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:toc:
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[[chp:opalcycl]]
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:stem: latexmath
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:sectnums:
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[[chp:element]]
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Elements
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--------
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... | ... | @@ -22,7 +28,7 @@ keyword:: |
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the example `QUADRUPOLE`),
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attribute::
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normally has the form
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+
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+
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....
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attribute-name=attribute-value
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....
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... | ... | @@ -56,33 +62,33 @@ APERTURE:: |
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aperture. All but the last attribute of the aperture have units of
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meter, the last one is optional and is a positive real number.
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Possible choices are
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+
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* `APERTURE`=```SQUARE`(`a,f`)'' has a square shape of width and
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+
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* `APERTURE`="SQUARE(a,f)" has a square shape of width and
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height `a`,
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* `APERTURE`=```RECTANGLE`(`a,b,f`)'' has a rectangular shape of width
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* `APERTURE`="RECTANGLE(a,b,f)" has a rectangular shape of width
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`a` and height `b`,
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* `APERTURE`=```CIRCLE`(`d,f`)'' has a circular shape of diameter `d`,
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* `APERTURE`=```ELLIPSE`(`a,b,f`)'' has an elliptical shape of major
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* `APERTURE`="CIRCLE(d,f)" has a circular shape of diameter `d`,
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* `APERTURE`="ELLIPSE(a,b,f)" has an elliptical shape of major
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`a` and minor `b`.
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+
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The option `SQUARE`(`a,f`) is equivalent to `RECTANGLE`(`a,a,f`) and
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`CIRCLE`(`d,f`) is equivalent to `ELLIPSE`(`d,d,f`). The size of the
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exit aperture is scaled by a factor latexmath:[$f$]. For
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latexmath:[$f < 1$] the exit aperture is smaller than the entrance
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aperture, for latexmath:[$f = 1$] they are the same and for
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latexmath:[$f > 1$] the exit aperture is bigger.
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+
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Dipoles have `GAP` and `HGAP` which define an aperture and hence do
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not recognise `APERTURE`. The aperture of the dipoles has rectangular
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shape of height `GAP` and width `HGAP`. In longitudinal direction it
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is bent such that its center coincides with the circular segment of
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the reference particle when ignoring fringe fields. Between the
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beginning of the fringe field and the entrance face and between the
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exit face and the end of the exit fringe field the rectangular shape
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has width and height that are twice of what they are inside the
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dipole.
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+
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Default aperture for all other elements is a circle of 1.0m.
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+
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The option `SQUARE`(`a,f`) is equivalent to `RECTANGLE`(`a,a,f`) and
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`CIRCLE`(`d,f`) is equivalent to `ELLIPSE`(`d,d,f`). The size of the
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exit aperture is scaled by a factor latexmath:[f]. For
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latexmath:[f < 1] the exit aperture is smaller than the entrance
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aperture, for latexmath:[f = 1] they are the same and for
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latexmath:[f > 1] the exit aperture is bigger.
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+
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Dipoles have `GAP` and `HGAP` which define an aperture and hence do
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not recognise `APERTURE`. The aperture of the dipoles has rectangular
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shape of height `GAP` and width `HGAP`. In longitudinal direction it
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is bent such that its center coincides with the circular segment of
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the reference particle when ignoring fringe fields. Between the
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beginning of the fringe field and the entrance face and between the
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exit face and the end of the exit fringe field the rectangular shape
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has width and height that are twice of what they are inside the
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dipole.
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+
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Default aperture for all other elements is a circle of 1.0m.
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L::
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The length of the element (default: 0m).
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WAKEF::
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... | ... | @@ -109,15 +115,15 @@ Z:: |
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THETA::
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Angle of rotation of the element about the y-axis relative to the
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default orientation,
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latexmath:[$\mathbf{n} = \transpose{\left(0, 0, 1\right)}$].
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latexmath:[\mathbf{n} = \left(0, 0, 1\right)^{\mathbf{T}}].
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PHI::
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Angle of rotation of the element about the x-axis relative to the
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default orientation,
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latexmath:[$\mathbf{n} = \transpose{\left(0, 0, 1\right)}$]
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latexmath:[\mathbf{n} = \left(0, 0, 1\right)^{\mathbf{T}}]
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PSI::
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Angle of rotation of the element about the z-axis relative to the
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default orientation,
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latexmath:[$\mathbf{n} = \transpose{\left(0, 0, 1\right)}$]
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latexmath:[\mathbf{n} = \left(0, 0, 1\right)^{\mathbf{T}}]
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ORIGIN::
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3D position vector. An alternative to using `X`, `Y` and `Z` to
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position the element. Can’t be combined with `THETA` and `PHI`. Use
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... | ... | @@ -186,21 +192,16 @@ _OPAL-t_ bend elements `RBEND` and `SBEND`. |
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3. Section [SBend3D] is self contained. It describes how to implement
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an `SBEND3D` element in an _OPAL-cycl_ simulation.
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image:figures/Elements/rbend.png[Illustration of a general rectangular
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bend () with a positive bend angle latexmath:[$\alpha$]. The entrance
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edge angle, latexmath:[$E_{1}$], is positive in this example. An has
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parallel entrance and exit pole faces, so the exit angle,
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latexmath:[$E_{2}$], is uniquely determined by the bend angle,
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latexmath:[$\alpha$], and latexmath:[$E_{1}$]
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(latexmath:[$E_{2}=\alpha - E_{1}$]). For a positively charge particle,
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the magnetic field is directed out of the page.]
