... | ... | @@ -102,7 +102,7 @@ found instead: '_found_'. |
|
|
**************************************************************
|
|
|
....
|
|
|
|
|
|
Where `_error_msg_` is either
|
|
|
Where `"`_error_msg_`"` is either
|
|
|
|
|
|
[cols="<,<",]
|
|
|
|=======================================================================
|
... | ... | @@ -116,9 +116,9 @@ this line. |
|
|
instead of an integer number.
|
|
|
|=======================================================================
|
|
|
|
|
|
`_expecting_` is replaced by the types of values _OPAL-t_ expects on the
|
|
|
`"`_expecting_`"` is replaced by the types of values _OPAL-t_ expects on the
|
|
|
line. E.g. it could be replaced by `double double int`. Finally
|
|
|
`_found_` is replaced by the actual content of the line without any
|
|
|
`"`_found_`"` is replaced by the actual content of the line without any
|
|
|
comment possibly following the values. If line 3 of a file consists of
|
|
|
`-60.0 60.0 # This is an other invalid comment # 9999` _OPAL-t_ will
|
|
|
output `-60.0 60.0`.
|
... | ... | @@ -162,11 +162,21 @@ This warning is issued when the low pass filter that is applied to the |
|
|
field sampling uses too few Fourier coefficients. In this case increase
|
|
|
the number of Fourier coefficients, see the next section for details.
|
|
|
The relevant criteria are that
|
|
|
latexmath:[\[\frac{\sum_{i=1}^N (F_{z,i} - \tilde{F}_{z,i})^2}{\sum_{i=1}^N F_{z,i}^2} \le 0.01,\]]
|
|
|
|
|
|
[latexmath]
|
|
|
++++
|
|
|
\frac{\sum_{i=1}^N (F_{z,i} - \tilde{F}_{z,i})^2}{\sum_{i=1}^N F_{z,i}^2} \le 0.01,
|
|
|
++++
|
|
|
|
|
|
and
|
|
|
latexmath:[\[\frac{\max_i |F_{z,i} - \tilde{F}_{z,i}|}{\max_i |F_{z,i}|} \le 0.01,\]]
|
|
|
where latexmath:[$F_{z_i}$] is the field sampling as in the file and
|
|
|
latexmath:[$\tilde{F}_{z,i}$] is the one-dimensional field reconstructed
|
|
|
|
|
|
[latexmath]
|
|
|
++++
|
|
|
\frac{\max_i |F_{z,i} - \tilde{F}_{z,i}|}{\max_i |F_{z,i}|} \le 0.01,
|
|
|
++++
|
|
|
|
|
|
where latexmath:[F_{z_i}] is the field sampling as in the file and
|
|
|
latexmath:[\tilde{F}_{z,i}] is the one-dimensional field reconstructed
|
|
|
from the result received after applying the low pass filter.
|
|
|
|
|
|
[[sec:fieldmaps]]
|
... | ... | @@ -283,29 +293,28 @@ Each line after the header corresponds to a grid point of the field map. |
|
|
This point can be referred to by two indices in the case of a 2D field
|
|
|
map and three indices in the case of a 3D field map, respectively. Each
|
|
|
column describes either
|
|
|
latexmath:[$E_z,\; E_r,\; B_z,\; B_r\; \text{or}\;H_{\phi}$] in the 2D
|
|
|
case and latexmath:[$E_x\;, E_y\;, E_z,\; B_x,\; B_y,\;B_z$] in the 3D
|
|
|
latexmath:[E_z,\; E_r,\; B_z,\; B_r\; \text{or}\;H_{\phi}] in the 2D
|
|
|
case and latexmath:[E_x\;, E_y\;, E_z,\; B_x,\; B_y,\;B_z] in the 3D
|
|
|
case.
|
|
|
|
|
|
By primary, secondary and tertiary direction is meant the following (see
|
|
|
also Figure [order1] and Figure [order2]):
|
|
|
also Figure 1):
|
|
|
|
|
|
* The index of the primary direction increases the fastest, the index of
|
|
|
the tertiary direction the slowest.
|
|
|
* The order of the columns is accordingly: if the z direction in an 2D
|
|
|
electrostatic field map is the primary direction then latexmath:[$E_z$]
|
|
|
is on the first column, latexmath:[$E_r$] on the second. For all other
|
|
|
electrostatic field map is the primary direction then latexmath:[E_z]
|
|
|
is on the first column, latexmath:[E_r] on the second. For all other
|
|
|
cases it’s analogous.
|
|
|
* For the 2D dynamic case in XZ orientation there are four columns:
|
|
|
latexmath:[$E_z$], latexmath:[$E_r$], latexmath:[$|E|$] (unused) and
|
|
|
latexmath:[$H_{\phi}$] in that order. In the other orientations the
|
|
|
latexmath:[E_z], latexmath:[E_r], latexmath:[|E|] (unused) and
|
|
|
latexmath:[H_{\phi}] in that order. In the other orientations the
|
|
|
first and the second columns are interchanged ,but the third and fourth
|
|
|
columns are unchanged.
|
|
|
|
|
|
[fig:order1] image:./figures/Fieldmaps/order-1.png[Ordering of points
|
|
|
for 2D field maps in T7 files,title="fig:",scaledwidth=45.0%]
|
|
|
[fig:order2] image:./figures/Fieldmaps/order-2.png[Ordering of points
|
|
|
for 2D field maps in T7 files,title="fig:",scaledwidth=45.0%]
|
|
|
.Figure 1: Ordering of points for 2D field maps in T7 files (left XZ orientation, right ZX orientation)
|
|
|
image:./figures/Fieldmaps/order-1.png[width=375]
|
|
|
image:./figures/Fieldmaps/order-2.png[width=375]
|
|
|
|
|
|
[[sec:fastattribute]]
|
|
|
FAST Attribute for 1D Field Maps
|
... | ... | @@ -322,33 +331,22 @@ numerical noise if you set the grid spacing too coarse for the 2D map. |
|
|
As a general warning: be wise when you choose the type of field map to
|
|
|
be used! Figure [fieldnoiseexample] shows three pictures of the
|
|
|
longitudinal phase space after three gun simulations using different
|
|
|
types of field maps. In the first picture, Figure [1ddynamic_step82], we
|
|
|
types of field maps. In the first picture we
|
|
|
used a 1DDynamic field map see Section [1DDynamic] resulting in a smooth
|
|
|
longitudinal distribution. In Figure [1ddynamic_fast_step82] we set the
|
|
|
longitudinal distribution. In the middle picture we set the
|
|
|
`FAST` attribute to true, resulting in some fine structure in the phase
|
|
|
space due to the bi-linear interpolation of the internally generated 2D
|
|
|
field map. Finally, in the last figure (Figure [2ddynamic_step82]), we
|
|
|
field map. Finally, in the last figure, we
|
|
|
generated directly a 2D field map from Superfish [superfish]. Here we
|
|
|
could observe two different structures: first the fine structure,
|
|
|
stemming from the bi-linear interpolation, and secondly a much stronger
|
|
|
structure of unknown origin, but presumably due to errors in the
|
|
|
Superfish [superfish] interpolation algorithm.
|
|
|
|
|
|
image:./figures/Fieldmaps/1DDynamic_step82.png[The longitudinal phase
|
|
|
space after a gun simulation using a 1D field map (on-axis field) of the
|
|
|
gun, a 1D field map (on-axis field) of the gun in combination with the
|
|
|
`FAST` switch, and a 2D field map of the gun generated by
|
|
|
Superfish [superfish].,title="fig:",scaledwidth=32.0%]
|
|
|
image:./figures/Fieldmaps/1DDynamic_fast_step82.png[The longitudinal
|
|
|
phase space after a gun simulation using a 1D field map (on-axis field)
|
|
|
of the gun, a 1D field map (on-axis field) of the gun in combination
|
|
|
with the `FAST` switch, and a 2D field map of the gun generated by
|
|
|
Superfish [superfish].,title="fig:",scaledwidth=32.0%]
|
|
|
image:./figures/Fieldmaps/2DDynamic_step82.png[The longitudinal phase
|
|
|
space after a gun simulation using a 1D field map (on-axis field) of the
|
|
|
gun, a 1D field map (on-axis field) of the gun in combination with the
|
|
|
`FAST` switch, and a 2D field map of the gun generated by
|
|
|
Superfish [superfish].,title="fig:",scaledwidth=32.0%]
|
|
|
.Figure 2: The longitudinal phase space after a gun simulation using a 1D field map (on-axis field) of the gun, a 1D field map (on-axis field) of the gun in combination with the `FAST` switch, and a 2D field map of the gun generated by Superfish [superfish].
