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Effect of magnetic drift on the stability structure of the ambipolar condition

Keiji Fujita, Shinsuke Satake

Abstract

In non-axisymmetric plasmas, the ambipolar condition may have multiple roots. In such cases, the evolution of the ambipolar electric field can be described by the dynamics in a bistable potential, where the relative depth of the potential wells primarily determines the realized root. In this study, we show that the inclusion of the magnetic drift in the orbit model can significantly modify the potential landscape and affect root selection. This effect provides a possible explanation for discrepancies between simulation results obtained using different orbit models, as well as between simulations and experimental observations of ambipolar radial electric field profiles. Further, the analysis suggests that the ambipolar electric field may be more susceptible to fluctuations than previously expected, indicating the potential relevance of noise-induced state transitions.

Effect of magnetic drift on the stability structure of the ambipolar condition

Abstract

In non-axisymmetric plasmas, the ambipolar condition may have multiple roots. In such cases, the evolution of the ambipolar electric field can be described by the dynamics in a bistable potential, where the relative depth of the potential wells primarily determines the realized root. In this study, we show that the inclusion of the magnetic drift in the orbit model can significantly modify the potential landscape and affect root selection. This effect provides a possible explanation for discrepancies between simulation results obtained using different orbit models, as well as between simulations and experimental observations of ambipolar radial electric field profiles. Further, the analysis suggests that the ambipolar electric field may be more susceptible to fluctuations than previously expected, indicating the potential relevance of noise-induced state transitions.
Paper Structure (14 sections, 26 equations, 5 figures, 2 tables)

This paper contains 14 sections, 26 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Stability of thermodynamic systems
  3. Prigogine's theorem and universal criterion of evolution
  4. Generalized entropy production
  5. Implications for neoclassical transport
  6. Ambipolar condition
  7. Deterministic model
  8. Stochastic model
  9. Impact of the magnetic drift
  10. Confirmation by numerical simulations
  11. Simulation models and setups
  12. Conventional local simulations
  13. Simulations with the magnetic drift effect
  14. Summary and discussion

Figures (5)

  • Figure 1: Schematic illustration of the potential function $\Psi(E_r)$ for a nonaxisymmetric plasma with two minima at $E_1$ and $E_3$, and a local maximum at $E_2$.
  • Figure 2: Upper panel: electron particle flux $\Gamma_e$ (orange solid line), ion particle flux $\Gamma_i$ (blue dashed line), and the radial current $J_r/e$ (red dotted line) as functions of the radial electric field $E_r$, obtained from DKES/PENTA calculations at $\rho=0.42$. Lower panel: potential function $\Psi(E_r)$ constructed from the radial current profile shown in the upper panel. The reference of $\Psi$ is chosen such that its local maximum is set to zero.
  • Figure 3: Time Evolution of the radial electric field $E_r$ obtained from a radially local FORTEC-3D simulation using the DKES-like model. The system evolves toward the ion-root solution predicted by the potential structure shown in Fig. \ref{['fig:DKES_result_Erscan']}.
  • Figure 4: Upper panel: electron particle flux $\Gamma_e$ (orange solid line), ion particle flux $\Gamma_i$ (blue dashed line), and the radial current $J_r/e$ (red dotted line) as functions of the radial electric field $E_r$, obtained from radially local FORTEC-3D simulations using the zero-orbit-width (ZOW) model. Lower panel: potential function $\Psi(E_r)$ constructed from the radial current profile in the upper panel. The reference of $\Psi$ is chosen such that its local maximum is set to zero.
  • Figure 5: Time Evolution of the radial electric field $E_r$ obtained from a radially local FORTEC-3D simulation using the ZOW model. The system evolves toward the electron-root solution predicted by the potential structure shown in Fig. \ref{['fig:ZOW_result_Erscan']}.