testing of the predictions of the standard model are often carried out in magnetic fusion energy experiments. In particular, the predictive power of transport theory has greatly advanced in the last few years and there are good reasons to expect this trend to continue. A burning plasma experiment has a clear scientific mission to test the standard model prediction of the threshold for new alpha-particle driven instabilities and to explore their non-linear properties.

In 1984 I completed my Ph.D. thesis in supergravity theory at the University of Colorado. After three years of postgraduate work in high energy theory I joined General Atomics and began learning plasma physics. My initial impression of fusion energy research in 1987 was similar to Dr. Heeter's. In some areas (MHD, wave-particle interactions) theory was respected and could produce accurate realistic calculations to compare with experiment, but transport theory was not predictive and the experimentalists resorted to empirical scaling laws. This was quite a contrast to the scientific culture in high energy physics I had known. As I have learned some transport theory, it has become clear that plasma physics does have a comprehensive standard model: the Fokker-Planck equation together with Maxwell's equations. From this standard model all of the special cases (MHD, gyrokinetic, etc.) of plasma theory follow. The problem with transport in fusion energy experiments is that the plasma is in a strongly non-linear turbulent state. The areas of plasma theory where linear theory is sufficient are just as predictive as other areas of physics which rely on linear theory, including high energy physics (QED). It is also true that the areas of other branches of physics where complex non-linear theory is required (e.g., lattice QCD) have the same limitations as plasma physics, the power of available computers. If it were not for the discovery of asymptotic freedom in 1968, high energy physics might still be struggling to be predictive.

In the late 1960s, the nuclear physics community was in a quandary. There was an expanding family of short lived hadrons (strongly interacting particles) observed in cosmic rays and accelerator laboratories. Some progress had been made at classification of hadrons as being composed of three quarks in 1964 but no quarks had been seen as free particles. The strong coupling aspect of nuclear forces made linear scattering theory unusable so it was not possible to predict what scattering from a quark would look like. Despite these difficulties, higher energy "atom smashers" were built and in 1968 the Stanford linear accelerator started to observe hard (i.e., large angle) scattering events in electron proton collisions. These "deep inelastic scattering" events were the first direct evidence of subnuclear particles. These experiments also showed that the subnuclear particles, although confined inside the hadrons, behaved more and more like free particles the higher the energy of the collision. This property of "asymptotic freedom" made linear scattering theory valid again at high energy and a new era of predictive high energy theory was born.

Transport theory in tokamaks has suffered from the same quandary as faced nuclear physics in the 60s. We have a theory of the fundamental linearly unstable modes responsible for transport but these modes are all present in the plasma at once and are strongly coupled. This made it beyond the capability of computers to calculate the nonlinear transport in a real magnetically confined plasma. Over time, many regimes of energy confinement have been observed in tokamaks with distinctive properties (neo-Alcator Ohmic, saturated Ohmic, L-mode, Z-mode, PEP-mode). It was not possible to definitively classify these confinement regimes based on the properties of the instabilities which are predicted to be active in them. As higher energy plasmas have been produced, we have found that "transport barriers", that is regions of suppressed turbulence, form spontaneously (H-mode, VH-mode, high beta-p, NCS, ERS). These confinement regimes can have reduced transport in only one or a particular mixture of transport channels (electron thermal, ion thermal, particle, toroidal momentum). This phenomenon of turbulence suppression can be characterized as a generalized second stability of the linear instabilities at high gradients. Second stability is like asymptotic freedom in many ways. It allows us to probe the substructure of the turbulence by turning off certain instabilities and selectively revealing the characteristics of the fundamental instabilities. We may also be able to turn off all of the turbulence for a time leaving only neoclassical transport. The recent achievement of neoclassical levels of ion energy transport across the whole plasma is a triumph to be celebrated. It was also the beginning of a new era for transport theory since we can now observe subdominant transport processes in experiments. Instead of having to deal with a strongly coupled soup of instabilities, over a large frequency range, we may have produced plasmas with only one instability. Generalized second stability has lead to rapid progress in testing the "standard model" for tokamak transport.

Just as hadrons inherit the characteristics of their constituent quarks, the various confinement regimes of a tokamak owe their unique properties to the differences in the mix of instabilities active in them. The various confinement regimes have begun to be classified in terms of the linear stability properties of the fundamental instabilities. A complete classification will probably require nonlinear simulations. Fully kinetic electron+ion turbulence simulations are just becoming practical. Already, the success of being able to predict the threshold condition for a transport barrier based on when theory calculates the ion temperature gradient mode will be quenched by ExB velocity shear (a generalized second stability condition) has helped change the way the fusion community regards transport theory. There are now theory based transport models which predict the confinement of current tokamaks as accurately and over a greater range of regimes than empirical scaling rules. Detailed experiments are now carried out to test specific properties of various driftwave instabilities predicted by theory. Plasma transport theory has come a long way since the first burning plasma experiments were proposed.