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[#fig:rbend]
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.Figure 1: Illustration of a general rectangular bend (`RBEND`) with a positive bend angle latexmath:[\alpha]. The entrance edge angle, latexmath:[E_{1}], is positive in this example. An `RBEND` has parallel entrance and exit pole faces, so the exit angle, latexmath:[E_{2}], is uniquely determined by the bend angle, latexmath:[\alpha], and latexmath:[E_{1}] (latexmath:[E_{2}=\alpha - E_{1}]). For a positively charge particle, the magnetic field is directed out of the page.
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image:figures/Elements/rbend.png[]
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[[ssec:RBend]]
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RBend (_OPAL-t_)
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^^^^^^^^^^^^^^^^
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An `RBEND` is a rectangular bending magnet. The key property of an
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`RBEND` is that is has parallel pole faces. Figure [rbend] shows an
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`RBEND` is that it has parallel pole faces. Figure [rbend] shows an
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`RBEND` with a positive bend angle and a positive entrance edge angle.
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L::
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... | ... | @@ -213,7 +214,7 @@ HAPERT:: |
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ANGLE::
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Bend angle (radians). Field amplitude of bend will be adjusted to
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achieve this angle. (Note that for an `RBEND`, the bend angle must be
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less than latexmath:[$\frac{\pi}{2} + E1$], where `E1` is the entrance
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less than latexmath:[\frac{\pi}{2} + E1], where `E1` is the entrance
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edge angle.)
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K0::
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Field amplitude in y direction (Tesla). If the `ANGLE` attribute is
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... | ... | @@ -223,15 +224,15 @@ K0S:: |
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set, `K0S` is ignored.
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K1::
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Field gradient index of the magnet,
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latexmath:[$K_1=-\frac{R}{B_{y}}\frac{\partial B_y}{\partial x}$],
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where latexmath:[$R$] is the bend radius as defined in Figure [rbend].
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latexmath:[K_1=-\frac{R}{B_{y}}\frac{\partial B_y}{\partial x}],
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where latexmath:[R] is the bend radius as defined in Figure [rbend].
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Not supported in `DOPAL-t` any more. Superimpose a `Quadrupole`
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instead.
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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:[$\text{\texttt{E2}} = \text{\texttt{ANGLE}} - \text{\texttt{E1}}$]).
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latexmath:[\texttt{E2} = \texttt{ANGLE} - \texttt{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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... | ... | @@ -247,7 +248,7 @@ RBend3D (_OPAL-t_) |
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^^^^^^^^^^^^^^^^^^
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An `RBEND3D3D` is a rectangular bending magnet. The key property of an
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`RBEND3D` is that is has parallel pole faces. Figure [rbend] shows an
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`RBEND3D` is that it has parallel pole faces. Figure [rbend] shows an
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`RBEND3D` with a positive bend angle and a positive entrance edge angle.
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L::
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... | ... | @@ -260,7 +261,7 @@ HAPERT:: |
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ANGLE::
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Bend angle (radians). Field amplitude of bend will be adjusted to
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achieve this angle. (Note that for an `RBEND3D`, the bend angle must
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be less than latexmath:[$\frac{\pi}{2} + E1$], where `E1` is the
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be less than latexmath:[\frac{\pi}{2} + E1], where `E1` is the
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entrance edge angle.)
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K0::
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Field amplitude in y direction (Tesla). If the `ANGLE` attribute is
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... | ... | @@ -270,15 +271,15 @@ K0S:: |
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set, `K0S` is ignored.
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K1::
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Field gradient index of the magnet,
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latexmath:[$K_1=-\frac{R}{B_{y}}\frac{\partial B_y}{\partial x}$],
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where latexmath:[$R$] is the bend radius as defined in Figure [rbend].
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latexmath:[K_1=-\frac{R}{B_{y}}\frac{\partial B_y}{\partial x}],
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where latexmath:[R] is the bend radius as defined in Figure [rbend].
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Not supported in `DOPAL-t` any more. Superimpose a `Quadrupole`
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instead.
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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 E2 = ANGLE
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latexmath:[$\text{\texttt{E2}} = \text{\texttt{ANGLE}} - \text{\texttt{E1}}$]).
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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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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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... | ... | @@ -289,12 +290,9 @@ FMAPFN:: |
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see Section [benddefaultfieldmapopalt]. The field map is used to
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describe the fringe fields of the magnet see Section [1DProfile1].
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image:figures/Elements/sbend.png[Illustration of a general sector bend
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() with a positive bend angle latexmath:[$\alpha$]. In this example the
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entrance and exit edge angles latexmath:[$E_{1}$] and
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latexmath:[$E_{2}$] have positive values. For a positively charge
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particle, the magnetic field is directed out of the page.,title="fig:"]
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[fig:sbend]
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[#fig:sbend]
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.Figure 2: Illustration of a general sector bend(`SBEND`) with a positive bend angle latexmath:[\alpha]. In this example the entrance and exit edge angles latexmath:[E_{1}] and latexmath:[E_{2}] have positive values. For a positively charge particle, the magnetic field is directed out of the page.
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image:figures/Elements/sbend.png[]
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[[ssec:SBend]]
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SBend (_OPAL-t_)
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... | ... | @@ -316,11 +314,11 @@ HAPERT:: |
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ANGLE::
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Bend angle (radians). Field amplitude of the bend will be adjusted to
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achieve this angle. (Note that practically speaking, bend angles
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greater than latexmath:[$\frac{3 \pi}{2}$] (270 degrees) can be
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greater than latexmath:[\frac{3 \pi}{2}] (270 degrees) can be
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problematic. Beyond this, the fringe fields from the entrance and exit
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pole faces could start to interfere, so be careful when setting up
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bend angles greater than this. An angle greater than or equal to
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latexmath:[$2 \pi$] (360 degrees) is not allowed.)