|
|
|
image:./figures/Fieldmaps/1DDynamic_step82.png[width=250]
|
|
|
image:./figures/Fieldmaps/1DDynamic_fast_step82.png[width=250]
|
|
|
image:./figures/Fieldmaps/2DDynamic_step82.png[width=250]
|
|
|
|
|
|
[[sec:1DMagnetoStatic]]
|
|
|
1DMagnetoStatic
|
... | ... | @@ -374,25 +372,28 @@ longitudinal direction. From the 10000 field values, 5000 complex |
|
|
Fourier coefficients are calculated. However, only 40 are kept when
|
|
|
calculating field values during a simulation. _OPAL-t_ normalizes the
|
|
|
field values internally such that
|
|
|
latexmath:[$\max(|B_{\text{on axis}}|) = {1.0}{T}$]. If the `FAST`
|
|
|
latexmath:[\max(|B_{\text{on axis}}|) = {1.0}{T}]. If the `FAST`
|
|
|
attribute is set to true in the input deck, a 2D field map is generated
|
|
|
internally with 200 values in the radial direction, from 0cm to 2cm, for
|
|
|
each longitudinal grid point.
|
|
|
|
|
|
.Layout of a `1DMagnetoStatic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<",]
|
|
|
|=======================================================================
|
|
|
|1DMagnetoStatic |latexmath:[$N_{Fourier}$] |TRUE | FALSE (optional)
|
|
|
|1DMagnetoStatic |latexmath:[N_{Fourier}] |TRUE \| FALSE (optional)
|
|
|
|
|
|
|latexmath:[$z_{start}$] (in cm) |latexmath:[$z_{end}$] (in cm)
|
|
|
|latexmath:[$N_{z}$]
|
|
|
|latexmath:[z_{start}] (in cm) |latexmath:[z_{end}] (in cm)
|
|
|
|latexmath:[N_{z}]
|
|
|
|
|
|
|latexmath:[$r_{start}$] (in cm) |latexmath:[$r_{end}$] (in cm)
|
|
|
|latexmath:[$N_{r}$]
|
|
|
|latexmath:[r_{start}] (in cm) |latexmath:[r_{end}] (in cm)
|
|
|
|latexmath:[N_{r}]
|
|
|
|
|
|
|latexmath:[$B_{z,\,1}$] (T) | |
|
|
|
|latexmath:[B_{z,\,1}] (T) | |
|
|
|
|
|
|
|latexmath:[$B_{z,\,2}$] (T) | |
|
|
|
|latexmath:[B_{z,\,2}] (T) | |
|
|
|
|
|
|
|. | |
|
|
|
|
... | ... | @@ -400,7 +401,7 @@ each longitudinal grid point. |
|
|
|
|
|
|. | |
|
|
|
|
|
|
|latexmath:[$B_{z,\,N_{z} + 1}$] (T) | |
|
|
|
|latexmath:[B_{z,\,N_{z} + 1}] (T) | |
|
|
|
|=======================================================================
|
|
|
|
|
|
A `1DMagnetoStatic` field map has the general form shown in
|
... | ... | @@ -409,11 +410,11 @@ tell _OPAL-t_ how the field map data is being presented: |
|
|
|
|
|
Line 1::
|
|
|
This tells _OPAL-t_ what type of field file it is (`1DMagnetoStatic`)
|
|
|
and how many Fourier coefficients to keep (latexmath:[$N_{Fourier}$])
|
|
|
and how many Fourier coefficients to keep (latexmath:[N_{Fourier}])
|
|
|
when doing field calculations.
|
|
|
Line 2::
|
|
|
This tells gives the extent of the field map (from
|
|
|
latexmath:[$z_{start}$] to latexmath:[$z_{end}$]) relative to the
|
|
|
latexmath:[z_{start}] to latexmath:[z_{end}]) relative to the
|
|
|
`ELEMEDGE` of the field map, and how many grid spacings there are in
|
|
|
the field map.
|
|
|
Line 3::
|
... | ... | @@ -422,9 +423,9 @@ Line 3:: |
|
|
line is ignored. (Although it must always be present.)
|
|
|
|
|
|
The lines following the header give the 1D field map grid values from
|
|
|
latexmath:[$1$] to latexmath:[$N_{z} + 1$]. From these,
|
|
|
latexmath:[$N_{z}/2$] complex Fourier coefficients are calculated, of
|
|
|
which only latexmath:[$N_{Fourier}$] are used when finding field values
|
|
|
latexmath:[1] to latexmath:[N_{z} + 1]. From these,
|
|
|
latexmath:[N_{z}/2] complex Fourier coefficients are calculated, of
|
|
|
which only latexmath:[N_{Fourier}] are used when finding field values
|
|
|
during the simulation.
|
|
|
|
|
|
Figure [1DMagnetoStatic] gives an example of a `1DMagnetoStatic` field
|
... | ... | @@ -451,31 +452,34 @@ AstraMagnetostatic 40 |
|
|
3.0000000e-01 0.0000000e+00
|
|
|
....
|
|
|
|
|
|
A 1D field map describing a magnetostatic field using latexmath:[$N$]
|
|
|
A 1D field map describing a magnetostatic field using latexmath:[N]
|
|
|
non-equidistant grid points in the longitudinal direction. From these
|
|
|
values latexmath:[$N$] equidistant field values are computed from which
|
|
|
in turn latexmath:[$N/2$] complex Fourier coefficients are calculated.
|
|
|
values latexmath:[N] equidistant field values are computed from which
|
|
|
in turn latexmath:[N/2] complex Fourier coefficients are calculated.
|
|
|
In this example only 40 Fourier coefficients are kept when calculating
|
|
|
field values during a simulation. The z-position of each field sampling
|
|
|
is in the first column (in meters), the corresponding longitudinal
|
|
|
on-axis magnetic field amplitude is in the second column. As with the
|
|
|
1DMagnetoStatic see Section [1DMagnetoStatic] field maps, _OPAL-t_
|
|
|
normalizes the field values to
|
|
|
latexmath:[$\max(|B_{\text{on axis}}|) = {1.0}{T}$]. In the header only
|
|
|
latexmath:[\max(|B_{\text{on axis}}|) = {1.0}{T}]. In the header only
|
|
|
the first line is needed since the information on the longitudinal
|
|
|
dimension is contained in the first column of the data. (_OPAL-t_ does
|
|
|
not provide a `FAST` version of this map type.)
|
|
|
|
|
|
.Layout of an `AstraMagnetoStatic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<",]
|
|
|
|======================================================================
|
|
|
|AstraMagnetoStatic |latexmath:[$N_{Fourier}$] |TRUE | FALSE (optional)
|
|
|
|latexmath:[$z_{1}$] (in meters) |latexmath:[$B_{z,\,1}$] (T) |
|
|
|
|latexmath:[$z_{2}$] (in meters) |latexmath:[$B_{z,\,s}$] (T) |
|
|
|
|AstraMagnetoStatic |latexmath:[N_{Fourier}] |TRUE \| FALSE (optional)
|
|
|
|latexmath:[z_{1}] (in meters) |latexmath:[B_{z,\,1}] (T) |
|
|
|
|latexmath:[z_{2}] (in meters) |latexmath:[B_{z,\,s}] (T) |
|
|
|
|. | |
|
|
|
|. | |
|
|
|
|. | |
|
|
|
|latexmath:[$z_{N}$] (in meters) |latexmath:[$B_{z,\,N}$] (T) |
|
|
|
|latexmath:[z_{N}] (in meters) |latexmath:[B_{z,\,N}] (T) |
|
|
|
|======================================================================
|
|
|
|
|
|
An `AstraMagnetoStatic` field map has the general form shown in
|
... | ... | @@ -485,15 +489,15 @@ tells _OPAL-t_ how the field map data is being presented: |
|
|
Line 1::
|
|
|
This tells _OPAL-t_ what type of field file it is
|
|
|
(`AstraMagnetoStatic`) and how many Fourier coefficients to keep
|
|
|
(latexmath:[$N_{Fourier}$]) when doing field calculations.
|
|
|
(latexmath:[N_{Fourier}]) when doing field calculations.
|
|
|
|
|
|
The lines following the header gives latexmath:[$N$] non-equidistant
|
|
|
field values and their corresponding latexmath:[$z$] positions (relative
|
|
|
The lines following the header gives latexmath:[N] non-equidistant
|
|
|
field values and their corresponding latexmath:[z] positions (relative
|
|
|
to `ELEMEDGE`). From these, _OPAL-t_ will use cubic spline interpolation
|
|
|
to find latexmath:[$N$] equidistant field values within the range
|
|
|
defined by the latexmath:[$z$] positions. From these equidistant field
|
|
|
values, latexmath:[$N/2$] complex Fourier coefficients are calculated,
|
|
|
of which only latexmath:[$N_{Fourier}$] are used when finding field
|
|
|
to find latexmath:[N] equidistant field values within the range
|
|
|
defined by the latexmath:[z] positions. From these equidistant field
|
|
|
values, latexmath:[N/2] complex Fourier coefficients are calculated,
|
|
|
of which only latexmath:[N_{Fourier}] are used when finding field
|
|
|
values during the simulation.
