Although electrostatic modes (coupled ITG and TEM) typically dominate core transport, we show there exists a particular physical regime in which these modes are severely weakened, enabling transport barriers (TBs) without velocity shear. Velocity shear is expected to be much less in burning plasmas than in existing experiments, so obtaining TBs without it may be crucial. The passage to this regime has apparently arisen in TBs in multiple experimental contexts where the velocity shear is likely low: ITB in JET pellet injection scenarios with magnetic shear s ̂ ≲0, high β_pol ITB in DIII-D, low transport observed in the stellarator Wendelstein 7X, ITB at low β_pol near the axis in EAST, wide pedestal QH-mode edge TBs on DIII-D, and some H-mode pedestals on JET-ILW. We examine representative cases of every one of these, and they are all instances of the new regime we explore. The clearest understanding of this regime is in terms of general concepts of non-equilibrium thermodynamics, a distinguishing and crucial feature of the analysis. These inspire novel concepts and metrics for the TB fluctuations. A huge number of linear and non-linear gyrokinetic simulations with GENE are used, in controlled scans, and for experimental cases, to reveal the crucial features of this regime and its underlying cause. Analytic and semi-analytic models greatly clarify the simulation’s dynamics, reproduce qualitative features, and in many cases give semi-quantitative agreement with them.
As is well known, ITG/TEM typically are very virulent, forcing temperature gradients dT/dr to be close to their onset condition. They are arguably the greatest obstacle to obtaining ion temperatures attractive for fusion without excessive energy losses, and hence, TBs are critical. This analysis helps resolve the paradox: how is it that the much stronger dT/dr in TBs do not drive even stronger instabilities and losses in the barrier, when velocity shear is weak? In the regime explored in this work (zero velocity shear), the ITG/TEM losses decrease by 2-3 orders of magnitude, eventually allowing steep dT/dr such as are observed. Furthermore, we show how TBs might be obtained in unanticipated new parameter regimes.
Two characteristics of the coupled ITG/TEM modes must be appreciated to understand this regime: 1) the modes are remarkably adaptive 2) there is a severe stabilizing constraint hidden in the dynamics. Due to the former, eigenfunctions adjust to stay virulent even in geometries that are apparently highly stabilizing, by concentrating in the bad curvature region. The mode averaged curvatures in TBs can stay robustly destabilizing for both ions and trapped electrons.
But the eigenfunction’s “contortions” to remain in the bad curvature may lead, in certain geometries, to a decoupling with the trapped electrons- they spend relatively little time of their orbit in regions of high mode amplitude. Electrons become nearly adiabatic, highly restricting their particle flux. It can become impossible to satisfy a rigorous microscopic constraint: the average flux of electrons from ExB fluctuations δnδV_ExB must equal ions (by quasi-neutrality δn_e= δn_i). A significant density gradient makes this nearly unattainable, and hence, incompatible with instability. This explains many simulation results better than previous curvature-based arguments. As in non-plasma systems with adaptive fluctuations that maximize entropy production, understanding the constraints is essential - for TBs, to understand how low heat loss (i.e. low entropy production) arises.
Compare two tokamak cases: 1) TB-like: high β_pol (high α =q2 Rdβ/dr) and very negative shear s ̂ 2) a typical core-like case (low α). Case 1 shows enormous reduction in the heat flux only as the fraction of the pressure gradient from density gradients (Fp) increases. The modes concentrate in destabilizing regions. In case 1, trapped electron orbits average over a much larger region than the mode, giving near adiabaticity; case 2 does not. Enforcing absolute adiabaticity on both cases, they behave the same. Analysis shows that electron adiabaticity is the key, not β_pol, curvature drive, etc. As another example, barriers form more easily nearer the axis in experiments. There are fewer trapped electrons there; we find the same heat flux dependence on Fp due to this very different route to near-adiabaticity.
Equivalent adiabaticity can be obtained by disparate geometric strategies. The analytic metrics show the similarity of disparate geometries with similar simulation behavior. Consider stellarator geometries. An equilibrium in National Compact Stellarator geometry, with β= 0, behaves like high α tokamaks, but, over the entire outer half of the minor radius, not just in a relatively thin TB region where α ~ dβ/dr is high. The Wendelstein 7X has metrics close to the JET pellet experiments with shear s ̂ ≲0; hence, similar TBs are seen. W7X geometry gives near adiabaticity by a totally different route: 1) relatively small |B| wells reduce the fraction of trapped electrons 2) remaining trapped electrons are located away from the bad curvature where the mode concentrates (an effect of max J). A clear understanding of the important geometric contributions to weak ITG/TEM should enable much higher confinement in future optimized stellarator designs, and, better TBs in tokamaks.
Ackowlegdements: We gratefully acknowledge important assistance from P. Xanthopoulos of Max Plank IPP. This material is based upon work supported by the U.S. Department of Energy grant DE-FG02-04ER54742 and DE-AC02-09CH11466, the National Energy Research Scientific Computing Center and the Texas Advanced Computing Center, DIII-D National Fusion Facility under DE-FC02-04ER54698. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the EURATOM research program 2014-2018 and 2019-2020 under grant agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission, or of the United States Government or any agency thereof.
|Country or International Organization||United States|
|Affiliation||University of Texas at Austin|