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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).
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[latexmath]
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++++++++++++++++++++++++++++++++++++++++++++
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E_r &=& -\frac{p \pi}{L} \frac{R}{x_{mn}} E_0 J_m^\prime(k_{mn} r) \cos(m \varphi) \sin(\frac{p\pi}{L}z)\exp(\dot{\iota} \omega t)
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++++++++++++++++++++++++++++++++++++++++++++
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[[sec.elements.travelingwave]]
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=== Traveling Wave Structure
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