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latexmath:[2 \pi] (360 degrees) is not allowed.)
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K0::
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Field amplitude in y direction (Tesla). If the `ANGLE` attribute is
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set, `K0` is ignored.
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... | ... | @@ -329,8 +327,8 @@ K0S:: |
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set, `K0S` is ignored.
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K1::
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Field gradient index of the magnet,
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latexmath:[$K_1=-\frac{R}{B_{y}}\frac{\partial B_y}{\partial x}$],
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where latexmath:[$R$] is the bend radius as defined in Figure [sbend].
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latexmath:[K_1=-\frac{R}{B_{y}}\frac{\partial B_y}{\partial x}],
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where latexmath:[R] is the bend radius as defined in Figure [sbend].
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Not supported in `DOPAL-t` any more. Superimpose a `Quadrupole`
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instead.
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E1::
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... | ... | @@ -400,8 +398,8 @@ Bend: RBend, ANGLE = 30.0 * Pi / 180.0, |
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This is a definition of a simple `RBEND` that bends the beam in a
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positive direction 30 degrees (towards the negative x axis as if
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Figure [rbend]). It has a design energy of 10MeV, a length of 0.5m, a
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vertical gap of 2cm and a 0latexmath:[$^{\circ}$] entrance edge angle.
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(Therefore the exit edge angle is 30latexmath:[$^{\circ}$].) We are
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vertical gap of 2cm and a 0latexmath:[^{\circ}] entrance edge angle.
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(Therefore the exit edge angle is 30latexmath:[^{\circ}].) We are
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using the default, internal field map ``1DPROFILE1-DEFAULT''
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see Section [benddefaultfieldmapopalt] which describes the magnet fringe
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fields see Section [1DProfile1]. When _OPAL_ is run, you will get the
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... | ... | @@ -438,12 +436,12 @@ The first section of this output gives the properties of the reference |
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trajectory like that described in Figure [rbend]. From the value of
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`ANGLE` and the length, `L`, of the magnet, _OPAL_ calculates the 10MeV
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reference particle trajectory radius, `R`. From the bend geometry and
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the entrance angle (0latexmath:[$^{\circ}$] in this case), the exit
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the entrance angle (0latexmath:[^{\circ}] in this case), the exit
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angle is calculated.
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The second section gives the field amplitude of the bend and its
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gradient (quadrupole focusing component), given the particle charge
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(latexmath:[$-e$] in this case so the amplitude is negative to get a
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(latexmath:[-e] in this case so the amplitude is negative to get a
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positive bend direction). Also listed is the rotation of the magnet
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about the various axes.
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... | ... | @@ -889,13 +887,8 @@ the same as the hard edge magnet described by the reference trajectory. |
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Bend Fields from 1D Field Maps (_OPAL-t_)
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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image:figures/Elements/Enge-func-plot.png[Plot of the entrance fringe
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field of a dipole magnet along the mid-plane, perpendicular to its
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entrance face. The field is normalized to 1.0. In this case, the fringe
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field is described by an Enge function see Equation [enge_func] with the
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parameters from the default `1DProfile1` field map described in
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Section [benddefaultfieldmapopalt]. The exit fringe field of this magnet
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is the mirror image.]
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.Figure 3: Plot of the entrance fringe field of a dipole magnet along the mid-plane, perpendicular to its entrance face. The field is normalized to 1.0. In this case, the fringe field is described by an Enge function see Equation [enge_func] with the parameters from the default `1DProfile1` field map described in Section [benddefaultfieldmapopalt]. The exit fringe field of this magnet is the mirror image.
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image:figures/Elements/Enge-func-plot.png[]
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So far we have described how to setup an `RBEND` or `SBEND` element, but
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have not explained how _OPAL-t_ uses this information to calculate the
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... | ... | @@ -918,12 +911,12 @@ and exit fringe fields to the Enge function: |
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latexmath:[\[\label{eq:enge_func}
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F(z) = \frac{1}{1 + e^{\sum\limits_{n=0}^{N_{order}} c_{n} (z/D)^{n}}}\]]
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where latexmath:[$D$] is the full gap of the magnet,
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latexmath:[$N_{order}$] is the Enge function order and latexmath:[$z$]
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where latexmath:[D] is the full gap of the magnet,
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latexmath:[N_{order}] is the Enge function order and latexmath:[z]
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is the distance from the origin of the Enge function perpendicular to
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the edge of the dipole. The origin of the Enge function, the order of
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the Enge function, latexmath:[$N_{order}$], and the constants
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latexmath:[$c_0$] to latexmath:[$c_{N_{order}}$] are free parameters
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the Enge function, latexmath:[N_{order}], and the constants
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latexmath:[c_0] to latexmath:[c_{N_{order}}] are free parameters
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that are chosen so that the function closely approximates the fringe
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region of the magnet being modeled. An example of the entrance fringe
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field is shown in Figure [rbend_enge_fringe].
