... | ... | @@ -232,7 +232,7 @@ E1:: |
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Entrance edge angle (radians). Figure [rbend] shows the definition of
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a positive entrance edge angle. (Note that the exit edge angle is
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fixed in an `RBEND` element to
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latexmath:[\texttt{E2} = \texttt{ANGLE} - \texttt{E1}]).
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latexmath:[\mathrm{E2} = \mathrm{ANGLE} - \mathrm{E1}]).
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DESIGNENERGY::
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Energy of the reference particle (MeV). The reference particle travels
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approximately the path shown in Figure [rbend].
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... | ... | @@ -279,7 +279,7 @@ E1:: |
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Entrance edge angle (radians). Figure [rbend] shows the definition of
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a positive entrance edge angle. (Note that the exit edge angle is
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fixed in an `RBEND3D` element to
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latexmath:[\texttt{E2} = \texttt{ANGLE} - \texttt{E1}]).
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latexmath:[\mathrm{E2} = \mathrm{ANGLE} - \mathrm{E1}]).
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DESIGNENERGY::
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Energy of the reference particle (MeV). The reference particle travels
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approximately the path shown in Figure [rbend].
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... | ... | @@ -938,7 +938,7 @@ following information: |
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\begin{aligned}
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B_0 &= \text{Field amplitude (T)} \\
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R &= \text{Bend radius (m)} \\
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n &= -\frac{R}{B_{y}}\frac{\partial B_y}{\partial x} \text{ (Field index, set using the parameter } \texttt{K1} \text{)} \\
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n &= -\frac{R}{B_{y}}\frac{\partial B_y}{\partial x} \text{ (Field index, set using the parameter } \mathrm{K1} \text{)} \\
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F(z) &= \left\{
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\begin{array}{lll}
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& F_{entrance}(z_{entrance}) \\
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... | ... | @@ -1637,7 +1637,7 @@ L:: |
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The length of the cavity (default: 0 m)
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VOLT::
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The peak RF voltage (default: 0 MV). The effect of the cavity is
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latexmath:[\delta E=\texttt{VOLT}\cdot\sin(2\pi(\texttt{LAG}-\texttt{HARMON}\cdot f_0 t))].
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latexmath:[\delta E=\mathrm{VOLT}\cdot\sin(2\pi(\mathrm{LAG}-\mathrm{HARMON}\cdot f_0 t))].
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LAG::
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The phase lag [rad] (default: 0). In _OPAL-t_ this phase is in general
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relative to the phase at which the reference particle gains the most
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... | ... | @@ -1827,15 +1827,15 @@ by: |
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[latexmath]
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++++
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\begin{aligned}
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\mathbf{E_{entrance}}(\mathbf{r}, t) &= \mathbf{E_{from-map}}(\mathbf{r}) \cdot \texttt{VOLT} \cdot \cos \left( 2\pi \cdot \texttt{FREQ} \cdot t
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\mathbf{E_{entrance}}(\mathbf{r}, t) &= \mathbf{E_{from-map}}(\mathbf{r}) \cdot \mathrm{VOLT} \cdot \cos \left( 2\pi \cdot \mathrm{FREQ} \cdot t
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+ \phi_{entrance} \right) \\
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\mathbf{E_{exit}}(\mathbf{r}, t) &= \mathbf{E_{from-map}}(\mathbf{r}) \cdot \texttt{VOLT} \cdot \cos \left( 2\pi \cdot \texttt{FREQ} \cdot t
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\mathbf{E_{exit}}(\mathbf{r}, t) &= \mathbf{E_{from-map}}(\mathbf{r}) \cdot \mathrm{VOLT} \cdot \cos \left( 2\pi \cdot \mathrm{FREQ} \cdot t
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+ \phi_{exit} \right)
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\end{aligned}
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++++
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where VOLT and FREQ are the field magnitude and
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frequency attributes (see below).
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latexmath:[ \phi_{entrance}= \texttt{LAG}], the phase attribute
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latexmath:[ \phi_{entrance}= \mathrm{LAG}], the phase attribute
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of the element (see below). latexmath:[ \phi_{exit} ] is dependent
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upon both LAG and the NUMCELLS attribute (see below) and is calculated
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internally by _OPAL-t_.
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... | ... | @@ -1847,16 +1847,16 @@ Figure [FINSB-RAC-field] using |
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[latexmath]
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++++
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\begin{split}
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\mathbf{E} ( \mathbf{r},t ) &= \frac{\texttt{VOLT}}{\sin (2 \pi \cdot \texttt{MODE})} \\
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\mathbf{E} ( \mathbf{r},t ) &= \frac{\mathrm{VOLT}}{\sin (2 \pi \cdot \mathrm{MODE})} \\
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&\phantom{=}
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\times \Biggl\{ \mathbf{E_{from-map}} (x,y,z) \cdot \cos \biggl( 2 \pi \cdot \texttt{FREQ} \cdot t + \texttt{LAG}+ \frac{\pi}{2} \cdot \texttt{MODE} \Bigr) \\
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\times \Biggl\{ \mathbf{E_{from-map}} (x,y,z) \cdot \cos \biggl( 2 \pi \cdot \mathrm{FREQ} \cdot t + \mathrm{LAG}+ \frac{\pi}{2} \cdot \mathrm{MODE} \Bigr) \\
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&\phantom{= \times \Biggl\{}
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+ \mathbf{E_{from-map}}(x,y,z+d) \cdot \cos \biggl( 2 \pi \cdot \texttt{FREQ} \cdot t + \texttt{LAG} + \frac{3 \pi}{2} \cdot \texttt{MODE} \Bigr) \Biggr\}
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+ \mathbf{E_{from-map}}(x,y,z+d) \cdot \cos \biggl( 2 \pi \cdot \mathrm{FREQ} \cdot t + \mathrm{LAG} + \frac{3 \pi}{2} \cdot \mathrm{MODE} \Bigr) \Biggr\}
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\end{split}
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++++
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where d is the cell length and is defined as
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latexmath:[\text{d} = \lambda \cdot \texttt{MODE} ]. MODE is an
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latexmath:[\text{d} = \lambda \cdot \mathrm{MODE} ]. MODE is an
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attribute of the element (see below). When calculating the field from
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the map (latexmath:[\mathbf{E_{from-map}}(x,y,z)]), the longitudinal
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position is referenced to the start of the cavity fields at
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... | ... | @@ -1882,7 +1882,7 @@ L:: |
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cells.
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VOLT::
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The peak RF voltage (default: 0 MV). The effect of the cavity is
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latexmath:[\delta E=\texttt{VOLT}\cdot\sin(\texttt{LAG}- 2\pi\cdot\texttt{FREQ}\cdot t)].
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latexmath:[\delta E=\mathrm{VOLT}\cdot\sin(\mathrm{LAG}- 2\pi\cdot\mathrm{FREQ}\cdot t)].
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LAG::
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The phase lag [rad] (default: 0). In _OPAL-t_ this phase is in general
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relative to the phase at which the reference particle gains the most
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... | ... | @@ -2255,7 +2255,7 @@ respectively. Use `KICK` for an `HKICKER` or `VKICKER` and `HKICK` and |
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could use an `HKICKER` and rotate it appropriately using `PSI`.
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Correctors don’t change the reference trajectory. Otherwise they are
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implemented as `RBEND` with latexmath:[\texttt{E1} = 0] and without
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implemented as `RBEND` with latexmath:[\mathrm{E1} = 0] and without
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fringe fields (hard edge model). They can be used to model earth’s
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magnetic field which is neglected in the design trajectory but which has
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a noticeable effect on the trajectory of a bunch at low energies.
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