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[[sec.elements.pillbox]]
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=== Pillbox RF Cavity
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The `PILLBOX` command provides an analytical model for a cylindrical RF cavity. Both TM~mnp~ and TE~mnp~ modes for latexmath:[m \ge 0], latexmath:[n \ge 1] and latexmath:[p \ge 0] \(TM) and latexmath:[p \ge 1] (TE) are supported. The computed field for TM~mnp~ is
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.A block equation
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[latexmath]
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++++
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... | ... | @@ -27,7 +29,8 @@ B_z = 0 |
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where latexmath:[ L ] is the length and latexmath:[ R ] the radius of the pillbox, latexmath:[ J_m ] is the m-th Bessel function of the first kind, latexmath:[ x_{mn} ] is the n-th root of latexmath:[ J_m ] and latexmath:[ k_{mn} = \frac{x_{mn}}{R}].
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And for the TE~mnp~:
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The computed field for TE~mnp~ is:
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.A block equation
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[latexmath]
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++++
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