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... | ... | @@ -945,7 +938,7 @@ F(z) &= \left\{ |
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\end{array}
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\right.\end{aligned}\]]
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Here, we have defined an overall Enge function, latexmath:[$F(z)$], with
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Here, we have defined an overall Enge function, latexmath:[F(z)], with
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three parts: entrance, center and exit. The exit and entrance fringe
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field regions have the form of Equation [enge_func] with parameters
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defined by the `1DProfile1` field map file given by the element
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... | ... | @@ -985,7 +978,7 @@ B_z(\Delta_x, y, \Delta_z) &= B_0 e^{-\frac{n}{R} \Delta_x} \left\{\frac{F'(\Del |
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&- \left. \left. y \frac{\cos \left[ \left( \sqrt{\frac{n^2}{R^2} + \frac{F''(\Delta_z)}{F(\Delta_z)}} \right) y \right]}{\sqrt{\frac{n^2}{R^2} + \frac{F''(\Delta_z)}{F(\Delta_z)}}} \right] \right\}\end{aligned}\]]
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These expression are not well suited for numerical calculation, so, we
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expand them about latexmath:[$y$] to latexmath:[$O(y^2)$] to obtain:
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expand them about latexmath:[y] to latexmath:[O(y^2)] to obtain:
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* In fringe field regions: latexmath:[\[\begin{aligned}
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B_x(\Delta_x, y, \Delta_z) &\approx -B_0 \frac{n}{R} e^{-\frac{n}{R} \Delta_x} y \\
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... | ... | @@ -1000,7 +993,7 @@ These are the expressions _OPAL-t_ uses to calculate the field inside an |
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`RBEND` or `SBEND`. First, a particle’s position inside the bend is
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determined (entrance region, center region, or exit region). Depending
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on the region, _OPAL-t_ then determines the values of
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latexmath:[$\Delta_x$], latexmath:[$y$] and latexmath:[$\Delta_z$], and
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latexmath:[\Delta_x], latexmath:[y] and latexmath:[\Delta_z], and
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then calculates the field values using the above expressions.
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[[ssec:benddefaultfieldmapopalt]]
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... | ... | @@ -1080,9 +1073,9 @@ geometry with the following restrictions/conventions: |
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coordinate in _OPAL-cycl_) from z = 0 upwards. It cannot be generated
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symmetrically about z = 0 towards negative z values.
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2. Field map file must be in the form with columns ordered as follows:
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[latexmath:[$x, z, y, B_{x}, B_{z}, B_{y}$]].
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[latexmath:[x, z, y, B_{x}, B_{z}, B_{y}]].
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3. Grid points of the position and field strength have to be written on
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|
a grid in (latexmath:[$r, z, \theta$]) with the primary direction
|
|
|
a grid in (latexmath:[r, z, \theta]) with the primary direction
|
|
|
corresponding to the azimuthal direction, secondary to the vertical
|
|
|
direction and tertiary to the radial direction.
|
|
|
|
... | ... | @@ -1135,16 +1128,9 @@ BY [FIELD_UNITS] |
|
|
|
|
|
This is a restricted feature: _OPAL-cycl_.
|
|
|
|
|
|
image:figures/Elements/sbend3d-1.png[A hard edge model of
|
|
|
latexmath:[$90$] degree dipole magnet with homogeneous magnetic field.
|
|
|
The right figure is showing the horizontal cross section of the 3D
|
|
|
magnetic field map when
|
|
|
latexmath:[$z = 0$],title="fig:",scaledwidth=58.0%]
|
|
|
image:figures/Elements/sbend3d-2.png[A hard edge model of
|
|
|
latexmath:[$90$] degree dipole magnet with homogeneous magnetic field.
|
|
|
The right figure is showing the horizontal cross section of the 3D
|
|
|
magnetic field map when
|
|
|
latexmath:[$z = 0$],title="fig:",scaledwidth=40.0%]
|
|
|
.Figure 4: A hard edge model of latexmath:[90] degree dipole magnet with homogeneous magnetic field. The right figure is showing the horizontal cross section of the 3D magnetic field map when latexmath:[z = 0]
|
|
|
image:figures/Elements/sbend3d-1.png[width=375]
|
|
|
image:figures/Elements/sbend3d-2.png[width=375]
|
|
|
|
|
|
[[sec:quadrupole]]
|
|
|
Quadrupole
|
... | ... | @@ -1162,16 +1148,16 @@ A `QUADRUPOLE` has three real attributes: |
|
|
|
|
|
K1::
|
|
|
The normal quadrupole component
|
|
|
latexmath:[$K_1=\frac{\partial B_y}{\partial x}$]. The default is
|
|
|
latexmath:[${0}{Tm^{-1}}$]. The component is positive, if
|
|
|
latexmath:[$B_y$] is positive on the positive latexmath:[$x$]-axis.
|
|
|
latexmath:[K_1=\frac{\partial B_y}{\partial x}]. The default is
|
|
|
latexmath:[{0}{Tm^{-1}}]. The component is positive, if
|
|
|
latexmath:[B_y] is positive on the positive latexmath:[x]-axis.
|
|
|
This implies horizontal focusing of positively charged particles which
|
|
|
travel in positive latexmath:[$s$]-direction.
|
|
|
travel in positive latexmath:[s]-direction.
|
|
|
K1S::
|
|
|
The skew quadrupole component.
|
|
|
latexmath:[$K_{1s}=-\frac{\partial B_x}{\partial x}$]. The default is
|
|
|
latexmath:[${0}{Tm^{-1}}$]. The component is negative, if
|
|
|
latexmath:[$B_x$] is positive on the positive latexmath:[$x$]-axis.
|
|
|
latexmath:[K_{1s}=-\frac{\partial B_x}{\partial x}]. The default is
|
|
|
latexmath:[{0}{Tm^{-1}}]. The component is negative, if
|
|
|
latexmath:[B_x] is positive on the positive latexmath:[x]-axis.
