... | ... | @@ -958,7 +958,7 @@ parameter `FMAPFN`. Defining the coordinates: |
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++++
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\begin{aligned}
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y &\equiv \text{Vertical distance from magnet mid-plane} \\
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\Delta_x &\equiv \text{Perpendicular distance to reference trajectory (see Figure~\ref{rbend,sbend})} \\
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\Delta_x &\equiv \text{Perpendicular distance to reference trajectory (see Figure <<rbend,sbend>>)} \\
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\Delta_z &\equiv \left\{
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\begin{array}{lll}
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& \text{Distance from entrance Enge function origin perpendicular to magnet entrance face.} \\
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... | ... | @@ -974,7 +974,8 @@ using the conditions |
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++++
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\begin{aligned}
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\nabla \cdot \overrightarrow{B} &= 0 \\
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\nabla \times \overrightarrow{B} &= 0\end{aligned}
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\nabla \times \overrightarrow{B} &= 0
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\end{aligned}
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++++
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and making the definitions:
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... | ... | @@ -984,7 +985,8 @@ and making the definitions: |
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\begin{aligned}
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F'(z) &\equiv \frac{\mathrm{d} F(z)}{\mathrm{d} z} \\
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F''(z) &\equiv \frac{\mathrm{d^{2}} F(z)}{\mathrm{d} z^{2}} \\
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F'''(z) &\equiv \frac{\mathrm{d^{3}} F(z)}{\mathrm{d} z^{3}}\end{aligned}
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F'''(z) &\equiv \frac{\mathrm{d^{3}} F(z)}{\mathrm{d} z^{3}}
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\end{aligned}
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++++
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we can expand the field off axis, with the result:
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... | ... | @@ -1002,7 +1004,7 @@ B_z(\Delta_x, y, \Delta_z) &= B_0 e^{-\frac{n}{R} \Delta_x} \left\{\frac{F'(\Del |
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These expression are not well suited for numerical calculation, so, we
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expand them about latexmath:[y] to latexmath:[O(y^2)] to obtain:
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* In fringe field regions:
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* In fringe field regions:
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[latexmath]
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++++
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\begin{aligned}
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... | ... | |