Effect of magnetic shearing on thermal transport of electrons in magnetic islands
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摘要: 通过数值求解托卡马克等离子体能量输运方程，研究了磁剪切参数对磁岛内电子温度分布和热输运的影响。结果表明，对于不同的安全因子的径向分布，磁剪切参数会影响有效径向热输运系数，剪切程度越高，有效径向热输运系数
${\chi _r}$ 越大；当磁场扰动程度足够高时，高剪切对有效径向热输运系数${\chi _r}$ 影响会降低。Abstract: The influence of magnetic shear parameters on the electron temperature distribution and heat transport in the magnetic island were studied by numerically solving the tokamak plasma energy transport equation. The results show that for different radial distributions of the safety factor, the magnitude of the magnetic shear parameter will affect the magnitude of the effective radial heat transport coefficient. The higher the shear degree, the greater the effective radial heat transport${\chi _r}$ coefficient. And when the magnetic field perturbation degree is high enough, the effect of high shear on radial heat transport${\chi _r}$ will be reduced.-
Key words:
- magnetic island /
- effective radial heat transport /
- magnetic shear
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图 2
$w = 0.005a$ 和$w = 0.05a$ 时，$\log \left( {{\chi _{r}}/{\chi _ \bot }\;} \right)$ 随剪切长度$ {L_q} $ 的变化Figure 2. With
$w = 0.005a$ and$w = 0.05a$ ,$\log \left( {{\chi _{r}}/{\chi _ \bot }\;} \right)$ vs shear length$ {L_q} $ 
图 3 磁剪切大小随径向位置变化的安全因子径向分布图
Figure 3. Radial distribution diagram of safety factor of magnetic shear size vs radial position
图 4
$\log \left( {{\chi _{r}}/{\chi _ \bot }\;} \right)$ 随$\log \left( {{\chi _\parallel }/{\chi _ \bot }\;} \right)$ 变化图Figure 4. variation diagram of
$\log \left( {{\chi _{r}}/{\chi _ \bot }\;} \right)$ vs$\log \left( {{\chi _\parallel }/{\chi _ \bot }\;} \right)$ 
图 5
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ，$ {L_q} = 0.05a $ ，$\phi = 0$ 时磁岛在$r - \theta $ 平面上的磁面结构图Figure 5. When
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ,$ {L_q} = 0.05a $ ,$\phi = 0$ , magnetic surface structure diagram of magnetic islandon$r - \theta $ plane
图 6
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ，$ {L_q} = 0.05a $ 时，各阶相加后的电子温度径向分布图Figure 6. When
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ,$ {L_q} = 0.05a $ , sum of each order of electron temperature radial distribution
图 7 不同径向格点数的电子温度的等高线分布图
Figure 7. Contour distribution map of electron temperature with different radial grid points
图 8
$\psi {\text{ = }}1 \times {10^{{-}4}}{a}{{B}_{t}}$ ，${L_q} = 0.05a$ 时，$\log ({\chi _r}/{\chi _ \bot })$ 的径向分布图Figure 8. When
$\psi {\text{ = }}1 \times {10^{{-}4}}{a}{{B}_{t}}$ ,${L_q} = 0.05a$ , radial distribution diagram of$\log ({\chi _r}/{\chi _ \bot })$ 
图 9
$\psi {\text{ = }}1 \times {10^{{{ - }}4}}{a}{{B}_{t}}$ ，${L_q} = 0.05a$ ，$\phi = 0$ 时磁岛在$r - \theta $ 平面上的磁面结构图Figure 9. When
$\psi {\text{ = }}1 \times {10^{{{ - }}4}}{a}{{B}_{t}}$ ,${L_q} = 0.05a$ ,$\phi = 0$ , magnetic surface structure diagram of magnetic island on$r - \theta $ plane
图 10
$\psi {\text{ = }}1 \times {10^{{{ - }}4}}{a}{{B}_{t}}$ ，${L_q} = 0.05a$ 时，各阶相加后的电子温度径向分布图Figure 10. When
$\psi {\text{ = }}1 \times {10^{{{ - }}4}}{a}{{B}_{t}}$ ,${L_q} = 0.05a$ , sum of each order of electron temperature radial distribution
图 11
$\psi {\text{ = }}1 \times {10^{{{ - }}4}}{a}{{B}_{t}}$ ，${L_q} = 0.05a$ 时，电子温度的等高线分布图Figure 11. When
$\psi {\text{ = }}1 \times {10^{{{ - }}4}}{a}{{B}_{t}}$ ,${L_q} = 0.05a$ , contour distribution map of electron temperature
图 12
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ，${L_q} = 0.3a$ 时，$\log ({\chi _r}/{\chi _ \bot })$ 的径向分布图Figure 12. When
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ,${L_q} = 0.3a$ , radial distribution diagram of$\log ({\chi _r}/{\chi _ \bot })$ 
图 13
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ，${L_q} = 0.3a$ ，$\phi = 0$ 时磁岛在$r - \theta $ 平面上的磁面结构图Figure 13. When
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ,${L_q} = 0.3a$ ,$\phi = 0$ , magnetic surface structure diagram of magnetic island on$r - \theta $ plane
图 14
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ，${L_q} = 0.3a$ 时，各阶相加后的电子温度径向分布图Figure 14. When
$\psi {\text{ = }}2 \times {10^{{{ - }}3}}{a}{{B}_{t}}$ ,${L_q} = 0.3a$ , sum of each order of electron temperature radial distribution -
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