|
|
|
|
|
|
Figure [AstraMagnetoStatic] gives an example of an `AstraMagnetoStatic`
|
... | ... | @@ -524,27 +528,30 @@ longitudinal direction. The field frequency is 1498.953425154MHz. From |
|
|
the 5000 field values, 2500 complex Fourier coefficients are calculated.
|
|
|
However, only 40 are kept when calculating field values during the
|
|
|
simulation. _OPAL-t_ normalizes the field values internally such that
|
|
|
latexmath:[$max(|E_{on axis}|) = {1}{MV/m}$]. If the `FAST` switch is
|
|
|
latexmath:[max(|E_{on axis}|) = {1}{MV/m}]. If the `FAST` switch is
|
|
|
set to true in the input deck, a 2D field map is generated internally
|
|
|
with 200 values in the radial direction, from 0.0cm to 2.0cm, for each
|
|
|
longitudinal grid point.
|
|
|
|
|
|
.Layout of a `1DDynamic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<",]
|
|
|
|=======================================================================
|
|
|
|1DDynamic |latexmath:[$N_{Fourier}$] |TRUE | FALSE (optional)
|
|
|
|1DDynamic |latexmath:[N_{Fourier}] |TRUE \| FALSE (optional)
|
|
|
|
|
|
|latexmath:[$z_{start}$] (in cm) |latexmath:[$z_{end}$] (in cm)
|
|
|
|latexmath:[$N_{z}$]
|
|
|
|latexmath:[z_{start}] (in cm) |latexmath:[z_{end}] (in cm)
|
|
|
|latexmath:[N_{z}]
|
|
|
|
|
|
|latexmath:[$Frequency$] (in MHz) | |
|
|
|
|latexmath:[Frequency] (in MHz) | |
|
|
|
|
|
|
|latexmath:[$r_{start}$] (in cm) |latexmath:[$r_{end}$] (in cm)
|
|
|
|latexmath:[$N_{r}$]
|
|
|
|latexmath:[r_{start}] (in cm) |latexmath:[r_{end}] (in cm)
|
|
|
|latexmath:[N_{r}]
|
|
|
|
|
|
|latexmath:[$E_{z,\,1}$] (MV/m) | |
|
|
|
|latexmath:[E_{z,\,1}] (MV/m) | |
|
|
|
|
|
|
|latexmath:[$E_{z,\,2}$] (MV/m) | |
|
|
|
|latexmath:[E_{z,\,2}] (MV/m) | |
|
|
|
|
|
|
|. | |
|
|
|
|
... | ... | @@ -552,7 +559,7 @@ longitudinal grid point. |
|
|
|
|
|
|. | |
|
|
|
|
|
|
|latexmath:[$E_{z,\,N_{z} + 1}$] (MV/m) | |
|
|
|
|latexmath:[E_{z,\,N_{z} + 1}] (MV/m) | |
|
|
|
|=======================================================================
|
|
|
|
|
|
A `1DDynamic` field map has the general form shown in Table [1DDynamic].
|
... | ... | @@ -561,11 +568,11 @@ field map data is being presented: |
|
|
|
|
|
Line 1::
|
|
|
This tells _OPAL-t_ what type of field file it is (`1DDynamic`) and
|
|
|
how many Fourier coefficients to keep (latexmath:[$N_{Fourier}$]) when
|
|
|
how many Fourier coefficients to keep (latexmath:[N_{Fourier}]) when
|
|
|
doing field calculations.
|
|
|
Line 2::
|
|
|
This tells gives the extent of the field map (from
|
|
|
latexmath:[$z_{start}$] to latexmath:[$z_{end}$]) relative to the
|
|
|
latexmath:[z_{start}] to latexmath:[z_{end}]) relative to the
|
|
|
`ELEMEDGE` of the field map, and how many grid spacings there are in
|
|
|
the field map.
|
|
|
Line 3::
|
... | ... | @@ -576,9 +583,9 @@ Line 4:: |
|
|
line is ignored. (Although it must always be present.)
|
|
|
|
|
|
The lines following the header give the 1D field map grid values from
|
|
|
latexmath:[$1$] to latexmath:[$N_{z} + 1$]. From these,
|
|
|
latexmath:[$N_{z}/2$] complex Fourier coefficients are calculated, of
|
|
|
which only latexmath:[$N_{Fourier}$] are used when finding field values
|
|
|
latexmath:[1] to latexmath:[N_{z} + 1]. From these,
|
|
|
latexmath:[N_{z}/2] complex Fourier coefficients are calculated, of
|
|
|
which only latexmath:[N_{Fourier}] are used when finding field values
|
|
|
during the simulation.
|
|
|
|
|
|
Figure [1DDynamic] gives an example of a `1DDynamic` field file.
|
... | ... | @@ -603,30 +610,33 @@ AstraDynamic 40 |
|
|
1.9991554e-01 0.0000000e+00
|
|
|
....
|
|
|
|
|
|
A 1D field map describing a dynamic field using latexmath:[$N$]
|
|
|
A 1D field map describing a dynamic field using latexmath:[N]
|
|
|
non-equidistant grid points in longitudinal direction. From these
|
|
|
latexmath:[$N$] non-equidistant field values latexmath:[$N$] equidistant
|
|
|
field values are computed from which in turn latexmath:[$N/2$] complex
|
|
|
latexmath:[N] non-equidistant field values latexmath:[N] equidistant
|
|
|
field values are computed from which in turn latexmath:[N/2] complex
|
|
|
Fourier coefficients are calculated. In this example only 40 Fourier
|
|
|
coefficients are kept when calculating field values during the
|
|
|
simulation. The z-position of each sampling is in the first column (in
|
|
|
meters), the corresponding longitudinal on-axis electric field amplitude
|
|
|
is in the second column. _OPAL-t_ normalizes the field values such that
|
|
|
latexmath:[$\max(|E_{\text{on axis}}|) = {1}{MV/m}$]. The frequency of
|
|
|
latexmath:[\max(|E_{\text{on axis}}|) = {1}{MV/m}]. The frequency of
|
|
|
this field is 2997.924MHz. (_OPAL-t_ does not provide a `FAST` version
|
|
|
of this map type.)
|
|
|
|
|
|
.Layout of an `AstraDynamic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<",]
|
|
|
|======================================================================
|
|
|
|AstraMagnetoStatic |latexmath:[$N_{Fourier}$] |TRUE | FALSE (optional)
|
|
|
|latexmath:[$Frequency$] (in MHz) | |
|
|
|
|latexmath:[$z_{1}$] (in meters) |latexmath:[$E_{z,\,1}$] (MV/m) |
|
|
|
|latexmath:[$z_{2}$] (in meters) |latexmath:[$E_{z,\,s}$] (MV/m) |
|
|
|
|AstraMagnetoStatic |latexmath:[N_{Fourier}] |TRUE \| FALSE (optional)
|
|
|
|latexmath:[Frequency] (in MHz) | |
|
|
|
|latexmath:[z_{1}] (in meters) |latexmath:[E_{z,\,1}] (MV/m) |
|
|
|
|latexmath:[z_{2}] (in meters) |latexmath:[E_{z,\,s}] (MV/m) |
|
|
|
|. | |
|
|
|
|. | |
|
|
|
|. | |
|
|
|
|latexmath:[$z_{N}$] (in meters) |latexmath:[$E_{z,\,N}$] (MV/m) |
|
|
|
|latexmath:[z_{N}] (in meters) |latexmath:[E_{z,\,N}] (MV/m) |
|
|
|
|======================================================================
|
|
|
|
|
|
An `AstraDynamic` field map has the general form shown in
|
... | ... | @@ -635,18 +645,18 @@ _OPAL-t_ how the field map data is being presented: |
|
|
|
|
|
Line 1::
|
|
|
This tells _OPAL-t_ what type of field file it is (`AstraDynamic`) and
|
|
|
how many Fourier coefficients to keep (latexmath:[$N_{Fourier}$]) when
|
|
|
how many Fourier coefficients to keep (latexmath:[N_{Fourier}]) when
|
|
|
doing field calculations.
|
|
|
Line 2::
|
|
|
Field frequency.
|
|
|
|
|
|
The lines following the header gives latexmath:[$N$] non-equidistant
|
|
|
field values and their corresponding latexmath:[$z$] positions (relative
|
|
|
The lines following the header gives latexmath:[N] non-equidistant
|
|
|
field values and their corresponding latexmath:[z] positions (relative
|
|
|
to `ELEMEDGE`). From these, _OPAL-t_ will use cubic spline interpolation
|
|
|
to find latexmath:[$N$] equidistant field values within the range
|
|
|
defined by the latexmath:[$z$] positions. From these equidistant field
|
|
|
values, latexmath:[$N/2$] complex Fourier coefficients are calculated,
|
|
|
of which only latexmath:[$N_{Fourier}$] are used when finding field
|
|
|
to find latexmath:[N] equidistant field values within the range
|
|
|
defined by the latexmath:[z] positions. From these equidistant field
|
|
|
values, latexmath:[N/2] complex Fourier coefficients are calculated,
|
|
|
of which only latexmath:[N_{Fourier}] are used when finding field
|
|
|
values during the simulation.
