... | ... | @@ -1949,8 +1949,41 @@ B_z &= B_0 J_m(k_{mn} r) \cos(m \varphi) \sin(\frac{p\pi}{L}z) \exp(\dot{\ |
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\end{aligned}
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++++
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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}^\prime ] is the n-th root of the first derivative of latexmath:[ J_m ] and latexmath:[ k_{mn} = \frac{x_{mn}^\prime}{R}].
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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}^\prime ] is the n-th root of the first derivative of latexmath:[ J_m ], latexmath:[ k_{mn} = \frac{x_{mn}^\prime}{R}] and latexmath:[ \omega = c\ctimes\sqrt{k_mn^2 + \frac{p\pi}{L}^2}].
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The attributes of the `PILLBOX` command are:
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---
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label:PILLBOX, L=real, SCALE=real, DSCALE=real, LAG=real, DLAG=real,
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RADIUS=real, M=real, N=real, P=real, APVETO=boolean;
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---
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L::
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The length of the cavity (default: 0_m)
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SCALE::
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The amplitude of the electric field (TM mode, latexmath:[E_0] in equation above) or magnetic field (TE mode, latexmath:[B_0] in equation above).
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DSCALE::
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The error of the amplitude (default: 0). This error isn't applied to
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the reference particle only to particles of the bunch. It is used to
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model imperfections of the machine and trajectory corrections.
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LAG::
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The phase lag [rad] (default: 0).
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DLAG::
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The phase lag error [rad] (default: 0). This error isn't applied to
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the reference particle only to particles of the bunch. It is used to
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model imperfections of the machine and trajectory corrections.
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RADIUS::
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The radius of the cavity [m] (default: 0).
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M::
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The number of variation of field of the azimuthal variable (default: 0).
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N::
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The number of nulls in Ez along the radial direction (default: 1).
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P::
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The number of nodes of Ez along the longitudinal direction (default: 0).
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APVETO::
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If `TRUE` this cavity will not be auto-phased. Instead the phase of
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the cavity is equal to `LAG` at the arrival time of the reference
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particle (arrival at the limit of its field *not* at `ELEMEDGE`).
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[[sec.elements.travelingwave]]
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=== Traveling Wave Structure
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