... | ... | @@ -1008,17 +1008,17 @@ expand them about latexmath:[y] to latexmath:[O(y^2)] to obtain: |
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[latexmath]
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++++
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\begin{aligned}
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B_x(\Delta_x, y, \Delta_z) &\approx -B_0 \frac{n}{R} e^{-\frac{n}{R} \Delta_x} y \\
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B_y(\Delta_x, y, \Delta_z) &\approx B_0 e^{-\frac{n}{R} \Delta_x} \left[ F(\Delta_z) - \left( \frac{n^2}{R^2} F(\Delta_z) + F''(\Delta_z) \right) \frac{y^2}{2} \right] \\
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B_z(\Delta_x, y, \Delta_z) &\approx B_0 e^{-\frac{n}{R} \Delta_x} y F'(\Delta_z)\end{aligned}
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B_x(\Delta_x, y, \Delta_z) & \approx -B_0 \frac{n}{R} e^{-\frac{n}{R} \Delta_x} y \\
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B_y(\Delta_x, y, \Delta_z) & \approx B_0 e^{-\frac{n}{R} \Delta_x} \left[ F(\Delta_z) - \left( \frac{n^2}{R^2} F(\Delta_z) + F''(\Delta_z) \right) \frac{y^2}{2} \right] \\
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B_z(\Delta_x, y, \Delta_z) & \approx B_0 e^{-\frac{n}{R} \Delta_x} y F'(\Delta_z)\end{aligned}
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++++
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* In central region:
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[latexmath]
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++++
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\begin{aligned}
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B_x(\Delta_x, y, \Delta_z) &\approx -B_0 \frac{n}{R} e^{-\frac{n}{R} \Delta_x} y \\
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B_y(\Delta_x, y, \Delta_z) &\approx B_0 e^{-\frac{n}{R} \Delta_x} \left[ 1 - \frac{n^2}{R^2} \frac{y^2}{2} \right] \\
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B_z(\Delta_x, y, \Delta_z) &\approx 0\end{aligned}
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B_x(\Delta_x, y, \Delta_z) & -B_0 \frac{n}{R} e^{-\frac{n}{R} \Delta_x} y \\
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B_y(\Delta_x, y, \Delta_z) & B_0 e^{-\frac{n}{R} \Delta_x} \left[ 1 - \frac{n^2}{R^2} \frac{y^2}{2} \right] \\
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B_z(\Delta_x, y, \Delta_z) & 0\end{aligned}
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++++
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These are the expressions _OPAL-t_ uses to calculate the field inside an
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