|
|
|
|
|
|
Figure [AstraDynamic] gives an example of an `AstraDynamic` field file.
|
... | ... | @@ -658,18 +668,23 @@ Figure [AstraDynamic] gives an example of an `AstraDynamic` field file. |
|
|
A `1DProfile1` field map is used to define Enge functions [enge] that
|
|
|
describe the fringe fields for the entrance and exit of a magnet:
|
|
|
|
|
|
latexmath:[\[F(z) = \frac{1}{1 + e^{\sum\limits_{n=0}^{N_{order}} c_{n} (z/D)^{n}}}\]]
|
|
|
|
|
|
where latexmath:[$D$] is the full gap of the magnet,
|
|
|
latexmath:[$N_{order}$] is the Enge function order and latexmath:[$z$]
|
|
|
[latexmath]
|
|
|
++++
|
|
|
F(z) = \frac{1}{1 + e^{\sum\limits_{n=0}^{N_{order}} c_{n} (z/D)^{n}}}
|
|
|
++++
|
|
|
|
|
|
|
|
|
where latexmath:[D] is the full gap of the magnet,
|
|
|
latexmath:[N_{order}] is the Enge function order and latexmath:[z]
|
|
|
is the distance from the Enge function origin perpendicular to the edge
|
|
|
of the magnet. The constants, latexmath:[$c_n$], and the Enge function
|
|
|
of the magnet. The constants, latexmath:[c_n], and the Enge function
|
|
|
origin are fitted parameters chosen to best represent the fringe field
|
|
|
of the magnet being modeled.
|
|
|
|
|
|
A `1DProfile1` field map describes two Enge functions: one for the
|
|
|
magnet entrance and one for the magnet exit. An illustration of this is
|
|
|
shown in Figure [rbend_field_profile]. In the top part of the figure we
|
|
|
shown in Figure 3. In the top part of the figure we
|
|
|
see a plot of the relative magnet field strength along the mid-plane for
|
|
|
a rectangular dipole magnet. To describe this field with a `1DProfile1`
|
|
|
field map, an Enge function is fit to the entrance fringe field between
|
... | ... | @@ -682,13 +697,8 @@ entered into a `1DProfile1` field map, as described below. |
|
|
Currently, `1DProfile1` field maps are only implemented for `RBEND` and
|
|
|
`SBEND` elements see Section [RBend,SBend,opaltrbendsbendfields].
|
|
|
|
|
|
image:./figures/Fieldmaps/profile-1.png[Example of Enge functions
|
|
|
describing the entrance and exit fringe fields of a rectangular bend
|
|
|
magnet. The top part of the figure shows the relative field strength on
|
|
|
the mid-plane. The bottom part of the figure shows an example of a
|
|
|
particle trajectory through the magnet. Note that the magnet field is
|
|
|
naturally divided into three regions: entrance fringe field, central
|
|
|
field, and exit fringe field.]
|
|
|
.Figure 3: Example of Enge functions describing the entrance and exit fringe fields of a rectangular bend magnet. The top part of the figure shows the relative field strength on the mid-plane. The bottom part of the figure shows an example of a particle trajectory through the magnet. Note that the magnet field is naturally divided into three regions: entrance fringe field, central field, and exit fringe field.
|
|
|
image:./figures/Fieldmaps/profile-1.png[width=700]
|
|
|
|
|
|
A `1DProfile1` field map has the general form shown in
|
|
|
Table [1DProfile1]. The first three lines form the file header and tell
|
... | ... | @@ -697,8 +707,8 @@ _OPAL-t_ how the field map data is being presented: |
|
|
Line 1::
|
|
|
This tells _OPAL-t_ what type of field file it is (`1DProfile1`), the
|
|
|
Enge coefficient order for the entrance fringe fields
|
|
|
(latexmath:[$N_{Enge\,Entrance}$]), the Enge coefficient order for the
|
|
|
exit fringe fields (latexmath:[$N_{Enge\,Exit}$]), and the gap of the
|
|
|
(latexmath:[N_{Enge\,Entrance}]), the Enge coefficient order for the
|
|
|
exit fringe fields (latexmath:[N_{Enge\,Exit}]), and the gap of the
|
|
|
magnet.
|
|
|
Line 2::
|
|
|
The first three values on the second line are used to define the
|
... | ... | @@ -714,9 +724,9 @@ Line 3:: |
|
|
line 3 is not currently used (but must still be present).
|
|
|
|
|
|
The lines following the three header lines give the entrance region Enge
|
|
|
coefficients from latexmath:[$c_0$] to
|
|
|
latexmath:[$c_{N_{Enge\,Entrance}}$], followed by the exit region Enge
|
|
|
coefficients from latexmath:[$c_0$] to latexmath:[$c_{N_{Enge\,Exit}}$].
|
|
|
coefficients from latexmath:[c_0] to
|
|
|
latexmath:[c_{N_{Enge\,Entrance}}], followed by the exit region Enge
|
|
|
coefficients from latexmath:[c_0] to latexmath:[c_{N_{Enge\,Exit}}].
|
|
|
|
|
|
There are two types of `1DProfile1` field map files: `1DProfile Type 1`
|
|
|
and `1DProfile1 Type 2`. The difference between the two is a small
|
... | ... | @@ -725,10 +735,13 @@ This will be explained in Section [1DProfile1Type1] and |
|
|
Section [1DProfile1Type2].
|
|
|
|
|
|
.Layout of a `1DProfile1` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<,<",]
|
|
|
|=======================================================================
|
|
|
|1DProfile1 |latexmath:[$N_{Enge\,Entrance}$]
|
|
|
|latexmath:[$N_{Enge\,Exit}$] |latexmath:[$Gap$] (in cm)
|
|
|
|1DProfile1 |latexmath:[N_{Enge\,Entrance}]
|
|
|
|latexmath:[N_{Enge\,Exit}] |latexmath:[Gap] (in cm)
|
|
|
|
|
|
|Entrance Parameter 1 (in cm) |Entrance Parameter 2 (in cm) |Entrance
|
|
|
Parameter 3 |Place Holder
|
... | ... | @@ -736,9 +749,9 @@ Parameter 3 |Place Holder |
|
|
|Exit Parameter 1 (in cm) |Exit Parameter 2 (in cm) |Exit Parameter 3
|
|
|
|Place Holder
|
|
|
|
|
|
|latexmath:[$c_{0\, Entrance}$] | | |
|
|
|
|latexmath:[c_{0\, Entrance}] | | |
|
|
|
|
|
|
|latexmath:[$c_{1\, Entrance}$] | | |
|
|
|
|latexmath:[c_{1\, Entrance}] | | |
|
|
|
|
|
|
|. | | |
|
|
|
|
... | ... | @@ -746,11 +759,11 @@ Parameter 3 |Place Holder |
|
|
|
|
|
|. | | |
|
|
|
|
|
|
|latexmath:[$c_{N_{Enge\,Entrance}}$] | | |
|
|
|
|latexmath:[c_{N_{Enge\,Entrance}}] | | |
|
|
|
|
|
|
|latexmath:[$c_{0\,Exit}$] | | |
|
|
|
|latexmath:[c_{0\,Exit}] | | |
|
|
|
|
|
|
|latexmath:[$c_{1\,Exit}$] | | |
|
|
|
|latexmath:[c_{1\,Exit}] | | |
|
|
|
|
|
|
|. | | |
|
|
|
|
... | ... | @@ -758,42 +771,14 @@ Parameter 3 |Place Holder |
|
|
|
|
|
|. | | |
|
|
|
|
|
|
|latexmath:[$c_{N_{Enge\,Exit}}$] | | |
|
|
|
|latexmath:[c_{N_{Enge\,Exit}}] | | |
|
|
|
|=======================================================================
|
|
|
|
|
|
image:./figures/Fieldmaps/RBendType1.png[Illustration of a rectangular
|
|
|
bend (`RBEND`, see Section [RBend]) showing the entrance and exit fringe
|
|
|
field regions. latexmath:[$\Delta_{1}$] is the perpendicular distance in
|
|
|
front of the entrance edge of the magnet where the magnet fringe fields
|
|
|
are non-negligible. latexmath:[$\Delta_{2}$] is the perpendicular
|
|
|
distance behind the entrance edge of the magnet where the entrance Enge
|
|
|
function stops being used to calculate the magnet field. The reference
|
|
|
trajectory entrance point is indicated by latexmath:[$O_{entrance}$].
