Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Neoclassical transport and profile prediction in transport barriers

Silvia Trinczek, Felix I. Parra

Abstract

Strong gradient regions in tokamaks, such as the pedestal or internal transport barriers, are regions of reduced turbulence where neoclassical transport can play a dominant role. However, standard neoclassical transport theory assumes that the gradient length scales of density, temperature, and potential are of the order of the system size. In the pedestal, gradient length scales are much shorter and are measured to be of the order of the ion poloidal gyroradius. We present an extension of neoclassical theory that is applicable in transport barriers of large aspect ratio tokamaks. We show that particle and momentum transport are connected in such a way that a source of parallel momentum can drive a significant neoclassical ion particle flux. In strong gradient regions, density, electric potential, mean parallel flow, and ion temperature are shown to no longer be flux functions. Instead, they have a small but important poloidally varying piece that modifies the transport equations to lowest order. This introduces a nonlinearity in the transport problem through the coupling with quasineutrality that yields multiple co-existing solutions when solving for the plasma profiles. The different solutions could be connected to low and high transport states and jumps between solutions could be an indication of H-L back-transitions.

Neoclassical transport and profile prediction in transport barriers

Abstract

Strong gradient regions in tokamaks, such as the pedestal or internal transport barriers, are regions of reduced turbulence where neoclassical transport can play a dominant role. However, standard neoclassical transport theory assumes that the gradient length scales of density, temperature, and potential are of the order of the system size. In the pedestal, gradient length scales are much shorter and are measured to be of the order of the ion poloidal gyroradius. We present an extension of neoclassical theory that is applicable in transport barriers of large aspect ratio tokamaks. We show that particle and momentum transport are connected in such a way that a source of parallel momentum can drive a significant neoclassical ion particle flux. In strong gradient regions, density, electric potential, mean parallel flow, and ion temperature are shown to no longer be flux functions. Instead, they have a small but important poloidally varying piece that modifies the transport equations to lowest order. This introduces a nonlinearity in the transport problem through the coupling with quasineutrality that yields multiple co-existing solutions when solving for the plasma profiles. The different solutions could be connected to low and high transport states and jumps between solutions could be an indication of H-L back-transitions.
Paper Structure (11 sections, 26 equations, 3 figures, 1 table)

This paper contains 11 sections, 26 equations, 3 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. STRONG GRADIENT NEOCLASSICAL THEORY
  3. PARTICLE AND MOMENTUM TRANSPORT
  4. Without a parallel momentum source
  5. With a parallel momentum source
  6. Ambipolarity
  7. PROFILE PREDICTION
  8. Density profile prediction
  9. Radial electric field prediction
  10. CONCLUSION
  11. Quasineutrality and modification functions

Figures (3)

  • Figure 1: The trapped region in the weak gradient limit is located around $v_\parallel\simeq0$ and gets shifted to $v_\parallel\simeq-u$ in the strong gradient limitshaing1992kagan2008. The number of co- (red) and counter-passing (blue) particles is equal in the weak gradient limit and unequal for $V_\parallel\neq-u$ in the strong gradient limit.
  • Figure 2: The circled values are the solutions to $\Gamma_i^{\text{neo}}=0.03$, $0.015$ and $0.005$ in \ref{['Gamma']} for $\bar{n}=1$, $\bar{T}=0.78$, $\bar{T}_e=1.2$, $\partial \bar{T}/\partial\bar{\psi}=-0.72$, $\bar{V}=-0.75$, $\bar{u}=0.67$, $\partial \bar{V}/\partial\bar{\psi}=0.7$, $S=1$ and $Z=1$. There exist up to three possible solutions. The points A, B and C could correspond to a H-L back-transition.
  • Figure 3: The circled values are the four solutions to $\Gamma_i^{\text{neo}}=0$ in \ref{['Gamma0']} for $\bar{n}=1$, $\bar{T}=0.78$, $\bar{T}_e=1.35$, $\partial \bar{T}/\partial\bar{\psi}=-0.72$, $\partial \bar{n}/\partial\bar{\psi}=-0.4$, $\bar{V}=-0.75$, $\partial \bar{V}/\partial\bar{\psi}=0.7$ and $Z=1$.