|
|
|
|
|
|
Example:
|
|
|
|
... | ... | @@ -1193,14 +1179,14 @@ A `SEXTUPOLE` has three real attributes: |
|
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|
|
|
K2::
|
|
|
The normal sextupole component
|
|
|
latexmath:[$K_2=\frac{\partial{^2} B_y}{\partial x^2}$]. The default
|
|
|
is latexmath:[${0}{T m^{-2}}$]. The component is positive, if
|
|
|
latexmath:[$B_y$] is positive on the latexmath:[$x$]-axis.
|
|
|
latexmath:[K_2=\frac{\partial{^2} B_y}{\partial x^2}]. The default
|
|
|
is latexmath:[{0}{T m^{-2}}]. The component is positive, if
|
|
|
latexmath:[B_y] is positive on the latexmath:[x]-axis.
|
|
|
K2S::
|
|
|
The skew sextupole component
|
|
|
latexmath:[$K_{2s}=-\frac{\partial{^2}B_x}{\partial x^{2}}$]. The
|
|
|
default is latexmath:[${0}{T m^{-2}}$]. The component is negative, if
|
|
|
latexmath:[$B_x$] is positive on the latexmath:[$x$]-axis.
|
|
|
latexmath:[K_{2s}=-\frac{\partial{^2}B_x}{\partial x^{2}}]. The
|
|
|
default is latexmath:[{0}{T m^{-2}}]. The component is negative, if
|
|
|
latexmath:[B_x] is positive on the latexmath:[x]-axis.
|
|
|
|
|
|
Example:
|
|
|
|
... | ... | @@ -1223,14 +1209,14 @@ An `OCTUPOLE` has three real attributes: |
|
|
|
|
|
K3::
|
|
|
The normal octupole component
|
|
|
latexmath:[$K_3=\frac{\partial{^3} B_y}{\partial x^3}$]. The default
|
|
|
is latexmath:[${0}{Tm^{-3}}$]. The component is positive, if
|
|
|
latexmath:[$B_y$] is positive on the positive latexmath:[$x$]-axis.
|
|
|
latexmath:[K_3=\frac{\partial{^3} B_y}{\partial x^3}]. The default
|
|
|
is latexmath:[{0}{Tm^{-3}}]. The component is positive, if
|
|
|
latexmath:[B_y] is positive on the positive latexmath:[x]-axis.
|
|
|
K3S::
|
|
|
The skew octupole component
|
|
|
latexmath:[$K_{3s}=-\frac{\partial{^3}B_x}{\partial x^{3}}$]. The
|
|
|
default is latexmath:[${0}{Tm^{-3}}$]. The component is negative, if
|
|
|
latexmath:[$B_x$] is positive on the positive latexmath:[$x$]-axis.
|
|
|
latexmath:[K_{3s}=-\frac{\partial{^3}B_x}{\partial x^{3}}]. The
|
|
|
default is latexmath:[{0}{Tm^{-3}}]. The component is negative, if
|
|
|
latexmath:[B_x] is positive on the positive latexmath:[x]-axis.
|
|
|
|
|
|
Example:
|
|
|
|
... | ... | @@ -1253,19 +1239,19 @@ label:MULTIPOLE, TYPE=string, APERTURE=real-vector, |
|
|
|
|
|
KN::
|
|
|
A real vector see Section [anarray], containing the normal multipole
|
|
|
coefficients, latexmath:[$K_n=\frac{\partial{^n} B_y}{\partial x^n}$].
|
|
|
(default is latexmath:[${0}{Tm^{-n}}$]). A component is positive, if
|
|
|
latexmath:[$B_y$] is positive on the positive latexmath:[$x$]-axis.
|
|
|
coefficients, latexmath:[K_n=\frac{\partial{^n} B_y}{\partial x^n}].
|
|
|
(default is latexmath:[{0}{Tm^{-n}}]). A component is positive, if
|
|
|
latexmath:[B_y] is positive on the positive latexmath:[x]-axis.
|
|
|
KS::
|
|
|
A real vector see Section [anarray], containing the skew multipole
|
|
|
coefficients,
|
|
|
latexmath:[$K_{n~s}=-\frac{\partial{^n}B_x}{\partial x^{n}}$].
|
|
|
(default is latexmath:[${0}{Tm^{-n}}$]). A component is negative, if
|
|
|
latexmath:[$B_x$] is positive on the positive latexmath:[$x$]-axis.
|
|
|
latexmath:[K_{n~s}=-\frac{\partial{^n}B_x}{\partial x^{n}}].
|
|
|
(default is latexmath:[{0}{Tm^{-n}}]). A component is negative, if
|
|
|
latexmath:[B_x] is positive on the positive latexmath:[x]-axis.
|
|
|
|
|
|
The order latexmath:[$n$] is unlimited, but all components up to the
|
|
|
The order latexmath:[n] is unlimited, but all components up to the
|
|
|
maximum must be given, even if they are zero. The number of poles of
|
|
|
each component is (latexmath:[$2 n + 2$]).
|
|
|
each component is (latexmath:[2 n + 2]).
