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[PyTokEq Enhancement] Improve q-profile accuracy at axis #12

@callme-YZ

Description

@callme-YZ

Problem

q(axis) has ~30% error due to cylindrical approximation

Evidence

From validation notes:

  • q(axis) error: ~30%
  • Root cause: Cylindrical approximation in profile model
  • Other q-values more accurate

Impact

  • Core safety factor不准确
  • May affect ballooning mode analysis
  • Limits physics fidelity

Proposed Solution

  1. Better profile model:

    • Use toroidal correction
    • Improve near-axis approximation
    • Reference: Literature formulas
  2. Alternative approaches:

    • Higher-order expansion
    • Direct integration along field lines
    • Adaptive grid near axis

Priority

Low 🟢 - Known limitation, acceptable for current use

Benefits

  • Improved physics accuracy
  • Better comparison with experiments
  • Enhanced credibility

Reported by: 小P ⚛️ + 小A 🤖
Date: 2026-03-23

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