|
|
|
latexmath:[$\Delta_{3}$] is the perpendicular distance in front of the
|
|
|
exit edge of the magnet where the exit Enge function starts being used
|
|
|
to calculate the magnet field. (In the region between
|
|
|
latexmath:[$\Delta_{2}$] and latexmath:[$\Delta_{3}$] the field of the
|
|
|
magnet is a constant value.) latexmath:[$\Delta_{4}$] is the
|
|
|
perpendicular distance after the exit edge of the magnet where the
|
|
|
magnet fringe fields are non-negligible. The reference trajectory exit
|
|
|
point is indicated by latexmath:[$O_{exit}$],scaledwidth=45.0%]
|
|
|
|
|
|
image:./figures/Fieldmaps/SBendType1.png[Illustration of a sector bend
|
|
|
(`SBEND`, see Section [SBend]) showing the entrance and exit fringe
|
|
|
field regions. latexmath:[$\Delta_{1}$] is the perpendicular distance in
|
|
|
front of the entrance edge of the magnet where the magnet fringe fields
|
|
|
are non-negligible. latexmath:[$\Delta_{2}$] is the perpendicular
|
|
|
distance behind the entrance edge of the magnet where the entrance Enge
|
|
|
function stops being used to calculate the magnet field. The reference
|
|
|
trajectory entrance point is indicated by latexmath:[$O_{entrance}$].
|
|
|
latexmath:[$\Delta_{3}$] is the perpendicular distance in front of the
|
|
|
exit edge of the magnet where the exit Enge function starts being used
|
|
|
to calculate the magnet field. (In the region between
|
|
|
latexmath:[$\Delta_{2}$] and latexmath:[$\Delta_{3}$] the field of the
|
|
|
magnet is a constant value.) latexmath:[$\Delta_{4}$] is the
|
|
|
perpendicular distance after the exit edge of the magnet where the
|
|
|
magnet fringe fields are non-negligible. The reference trajectory exit
|
|
|
point is indicated by latexmath:[$O_{exit}$].,scaledwidth=45.0%]
|
|
|
.Figure 4: Illustration of a rectangular bend (`RBEND`, see Section [RBend]) showing the entrance and exit fringe field regions. latexmath:[\Delta_{1}] is the perpendicular distance in front of the entrance edge of the magnet where the magnet fringe fields are non-negligible. latexmath:[\Delta_{2}] is the perpendicular distance behind the entrance edge of the magnet where the entrance Enge function stops being used to calculate the magnet field. The reference trajectory entrance point is indicated by latexmath:[O_{entrance}]. latexmath:[\Delta_{3}] is the perpendicular distance in front of the exit edge of the magnet where the exit Enge function starts being used to calculate the magnet field. (In the region between latexmath:[\Delta_{2}] and latexmath:[\Delta_{3}] the field of the magnet is a constant value.) latexmath:[\Delta_{4}] is the perpendicular distance after the exit edge of the magnet where the magnet fringe fields are non-negligible. The reference trajectory exit point is indicated by latexmath:[O_{exit}]
|
|
|
image:./figures/Fieldmaps/RBendType1.png[]
|
|
|
|
|
|
.Figure 5: Illustration of a sector bend (`SBEND`, see Section [SBend]) showing the entrance and exit fringe field regions. latexmath:[\Delta_{1}] is the perpendicular distance in front of the entrance edge of the magnet where the magnet fringe fields are non-negligible. latexmath:[\Delta_{2}] is the perpendicular distance behind the entrance edge of the magnet where the entrance Enge function stops being used to calculate the magnet field. The reference trajectory entrance point is indicated by latexmath:[O_{entrance}]. latexmath:[\Delta_{3}] is the perpendicular distance in front of the exit edge of the magnet where the exit Enge function starts being used to calculate the magnet field. (In the region between latexmath:[\Delta_{2}] and latexmath:[\Delta_{3}] the field of the magnet is a constant value.) latexmath:[\Delta_{4}] is the perpendicular distance after the exit edge of the magnet where the magnet fringe fields are non-negligible. The reference trajectory exit point is indicated by latexmath:[O_{exit}].
|
|
|
image:./figures/Fieldmaps/SBendType1.png[]
|
|
|
|
|
|
[[ssec:1DProfile1Type1]]
|
|
|
1DProfile1 Type 1 for Bend Magnet
|
... | ... | @@ -806,14 +791,19 @@ regions for an `RBEND` and an `SBEND` element. Referring to the general |
|
|
field map file shown in Table [1DProfile1], the values on lines 2 and 3
|
|
|
are given by:
|
|
|
|
|
|
latexmath:[\[\begin{aligned}
|
|
|
|
|
|
[latexmath]
|
|
|
++++
|
|
|
\begin{aligned}
|
|
|
Entrance\,Parameter\,1 &= Entrance\,Parameter\,2 - \Delta_{1} \\
|
|
|
Entrance\,Parameter\,3 &= Entrance\,Parameter\,2 + \Delta_{2} \\
|
|
|
Exit\,Parameter\,2 &= L - Entrance\,Parameter\,2 \\
|
|
|
Exit\,Parameter\,1 &= Exit\,Parameter\,2 - \Delta_{3} \\
|
|
|
Exit\,Parameter\,3 &= Exit\,Parameter\,2 + \Delta_{4}\end{aligned}\]]
|
|
|
Exit\,Parameter\,3 &= Exit\,Parameter\,2 + \Delta_{4}\end{aligned}
|
|
|
++++
|
|
|
|
|
|
|
|
|
The value of latexmath:[$Entrance\,Parameter\,2$] can be any value.
|
|
|
The value of latexmath:[Entrance\,Parameter\,2] can be any value.
|
|
|
_OPAL_ only cares about the relative differences between parameters.
|
|
|
Also note that, internally, the origins of the entrance and exit Enge
|
|
|
functions correspond to the reference trajectory entrance and exit
|
... | ... | @@ -822,17 +812,22 @@ points see Figure [rbendengetype1,sbendengetype1]. |
|
|
Internally, _OPAL_ reads in a `1DProfile Type 1` map and uses the
|
|
|
provided parameters to calculate the values of:
|
|
|
|
|
|
latexmath:[\[\begin{aligned}
|
|
|
|
|
|
[latexmath]
|
|
|
++++
|
|
|
\begin{aligned}
|
|
|
L &= Exit\,Parameter\,2 - Entrance\,Parameter\,2 \\
|
|
|
\Delta_{1} &= Entrance\,Parameter\,2 - Entrance\,Parameter\,1 \\
|
|
|
\Delta_{2} &= Entrance\,Parameter\,3 - Entrance\,Parameter\,2 \\
|
|
|
\Delta_{3} &= Exit\,Parameter\,2 - Exit\,Parameter\,1 \\
|
|
|
\Delta_{4} &= Exit\,Parameter\,3 - Exit\,Parameter\,2\end{aligned}\]]
|
|
|
\Delta_{4} &= Exit\,Parameter\,3 - Exit\,Parameter\,2\end{aligned}
|
|
|
++++
|
|
|
|
|
|
|
|
|
These values, combined with the entrance fringe field Enge coefficients
|
|
|
latexmath:[$c_0$] through latexmath:[$c_{N_{Enge_Entrance}}$] and exit
|
|
|
fringe field Enge coefficients latexmath:[$c_0$] through
|
|
|
latexmath:[$c_{N_{Enge_Exit}}$], allow _OPAL_ to find field values
|
|
|
latexmath:[c_0] through latexmath:[c_{N_{Enge_Entrance}}] and exit
|
|
|
fringe field Enge coefficients latexmath:[c_0] through
|
|
|
latexmath:[c_{N_{Enge_Exit}}], allow _OPAL_ to find field values
|
|
|
anywhere within the magnet. (Again, note that a `1DProfile Type 1` map
|