|
|
|
|
|
|
Superposition of many multipole components is permitted. The reference
|
|
|
system for a multipole is a Cartesian coordinate system
|
... | ... | @@ -1318,17 +1304,17 @@ TP:: |
|
|
A real vector see Section [anarray], containing the multipole
|
|
|
coefficients of the field expansion on the mid-plane in the body of
|
|
|
the magnet: the transverse profile
|
|
|
latexmath:[$ T(x) = B_0 + B_1 x + B_2 x^2 + \dots $] is set by
|
|
|
TP=latexmath:[$B_0$], latexmath:[$B_1$], latexmath:[$B_2$] (units:
|
|
|
latexmath:[$ T \cdot m^{-n}$]). The order of highest multipole
|
|
|
latexmath:[ T(x) = B_0 + B_1 x + B_2 x^2 + \dots ] is set by
|
|
|
TP=latexmath:[B_0], latexmath:[B_1], latexmath:[B_2] (units:
|
|
|
latexmath:[ T \cdot m^{-n}]). The order of highest multipole
|
|
|
component is arbitrary, but all components up to the maximum must be
|
|
|
given, even if they are zero.
|
|
|
MAXFORDER::
|
|
|
The order of the maximum function latexmath:[$f_n$] used in the field
|
|
|
The order of the maximum function latexmath:[f_n] used in the field
|
|
|
expansion (default: 5). See the scalar magnetic potential below. This
|
|
|
sets for example the maximum power of latexmath:[$z$] in the field
|
|
|
expansion of vertical component latexmath:[$B_z$] to
|
|
|
latexmath:[$2 \cdot \text{MAXFORDER} $].
|
|
|
sets for example the maximum power of latexmath:[z] in the field
|
|
|
expansion of vertical component latexmath:[B_z] to
|
|
|
latexmath:[2 \cdot \text{MAXFORDER} ].
|
|
|
EANGLE::
|
|
|
Entrance edge angle (radians).
|
|
|
ROTATION::
|
... | ... | @@ -1352,8 +1338,8 @@ VARSTEP:: |
|
|
|
|
|
Superposition of many multipole components is permitted. The reference
|
|
|
system for a multipole is a Cartesian coordinate system for straight
|
|
|
geometry and a latexmath:[$(x,s,z)$] Frenet-Serret coordinate system for
|
|
|
curved geometry. In the latter case, the axis latexmath:[$\hat{s}$] is
|
|
|
geometry and a latexmath:[(x,s,z)] Frenet-Serret coordinate system for
|
|
|
curved geometry. In the latter case, the axis latexmath:[\hat{s}] is
|
|
|
the central axis of the magnet.
|
|
|
|
|
|
[[sec:solenoid]]
|
... | ... | @@ -1369,10 +1355,10 @@ A `SOLENOID` has two real attributes: |
|
|
|
|
|
KS::
|
|
|
The solenoid strength
|
|
|
latexmath:[$K_s=\frac{\partial B_s}{\partial s}$], default is
|
|
|
latexmath:[${0}{Tm^{-1}}$]. For positive `KS` and positive particle
|
|
|
latexmath:[K_s=\frac{\partial B_s}{\partial s}], default is
|
|
|
latexmath:[{0}{Tm^{-1}}]. For positive `KS` and positive particle
|
|
|
charge, the solenoid field points in the direction of increasing
|
|
|
latexmath:[$s$].
|
|
|
latexmath:[s].
|
|
|
|
|
|
The reference system for a solenoid is a Cartesian coordinate system
|
|
|
Using a solenoid in _OPAL-t_ mode, the following additional parameters
|
... | ... | @@ -1408,11 +1394,11 @@ TYPE:: |
|
|
the details of their data format, please read
|
|
|
Section [opalcycl:fieldmap].
|
|
|
CYHARMON::
|
|
|
The harmonic number of the cyclotron latexmath:[$h$].
|
|
|
The harmonic number of the cyclotron latexmath:[h].
|
|
|
RFFREQ::
|
|
|
The RF system latexmath:[$f_{rf}$] (unit:MHz, default: 0). The
|
|
|
particle revolution frequency latexmath:[$f_{rev}$] =
|
|
|
latexmath:[$f_{rf}$] / latexmath:[$h$].
|
|
|
The RF system latexmath:[f_{rf}] (unit:MHz, default: 0). The
|
|
|
particle revolution frequency latexmath:[f_{rev}] =
|
|
|
latexmath:[f_{rf}] / latexmath:[h].
|
|
|
FMAPFN::
|
|
|
File name for the magnetic field map.
|
|
|
SYMMETRY::
|
... | ... | @@ -1427,10 +1413,10 @@ ZINIT:: |
|
|
default: 0)
|
|
|
PRINIT::
|
|
|
Initial radial momentum of the reference particle
|
|
|
latexmath:[$P_r=\beta_r\gamma$] (default : 0)
|
|
|
latexmath:[P_r=\beta_r\gamma] (default : 0)
|
|
|
PZINIT::
|
|
|
Initial axial momentum of the reference particle
|
|
|
latexmath:[$P_z=\beta_z\gamma$] (default : 0)
|
|
|
latexmath:[P_z=\beta_z\gamma] (default : 0)
|
|
|
MINZ::
|
|
|
The minimal vertical extent of the machine (unit: mm, default :
|
|
|
-10000.0)
|
... | ... | @@ -1442,8 +1428,8 @@ MINR:: |
|
|
MAXR::
|
|
|
Minimal radial extent of the machine (unit: mm, default : 10000.0)
|
|
|
|
|
|
During the tracking, the particle (latexmath:[$r, z, \theta$]) will be
|
|
|
deleted if MINZ latexmath:[$< z <$] MAXZ or MINR latexmath:[$< r <$]
|
|
|
During the tracking, the particle (latexmath:[r, z, \theta]) will be
|
|
|
deleted if MINZ latexmath:[< z <] MAXZ or MINR latexmath:[< r <]
|
|
|
MAXR, and it will be recorded in the ASCII file _<inputfilename>.loss_.
