... | ... | @@ -1923,12 +1923,12 @@ The `PILLBOX` command provides an analytical model for a cylindrical RF cavity. |
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[latexmath]
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++++
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\begin{aligned}
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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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E_\varphi &=& -\frac{p \pi}{L} \frac{m R^2}{x_{mn}^2 r} E_0 J_m(k_{mn} r) \sin(m \varphi) \sin(\frac{p\pi}{L}z)\exp(\dot{\iota} \omega t)\\
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E_z &=& E_0 J_m(k_{mn} r) \cos(m \varphi) \cos(\frac{p\pi}{L} z)\exp(\dot{\iota} \omega t) \\
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B_r &=& -\dot{\iota} \omega \frac{m R^2}{x_{mn}^2 r c^2} E_0 J_m(k_{mn} r) \sin(m \varphi) \cos(\frac{p\pi}{L}z)\exp(\dot{\iota} \omega t) \\
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B_\varphi &=& -\dot{\iota} \omega \frac{R}{x_{mn} c^2} E_0 J_m^\prime (k_{mn} r) \cos(m \varphi) \cos(\frac{p\pi}{L}z)\exp(\dot{\iota} \omega t) \\
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B_z &=& 0
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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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E_\varphi &= -\frac{p \pi}{L} \frac{m R^2}{x_{mn}^2 r} E_0 J_m(k_{mn} r) \sin(m \varphi) \sin(\frac{p\pi}{L}z)\exp(\dot{\iota} \omega t)\\
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E_z &= E_0 J_m(k_{mn} r) \cos(m \varphi) \cos(\frac{p\pi}{L} z)\exp(\dot{\iota} \omega t) \\
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B_r &= -\dot{\iota} \omega \frac{m R^2}{x_{mn}^2 r c^2} E_0 J_m(k_{mn} r) \sin(m \varphi) \cos(\frac{p\pi}{L}z)\exp(\dot{\iota} \omega t) \\
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B_\varphi &= -\dot{\iota} \omega \frac{R}{x_{mn} c^2} E_0 J_m^\prime (k_{mn} r) \cos(m \varphi) \cos(\frac{p\pi}{L}z)\exp(\dot{\iota} \omega t) \\
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B_z &= 0
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\end{aligned}
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++++
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... | ... | @@ -1940,12 +1940,12 @@ The computed field for TE~mnp~ is: |
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[latexmath]
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++++
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\begin{aligned}
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E_r &=& \dot{\iota} \omega \frac{m R^2}{x_{mn}^{\prime 2} R} B_0 J_m(k_{mn} r)\sin(m \varphi) \sin(\frac{p\pi}{L} z) \exp(\dot{\iota} \omega t) \\
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E_\varphi &=& \dot{\iota} \omega \frac{R}{x_{mn}^\prime} B_0 J^\prime_{m}(k_{mn} r)\cos(m \varphi) \sin(\frac{p\pi}{L} z) \exp(\dot{\iota} \omega t) \\
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E_z &=& 0 \\
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B_r &=& \frac{p\pi}{L}\frac{R}{x_{mn}^\prime} B_0 J_m^\prime(k_{mn} r)\cos(m \varphi) \cos(\frac{p\pi}{L} z) \exp(\dot{\iota} \omega t) \\
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B_\varphi &=& -\frac{p \pi}{L}\frac{m R^2}{x_{mn}^{\prime 2} r} B_0 J_m(k_{mn} r) \sin(m \varphi) \cos(\frac{p\pi}{L} z) \exp(\dot{\iota} \omega t) \\
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B_z &=& B_0 J_m(k_{mn} r) \cos(m \varphi) \sin(\frac{p\pi}{L}z) \exp(\dot{\iota} \omega t)
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E_r &= \dot{\iota} \omega \frac{m R^2}{x_{mn}^{\prime 2} R} B_0 J_m(k_{mn} r)\sin(m \varphi) \sin(\frac{p\pi}{L} z) \exp(\dot{\iota} \omega t) \\
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E_\varphi &= \dot{\iota} \omega \frac{R}{x_{mn}^\prime} B_0 J^\prime_{m}(k_{mn} r)\cos(m \varphi) \sin(\frac{p\pi}{L} z) \exp(\dot{\iota} \omega t) \\
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E_z &= 0 \\
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B_r &= \frac{p\pi}{L}\frac{R}{x_{mn}^\prime} B_0 J_m^\prime(k_{mn} r)\cos(m \varphi) \cos(\frac{p\pi}{L} z) \exp(\dot{\iota} \omega t) \\
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B_\varphi &= -\frac{p \pi}{L}\frac{m R^2}{x_{mn}^{\prime 2} r} B_0 J_m(k_{mn} r) \sin(m \varphi) \cos(\frac{p\pi}{L} z) \exp(\dot{\iota} \omega t) \\
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B_z &= B_0 J_m(k_{mn} r) \cos(m \varphi) \sin(\frac{p\pi}{L}z) \exp(\dot{\iota} \omega t)
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\end{aligned}
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++++
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... | ... | |