|
|
always places the entrance Enge function origin at the entrance point of
|
|
|
the reference trajectory and the exit Enge function origin at the exit
|
... | ... | @@ -879,30 +874,45 @@ attribute. In turn, this allows us the freedom to make slight changes to |
|
|
how the parameters on lines 2 and 3 of the field map file shown in
|
|
|
Table [1DProfile1] are defined. Now
|
|
|
|
|
|
latexmath:[\[\begin{aligned}
|
|
|
|
|
|
[latexmath]
|
|
|
++++
|
|
|
\begin{aligned}
|
|
|
Entrance\,Parameter\,2 &= \perp \text{distance of entrance Enge function origin from magnet entrance edge} \\
|
|
|
Exit\,Parameter\,2 &= \perp \text{distance of exit Enge function origin from magnet exit edge}\end{aligned}\]]
|
|
|
Exit\,Parameter\,2 &= \perp \text{distance of exit Enge function origin from magnet exit edge}\end{aligned}
|
|
|
++++
|
|
|
|
|
|
|
|
|
The other parameters are defined the same as before:
|
|
|
|
|
|
latexmath:[\[\begin{aligned}
|
|
|
|
|
|
[latexmath]
|
|
|
++++
|
|
|
\begin{aligned}
|
|
|
Entrance\,Parameter\,1 &= Entrance\,Parameter\,2 - \Delta_{1} \\
|
|
|
Entrance\,Parameter\,3 &= Entrance\,Parameter\,2 + \Delta_{2} \\
|
|
|
Exit\,Parameter\,1 &= Exit\,Parameter\,2 - \Delta_{3} \\
|
|
|
Exit\,Parameter\,3 &= Exit\,Parameter\,2 + \Delta_{4}\end{aligned}\]]
|
|
|
Exit\,Parameter\,3 &= Exit\,Parameter\,2 + \Delta_{4}\end{aligned}
|
|
|
++++
|
|
|
|
|
|
|
|
|
As before, internally, _OPAL_ reads in a `1DProfile Type 2` map and uses
|
|
|
the provided parameters to calculate the values of:
|
|
|
latexmath:[\[\begin{aligned}
|
|
|
|
|
|
[latexmath]
|
|
|
++++
|
|
|
\begin{aligned}
|
|
|
\Delta_{1} &= Entrance\,Parameter\,2 - Entrance\,Parameter\,1 \\
|
|
|
\Delta_{2} &= Entrance\,Parameter\,3 - Entrance\,Parameter\,2 \\
|
|
|
\Delta_{3} &= Exit\,Parameter\,2 - Exit\,Parameter\,1 \\
|
|
|
\Delta_{4} &= Exit\,Parameter\,3 - Exit\,Parameter\,2\end{aligned}\]]
|
|
|
\Delta_{4} &= Exit\,Parameter\,3 - Exit\,Parameter\,2\end{aligned}
|
|
|
++++
|
|
|
|
|
|
These values, combined with the length of the magnet, `L` ( set by the
|
|
|
element attribute) and the entrance fringe field Enge coefficients
|
|
|
latexmath:[$c_0$] through latexmath:[$c_{N_{Enge_Entrance}}$] and exit
|
|
|
fringe field Enge coefficients latexmath:[$c_0$] through
|
|
|
latexmath:[$c_{N_{Enge_Exit}}$], allow _OPAL_ to find field values
|
|
|
latexmath:[c_0] through latexmath:[c_{N_{Enge_Entrance}}] and exit
|
|
|
fringe field Enge coefficients latexmath:[c_0] through
|
|
|
latexmath:[c_{N_{Enge_Exit}}], allow _OPAL_ to find field values
|
|
|
anywhere within the magnet.
|
|
|
|
|
|
The `1DProfile1 Type 2` field map file format has two main advantages:
|
... | ... | @@ -967,29 +977,32 @@ bi-linear interpolation. The field is non-negligible from -3.0cm to |
|
|
51.0cm relative to `ELEMEDGE` and the 200 grid points in the radial
|
|
|
direction span the distance from 0.0cm to 2.0cm. The field values are
|
|
|
ordered in XZ orientation, so the index in the longitudinal direction
|
|
|
changes fastest and therefore latexmath:[$E_z$] values are stored in the
|
|
|
first column and latexmath:[$E_r$] values in the second
|
|
|
changes fastest and therefore latexmath:[E_z] values are stored in the
|
|
|
first column and latexmath:[E_r] values in the second
|
|
|
see Section [fieldorientation]. _OPAL-t_ normalizes the field so that
|
|
|
latexmath:[$max(|E_{z, \text{ on axis}}|) = {1}{MVm^{-1}}$].
|
|
|
latexmath:[max(|E_{z, \text{ on axis}}|) = {1}{MVm^{-1}}].
|
|
|
|
|
|
.Layout of a `2DElectroStatic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<",]
|
|
|
|=======================================================================
|
|
|
|2DElectroStatic |Orientation (XZ or ZX) |TRUE | FALSE (optional)
|
|
|
|2DElectroStatic |Orientation (XZ or ZX) |TRUE \| FALSE (optional)
|
|
|
|
|
|
|latexmath:[$z_{start}$] (or latexmath:[$r_{start}$]) (in cm)
|
|
|
|latexmath:[$z_{end}$] (or latexmath:[$r_{end}$]) (in cm)
|
|
|
|latexmath:[$N_{z}$] (or latexmath:[$N_{r}$])
|
|
|
|latexmath:[z_{start}] (or latexmath:[r_{start}]) (in cm)
|
|
|
|latexmath:[z_{end}] (or latexmath:[r_{end}]) (in cm)
|
|
|
|latexmath:[N_{z}] (or latexmath:[N_{r}])
|
|
|
|
|
|
|latexmath:[$r_{start}$] (or latexmath:[$z_{start}$]) (in cm)
|
|
|
|latexmath:[$r_{end}$] (or latexmath:[$z_{end}$]) (in cm)
|
|
|
|latexmath:[$N_{r}$] (or latexmath:[$N_{z}$])
|
|
|
|latexmath:[r_{start}] (or latexmath:[z_{start}]) (in cm)
|
|
|
|latexmath:[r_{end}] (or latexmath:[z_{end}]) (in cm)
|
|
|
|latexmath:[N_{r}] (or latexmath:[N_{z}])
|
|
|
|
|
|
|latexmath:[$E_{z,\,1}$] (or latexmath:[$E_{r,\,1}$]) (MV/m)
|
|
|
|latexmath:[$E_{r,\,1}$] (or latexmath:[$E_{z,\,1}$]) (MV/m) |
|
|
|
|latexmath:[E_{z,\,1}] (or latexmath:[E_{r,\,1}]) (MV/m)
|
|
|
|latexmath:[E_{r,\,1}] (or latexmath:[E_{z,\,1}]) (MV/m) |
|
|
|
|
|
|
|latexmath:[$E_{z,\,2}$] (or latexmath:[$E_{r,\,2}$]) (MV/m)
|
|
|
|latexmath:[$E_{r,\,2}$] (or latexmath:[$E_{z,\,2}$]) (MV/m) |
|
|
|
|latexmath:[E_{z,\,2}] (or latexmath:[E_{r,\,2}]) (MV/m)
|
|
|
|latexmath:[E_{r,\,2}] (or latexmath:[E_{z,\,2}]) (MV/m) |
|
|
|
|
|
|
|. | |
|
|
|
|
... | ... | @@ -997,8 +1010,8 @@ latexmath:[$max(|E_{z, \text{ on axis}}|) = {1}{MVm^{-1}}$]. |
|
|
|
|
|
|. | |
|
|
|
|
|
|
|latexmath:[$E_{z,\,N}$] (or latexmath:[$E_{r,\,N}$]) (MV/m)
|
|
|
|latexmath:[$E_{r,\,N}$] (or latexmath:[$E_{z,\,N}$]) (MV/m) |
|
|
|
|latexmath:[E_{z,\,N}] (or latexmath:[E_{r,\,N}]) (MV/m)
|
|
|
|latexmath:[E_{r,\,N}] (or latexmath:[E_{z,\,N}]) (MV/m) |
|
|
|
|=======================================================================
|
|
|
|
|
|
A `2DElectroStatic` field map has the general form shown in
|
... | ... | @@ -1018,14 +1031,14 @@ Line 3:: |
|
|
Section [fieldorientation].
|
|
|
|
|
|
The lines following the header give the 2D field map grid values from
|
|
|
latexmath:[$1$] to latexmath:[$N = (N_{z} + 1) \times (N_{r} + 1)$]. The
|
|
|
latexmath:[1] to latexmath:[N = (N_{z} + 1) \times (N_{r} + 1)]. The
|
|
|
order of these depend on the field orientation
|
|
|
see Section [fieldorientation] and can be one of two formats:
|
|
|
|
|
|
If Orientation = XZ:::
|
|
|
latexmath:[$E_{z}$] (MV/m) latexmath:[$E_{r}$] (MV/m)
|
|
|
latexmath:[E_{z}] (MV/m) latexmath:[E_{r}] (MV/m)
|
|
|
If Orientation = ZX:::
|
|
|
latexmath:[$E_{r}$] (MV/m) latexmath:[$E_{z}$] (MV/m)
|
|
|
latexmath:[E_{r}] (MV/m) latexmath:[E_{z}] (MV/m)
|
|
|
|
|
|
Figure [2DElectroStatic] gives an example of a `2DElectroStatic` field
|
|
|
file.