|
|
|
Example:
|
|
|
|
... | ... | @@ -1561,7 +1547,7 @@ BEAM_RINIT:: |
|
|
BEAM_PHIINIT::
|
|
|
Initial azimuthal angle of the reference trajectory [degree].
|
|
|
BEAM_PRINIT::
|
|
|
Transverse momentum latexmath:[$\beta \gamma$] for the reference
|
|
|
Transverse momentum latexmath:[\beta \gamma] for the reference
|
|
|
trajectory.
|
|
|
|
|
|
In the following example, we define a ring with radius 2.35 m and 4
|
... | ... | @@ -1618,7 +1604,7 @@ L:: |
|
|
The length of the cavity (default: 0 m)
|
|
|
VOLT::
|
|
|
The peak RF voltage (default: 0 MV). The effect of the cavity is
|
|
|
latexmath:[$\delta E=\text{\texttt{VOLT}}\cdot\sin(2\pi(\text{\texttt{LAG}}-\text{\texttt{HARMON}}\cdot f_0 t))$].
|
|
|
latexmath:[\delta E=\text{\texttt{VOLT}}\cdot\sin(2\pi(\text{\texttt{LAG}}-\text{\texttt{HARMON}}\cdot f_0 t))].
|
|
|
LAG::
|
|
|
The phase lag [rad] (default: 0). In _OPAL-t_ this phase is in general
|
|
|
relative to the phase at which the reference particle gains the most
|
... | ... | @@ -1710,8 +1696,8 @@ rf0: RFCavity, VOLT=0.25796, FMAPFN="Cav1.dat", |
|
|
Figure [Cyclotron_cavity] shows the simplified geometry of a cavity gap
|
|
|
and its parameters.
|
|
|
|
|
|
image:./figures/cyclotron/Cavity.png[Schematic of the simplified
|
|
|
geometry of a cavity gap and parameters]
|
|
|
.Figure 5:Schematic of the simplified geometry of a cavity gap and parameters
|
|
|
image:./figures/cyclotron/Cavity.png[]
|
|
|
|
|
|
[[sec:variable-rf-cavity-cycl]]
|
|
|
RF Cavities with Time Dependent Parameters
|
... | ... | @@ -1723,13 +1709,13 @@ be placed using the `RingDefinition` element. |
|
|
|
|
|
FREQUENCY_MODEL::
|
|
|
String naming the time dependence model of the cavity frequency,
|
|
|
latexmath:[$f$] [MHz].
|
|
|
latexmath:[f] [MHz].
|
|
|
AMPLITUDE_MODEL::
|
|
|
String naming the time dependence model of the cavity amplitude,
|
|
|
latexmath:[$E_0$] [MV/m].
|
|
|
latexmath:[E_0] [MV/m].
|
|
|
PHASE_MODEL::
|
|
|
String naming the time dependence model of the cavity phase offset,
|
|
|
latexmath:[$\phi$].
|
|
|
latexmath:[\phi].
|
|
|
WIDTH::
|
|
|
Full width of the cavity [mm].
|
|
|
HEIGHT::
|
... | ... | @@ -1753,11 +1739,11 @@ polynomial. |
|
|
P0::
|
|
|
Constant term in the polynomial expansion.
|
|
|
P1::
|
|
|
First order term in the polynomial expansion [nslatexmath:[$^{-1}$]].
|
|
|
First order term in the polynomial expansion [nslatexmath:[^{-1}]].
|
|
|
P2::
|
|
|
Second order term in the polynomial expansion [nslatexmath:[$^{-2}$]].
|
|
|
Second order term in the polynomial expansion [nslatexmath:[^{-2}]].
|
|
|
P3::
|
|
|
Third order term in the polynomial expansion [nslatexmath:[$^{-3}$]].
|
|
|
Third order term in the polynomial expansion [nslatexmath:[^{-3}]].
|
|
|
|
|
|
The polynomial is evaluated as
|
|
|
latexmath:[\[g(t) = p_0 + p_1 t + p_2 t^2 + p_3 t^3 %% + p_4 t^4
|
... | ... | @@ -1786,11 +1772,8 @@ RF_CAVITY: VARIABLE_RF_CAVITY, PHASE_MODEL="RF_PHASE", AMPLITUDE_MODEL="RF_AMPLI |
|
|
Traveling Wave Structure
|
|
|
~~~~~~~~~~~~~~~~~~~~~~~~
|
|
|
|
|
|
image:./figures/traveling-wave-structure/FINSB-RAC-field.png[The on-axis
|
|
|
field of an S-band (2997.924 MHz) `TRAVELINGWAVE` structure. The field
|
|
|
of a single cavity is shown between its entrance and exit fringe fields.
|
|
|
The fringe fields extend one half wavelength (latexmath:[$\lambda/2$])
|
|
|
to either side.,scaledwidth=70.0%]
|
|
|
. Figure 6:The on-axis field of an S-band (2997.924 MHz) `TRAVELINGWAVE` structure. The field of a single cavity is shown between its entrance and exit fringe fields. The fringe fields extend one half wavelength (latexmath:[\lambda/2]) to either side.
|
|
|
image:./figures/traveling-wave-structure/FINSB-RAC-field.png[]
|
|
|
|
|
|
An example of a 1D `TRAVELINGWAVE` structure field map is shown in
|
|
|
Figure [FINSB-RAC-field]. This map is a standing wave solution generated
|
... | ... | @@ -1808,8 +1791,8 @@ by: latexmath:[\[\begin{aligned} |
|
|
+ \phi_{exit} \right)
|
|
|
\end{aligned}\]] where VOLT and FREQ are the field magnitude and
|
|
|
frequency attributes (see below).