|
... | ... | @@ -1054,29 +1067,32 @@ bi-linear interpolation. The field is non-negligible from -3.0cm to |
|
|
51.0cm relative to `ELEMEDGE` and the 200 grid points in the radial
|
|
|
direction span the distance from 0.0cm to 2.0cm. The field values are
|
|
|
ordered in the ZX orientation, so the index in the radial direction
|
|
|
changes fastest and therefore latexmath:[$B_r$] values are stored in the
|
|
|
first column and latexmath:[$B_z$] values in the second
|
|
|
changes fastest and therefore latexmath:[B_r] values are stored in the
|
|
|
first column and latexmath:[B_z] values in the second
|
|
|
see Section [fieldorientation]. _OPAL-t_ normalizes the field so that
|
|
|
latexmath:[$max(|B_{z,\text{ on axis}}|) = {1}{T}$].
|
|
|
latexmath:[max(|B_{z,\text{ on axis}}|) = {1}{T}].
|
|
|
|
|
|
.Layout of a `2DMagnetoStatic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<",]
|
|
|
|=======================================================================
|
|
|
|2DMagnetoStatic |Orientation (XZ or ZX) |TRUE | FALSE (optional)
|
|
|
|2DMagnetoStatic |Orientation (XZ or ZX) |TRUE \| FALSE (optional)
|
|
|
|
|
|
|latexmath:[$z_{start}$] (or latexmath:[$r_{start}$]) (in cm)
|
|
|
|latexmath:[$z_{end}$] (or latexmath:[$r_{end}$]) (in cm)
|
|
|
|latexmath:[$N_{z}$] (or latexmath:[$N_{r}$])
|
|
|
|latexmath:[z_{start}] (or latexmath:[r_{start}]) (in cm)
|
|
|
|latexmath:[z_{end}] (or latexmath:[r_{end}]) (in cm)
|
|
|
|latexmath:[N_{z}] (or latexmath:[N_{r}])
|
|
|
|
|
|
|latexmath:[$r_{start}$] (or latexmath:[$z_{start}$]) (in cm)
|
|
|
|latexmath:[$r_{end}$] (or latexmath:[$z_{end}$]) (in cm)
|
|
|
|latexmath:[$N_{r}$] (or latexmath:[$N_{z}$])
|
|
|
|latexmath:[r_{start}] (or latexmath:[z_{start}]) (in cm)
|
|
|
|latexmath:[r_{end}] (or latexmath:[z_{end}]) (in cm)
|
|
|
|latexmath:[N_{r}] (or latexmath:[N_{z}])
|
|
|
|
|
|
|latexmath:[$B_{z,\,1}$] (or latexmath:[$B_{r,\,1}$]) (T)
|
|
|
|latexmath:[$B_{r,\,1}$] (or latexmath:[$B_{z,\,1}$]) (T) |
|
|
|
|latexmath:[B_{z,\,1}] (or latexmath:[B_{r,\,1}]) (T)
|
|
|
|latexmath:[B_{r,\,1}] (or latexmath:[B_{z,\,1}]) (T) |
|
|
|
|
|
|
|latexmath:[$B_{z,\,2}$] (or latexmath:[$B_{r,\,2}$]) (T)
|
|
|
|latexmath:[$B_{r,\,2}$] (or latexmath:[$B_{z,\,2}$]) (T) |
|
|
|
|latexmath:[B_{z,\,2}] (or latexmath:[B_{r,\,2}]) (T)
|
|
|
|latexmath:[B_{r,\,2}] (or latexmath:[B_{z,\,2}]) (T) |
|
|
|
|
|
|
|. | |
|
|
|
|
... | ... | @@ -1084,8 +1100,8 @@ latexmath:[$max(|B_{z,\text{ on axis}}|) = {1}{T}$]. |
|
|
|
|
|
|. | |
|
|
|
|
|
|
|latexmath:[$B_{z,\,N}$] (or latexmath:[$B_{r,\,N}$]) (T)
|
|
|
|latexmath:[$B_{r,\,N}$] (or latexmath:[$B_{z,\,N}$]) (T) |
|
|
|
|latexmath:[B_{z,\,N}] (or latexmath:[B_{r,\,N}]) (T)
|
|
|
|latexmath:[B_{r,\,N}] (or latexmath:[B_{z,\,N}]) (T) |
|
|
|
|=======================================================================
|
|
|
|
|
|
A `2MagnetoStatic` field map has the general form shown in
|
... | ... | @@ -1105,14 +1121,14 @@ Line 3:: |
|
|
Section [fieldorientation].
|
|
|
|
|
|
The lines following the header give the 2D field map grid values from
|
|
|
latexmath:[$1$] to latexmath:[$N = (N_{z} + 1) \times (N_{r} + 1)$]. The
|
|
|
latexmath:[1] to latexmath:[N = (N_{z} + 1) \times (N_{r} + 1)]. The
|
|
|
order of these depend on the field orientation
|
|
|
see Section [fieldorientation] and can be one of two formats:
|
|
|
|
|
|
If Orientation = XZ:::
|
|
|
latexmath:[$B_{z}$] (T) latexmath:[$B_{r}$] (T)
|
|
|
latexmath:[B_{z}] (T) latexmath:[B_{r}] (T)
|
|
|
If Orientation = ZX:::
|
|
|
latexmath:[$B_{r}$] (T) latexmath:[$B_{z}$] (T)
|
|
|
latexmath:[B_{r}] (T) latexmath:[B_{z}] (T)
|
|
|
|
|
|
Figure [2DMagnetoStatic] gives an example of a `2DMagnetoStatic` field
|
|
|
file.
|
... | ... | @@ -1143,37 +1159,40 @@ interpolation. The field is non-negligible between -3.0cm and 51.0cm |
|
|
relative to `ELEMEDGE` and the 76 grid points in radial direction span
|
|
|
the distance from 0.0cm to 1.0cm. The field values are ordered in the XZ
|
|
|
orientation, so the index in the longitudinal direction changes fastest
|
|
|
and therefore latexmath:[$E_z$] values are stored in the first column
|
|
|
and latexmath:[$E_r$] values in the second. The third column contains
|
|
|
the electric field magnitude, latexmath:[$|E|$], and is not used (but
|
|
|
must still be included). The fourth column is latexmath:[$H_{\phi}$] in
|
|
|
and therefore latexmath:[E_z] values are stored in the first column
|
|
|
and latexmath:[E_r] values in the second. The third column contains
|
|
|
the electric field magnitude, latexmath:[|E|], and is not used (but
|
|
|
must still be included). The fourth column is latexmath:[H_{\phi}] in
|
|
|
A/m. The third and fourth columns are always the same and do not depend
|
|
|
on the field orientation see Section [fieldorientation]. _OPAL-t_
|
|
|
normalizes the field so that
|
|
|
latexmath:[$max(|E_{z,\text{ on axis}}|) = {1}{MVm^{-1}}$].
|
|
|
latexmath:[max(|E_{z,\text{ on axis}}|) = {1}{MVm^{-1}}].