|
|
|
latexmath:[$ \phi_{entrance}= \text{\texttt{LAG}}$], the phase attribute
|
|
|
of the element (see below). latexmath:[$ \phi_{exit} $] is dependent
|
|
|
latexmath:[ \phi_{entrance}= \text{\texttt{LAG}}], the phase attribute
|
|
|
of the element (see below). latexmath:[ \phi_{exit} ] is dependent
|
|
|
upon both LAG and the NUMCELLS attribute (see below) and is calculated
|
|
|
internally by _OPAL-t_.
|
|
|
|
... | ... | @@ -1826,13 +1809,13 @@ latexmath:[\[\begin{split} |
|
|
\end{split}\]]
|
|
|
|
|
|
where d is the cell length and is defined as
|
|
|
latexmath:[$\text{d} = \lambda \cdot \text{\texttt{MODE}} $]. MODE is an
|
|
|
latexmath:[\text{d} = \lambda \cdot \text{\texttt{MODE}} ]. MODE is an
|
|
|
attribute of the element (see below). When calculating the field from
|
|
|
the map (latexmath:[$\mathbf{E_{from-map}}(x,y,z)$]), the longitudinal
|
|
|
the map (latexmath:[\mathbf{E_{from-map}}(x,y,z)]), the longitudinal
|
|
|
position is referenced to the start of the cavity fields at
|
|
|
latexmath:[$\frac{\lambda}{2}$] (In this case starting at
|
|
|
latexmath:[$z = {5.0}cm$]). If the longitudinal position advances past
|
|
|
the end of the cavity map (latexmath:[$\frac{3\lambda}{2} = {15.0}cm$]
|
|
|
latexmath:[\frac{\lambda}{2}] (In this case starting at
|
|
|
latexmath:[z = {5.0}cm]). If the longitudinal position advances past
|
|
|
the end of the cavity map (latexmath:[\frac{3\lambda}{2} = {15.0}cm]
|
|
|
in this example), an integer number of cavity wavelengths is subtracted
|
|
|
from the position until it is back within the map’s longitudinal range.
|
|
|
|
... | ... | @@ -1852,7 +1835,7 @@ L:: |
|
|
cells.
|
|
|
VOLT::
|
|
|
The peak RF voltage (default: 0 MV). The effect of the cavity is
|
|
|
latexmath:[$\delta E=\text{\texttt{VOLT}}\cdot\sin(\text{\texttt{LAG}}- 2\pi\cdot\text{\texttt{FREQ}}\cdot t)$].
|
|
|
latexmath:[\delta E=\text{\texttt{VOLT}}\cdot\sin(\text{\texttt{LAG}}- 2\pi\cdot\text{\texttt{FREQ}}\cdot t)].
|
|
|
LAG::
|
|
|
The phase lag [rad] (default: 0). In _OPAL-t_ this phase is in general
|
|
|
relative to the phase at which the reference particle gains the most
|
... | ... | @@ -1871,8 +1854,8 @@ NUMCELLS:: |
|
|
Defines the number of cells in the tank. (The cell count should not
|
|
|
include the entry and exit half cell fringe fields.)
|
|
|
MODE::
|
|
|
Defines the mode in units of latexmath:[$2\pi$], for example
|
|
|
latexmath:[$\frac{1}{3}$] stands for a latexmath:[$\frac{2 \pi}{3}$]
|
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Defines the mode in units of latexmath:[2\pi], for example
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latexmath:[\frac{1}{3}] stands for a latexmath:[\frac{2 \pi}{3}]
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structure.
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FAST::
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If FAST is true and the provided field map is in 1D then a 2D field
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... | ... | @@ -2025,7 +2008,7 @@ PARTICLEMATTERINTERACTION:: |
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particle hitting collimator will be recorded and directly deleted from
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the simulation.
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image:figures/Elements/collimator.png[image]
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image:figures/Elements/collimator.png[]
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Example:
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... | ... | @@ -2067,7 +2050,7 @@ YEND:: |
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WIDTH::
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The width of the septum. [mm]
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image:figures/Elements/septum.png[image]
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image:figures/Elements/septum.png[]
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Example:
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... | ... | @@ -2097,7 +2080,7 @@ YEND:: |
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WIDTH::
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The width of the probe, NOT used yet.
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image:figures/Elements/probe.png[image]
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image:figures/Elements/probe.png[]
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Example:
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... | ... | @@ -2146,7 +2129,7 @@ STOP:: |
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simulation; Otherwise, the out-coming particle continues to be tracked
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along the extraction path.
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Example: latexmath:[$H_2^+$] particle stripping
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Example: latexmath:[H_2^+] particle stripping
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....
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prob1: Stripper, xstart=4166.16, xend=4250.0,
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... | ... | @@ -2219,13 +2202,13 @@ DESIGNENERGY:: |
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set then the actual energy of the reference particle at the position
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of the corrector is used. The `DESIGNENERGY` is expected in MeV.
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A positive kick increases latexmath:[$p_{x}$] or latexmath:[$p_{y}$]
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A positive kick increases latexmath:[p_{x}] or latexmath:[p_{y}]
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respectively. Use `KICK` for an `HKICKER` or `VKICKER` and `HKICK` and
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`VKICK` for a `KICKER`. Instead of using a `KICKER` or a `VKICKER` one
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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:[\texttt{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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... | ... | |