|
|
|
|
|
|
.Layout of a `2DDynamic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<,<",]
|
|
|
|=======================================================================
|
|
|
|2DDynamic |Orientation (XZ or ZX) |TRUE | FALSE (optional) |
|
|
|
|2DDynamic |Orientation (XZ or ZX) |TRUE \| FALSE (optional) |
|
|
|
|
|
|
|latexmath:[$z_{start}$] (or latexmath:[$r_{start}$]) (in cm)
|
|
|
|latexmath:[$z_{end}$] (or latexmath:[$r_{end}$]) (in cm)
|
|
|
|latexmath:[$N_{z}$] (or latexmath:[$N_{r}$]) |
|
|
|
|latexmath:[z_{start}] (or latexmath:[r_{start}]) (in cm)
|
|
|
|latexmath:[z_{end}] (or latexmath:[r_{end}]) (in cm)
|
|
|
|latexmath:[N_{z}] (or latexmath:[N_{r}]) |
|
|
|
|
|
|
|latexmath:[$Frequency$] (in MHz) | | |
|
|
|
|latexmath:[Frequency] (in MHz) | | |
|
|
|
|
|
|
|latexmath:[$r_{start}$] (or latexmath:[$z_{start}$]) (in cm)
|
|
|
|latexmath:[$r_{end}$] (or latexmath:[$z_{end}$]) (in cm)
|
|
|
|latexmath:[$N_{r}$] (or latexmath:[$N_{z}$]) |
|
|
|
|latexmath:[r_{start}] (or latexmath:[z_{start}]) (in cm)
|
|
|
|latexmath:[r_{end}] (or latexmath:[z_{end}]) (in cm)
|
|
|
|latexmath:[N_{r}] (or latexmath:[N_{z}]) |
|
|
|
|
|
|
|latexmath:[$E_{z,\,1}$] (or latexmath:[$E_{r,\,1}$]) (MV/m))
|
|
|
|latexmath:[$E_{r,\,1}$] (or latexmath:[$E_{z,\,1}$]) (MV/m)
|
|
|
|latexmath:[$|E_1|$] (MV/m) |latexmath:[$H_{\phi,\,1}$] (A/m)
|
|
|
|latexmath:[E_{z,\,1}] (or latexmath:[E_{r,\,1}]) (MV/m))
|
|
|
|latexmath:[E_{r,\,1}] (or latexmath:[E_{z,\,1}]) (MV/m)
|
|
|
|latexmath:[\|E_1\|] (MV/m) |latexmath:[H_{\phi,\,1}] (A/m)
|
|
|
|
|
|
|latexmath:[$E_{z,\,2}$] (or latexmath:[$E_{r,\,2}$]) (MV/m))
|
|
|
|latexmath:[$E_{r,\,2}$] (or latexmath:[$E_{z,\,2}$]) (MV/m)
|
|
|
|latexmath:[$|E_2|$] (MV/m) |latexmath:[$H_{\phi,\,2}$] (A/m)
|
|
|
|latexmath:[E_{z,\,2}] (or latexmath:[E_{r,\,2}]) (MV/m))
|
|
|
|latexmath:[E_{r,\,2}] (or latexmath:[E_{z,\,2}]) (MV/m)
|
|
|
|latexmath:[\|E_2\|] (MV/m) |latexmath:[H_{\phi,\,2}] (A/m)
|
|
|
|
|
|
|. | | |
|
|
|
|
... | ... | @@ -1181,9 +1200,9 @@ latexmath:[$max(|E_{z,\text{ on axis}}|) = {1}{MVm^{-1}}$]. |
|
|
|
|
|
|. | | |
|
|
|
|
|
|
|latexmath:[$E_{z,\,N}$] (or latexmath:[$E_{r,\,N}$]) (MV/m))
|
|
|
|latexmath:[$E_{r,\,N}$] (or latexmath:[$E_{z,\,N}$]) (MV/m)
|
|
|
|latexmath:[$|E_N|$] (MV/m) |latexmath:[$H_{\phi,\,N}$] (A/m)
|
|
|
|latexmath:[E_{z,\,N}] (or latexmath:[E_{r,\,N}]) (MV/m))
|
|
|
|latexmath:[E_{r,\,N}] (or latexmath:[E_{z,\,N}]) (MV/m)
|
|
|
|latexmath:[|E_N|] (MV/m) |latexmath:[H_{\phi,\,N}] (A/m)
|
|
|
|=======================================================================
|
|
|
|
|
|
A `2DDynamic` field map has the general form shown in Table [2DDynamic].
|
... | ... | @@ -1205,16 +1224,16 @@ Line 4:: |
|
|
see Section [fieldorientation].
|
|
|
|
|
|
The lines following the header give the 2D field map grid values from
|
|
|
latexmath:[$1$] to latexmath:[$N= (N_{z} + 1) \times (N_{r} + 1)$]. The
|
|
|
latexmath:[1] to latexmath:[N= (N_{z} + 1) \times (N_{r} + 1)]. The
|
|
|
order of these depend on the field orientation
|
|
|
see Section [fieldorientation] and can be one of two formats:
|
|
|
|
|
|
If Orientation = XZ:::
|
|
|
latexmath:[$E_{z}$] (MV/m) latexmath:[$E_{r}$] (MV/m)
|
|
|
latexmath:[$|E|$] (MV/m) latexmath:[$H_{\phi}$] (A/m)
|
|
|
latexmath:[E_{z}] (MV/m) latexmath:[E_{r}] (MV/m)
|
|
|
latexmath:[|E|] (MV/m) latexmath:[H_{\phi}] (A/m)
|
|
|
If Orientation = ZX:::
|
|
|
latexmath:[$E_{r}$] (MV/m) latexmath:[$E_{z}$] (MV/m)
|
|
|
latexmath:[$|E|$] (MV/m) latexmath:[$H_{\phi}$] (A/m)
|
|
|
latexmath:[E_{r}] (MV/m) latexmath:[E_{z}] (MV/m)
|
|
|
latexmath:[|E|] (MV/m) latexmath:[H_{\phi}] (A/m)
|
|
|
|
|
|
The third item (the field magnitude) on each data line is not used by
|
|
|
_OPAL-t_, but must be there.
|
... | ... | @@ -1248,28 +1267,31 @@ x-direction range from -1.5cm to 1.5cm and the 152 grid points in |
|
|
y-direction range from -1.0cm to 1.0cm relative to the design path. The
|
|
|
field values are ordered such that the index in z-direction changes
|
|
|
fastest, then the index in y-direction while the index in x-direction
|
|
|
changes slowest. The columns correspond to latexmath:[$B_x$],
|
|
|
latexmath:[$B_y$] and latexmath:[$B_z$].
|
|
|
changes slowest. The columns correspond to latexmath:[B_x],
|
|
|
latexmath:[B_y] and latexmath:[B_z].
|
|
|
|
|
|
.Layout of a `3DMagnetoStatic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<,<,<,<",]
|
|
|
|=======================================================================
|
|
|
|3DMagnetoStatic |TRUE | FALSE (optional) | | | |
|
|
|
|3DMagnetoStatic |TRUE \| FALSE (optional) | | | |
|
|
|
|
|
|
|latexmath:[$x_{start}$] (in cm) |latexmath:[$x_{end}$] (in cm)
|
|
|
|latexmath:[$N_{x}$] | | |
|
|
|
|latexmath:[x_{start}] (in cm) |latexmath:[x_{end}] (in cm)
|
|
|
|latexmath:[N_{x}] | | |
|
|
|
|
|
|
|latexmath:[$y_{start}$] (in cm) |latexmath:[$y_{end}$] (in cm)
|
|
|
|latexmath:[$N_{y}$] | | |
|
|
|
|latexmath:[y_{start}] (in cm) |latexmath:[y_{end}] (in cm)
|
|
|
|latexmath:[N_{y}] | | |
|
|
|
|
|
|
|latexmath:[$z_{start}$] (in cm) |latexmath:[$z_{end}$] (in cm)
|
|
|
|latexmath:[$N_{z}$] | | |
|
|
|
|latexmath:[z_{start}] (in cm) |latexmath:[z_{end}] (in cm)
|
|
|
|latexmath:[N_{z}] | | |
|
|
|
|
|
|
|latexmath:[$B_{x,\,1}$] (A/m) |latexmath:[$B_{y,\,1}$] (A/m)
|
|
|
|latexmath:[$B_{z,\,1}$] (A/m) | | |
|
|
|
|latexmath:[B_{x,\,1}] (A/m) |latexmath:[B_{y,\,1}] (A/m)
|
|
|
|latexmath:[B_{z,\,1}] (A/m) | | |
|
|
|
|
|
|
|latexmath:[$B_{x,\,2}$] (A/m) |latexmath:[$B_{y,\,2}$] (A/m)
|
|
|
|latexmath:[$B_{z,\,2}$] (A/m) | | |
|
|
|
|latexmath:[B_{x,\,2}] (A/m) |latexmath:[B_{y,\,2}] (A/m)
|
|
|
|latexmath:[B_{z,\,2}] (A/m) | | |
|
|
|
|
|
|
|. | | | | |
|
|
|
|
... | ... | @@ -1277,8 +1299,8 @@ latexmath:[$B_y$] and latexmath:[$B_z$]. |
|
|
|
|
|
|. | | | | |
|
|
|
|
|
|
|latexmath:[$B_{x,\,N}$] (A/m) |latexmath:[$B_{y,\,N}$] (A/m)
|
|
|
|latexmath:[$B_{z,\,N}$] (A/m) | | |
|
|
|
|latexmath:[B_{x,\,N}] (A/m) |latexmath:[B_{y,\,N}] (A/m)
|
|
|
|latexmath:[B_{z,\,N}] (A/m) | | |
|
|
|
|=======================================================================
|
|
|
|
|
|
A `3DMagnetoStatic` field map has the general form shown in
|
... | ... | @@ -1298,8 +1320,8 @@ Line 5:: |
|
|
there are in the fastest changing index direction.
|
|
|
|
|
|
The lines following the header give the 3D field map grid values from
|
|
|
latexmath:[$1$] to
|
|
|
latexmath:[$N= (N_{z} + 1) \times (N_{y} + 1) \times (N_{x} + 1)$].
|
|
|
latexmath:[1] to
|
|
|
latexmath:[N= (N_{z} + 1) \times (N_{y} + 1) \times (N_{x} + 1)].
|
|
|
Figure [3DMagnetoStatic] gives an example of a `3DMagnetoStatic` field
|
|
|
file.
|
|
|
|
... | ... | @@ -1333,26 +1355,29 @@ to a symmetry where the perpendicular component is mirrored whereas the |
|
|
tangential component is anti-parallel. Instead of integrating the field
|
|
|
from the mid-plane to -2.0cm and 1.0cm we only integrate it to +2.0cm
|
|
|
and store only the upper half of the field map. For positions
|
|
|
latexmath:[$R(x,\;-y,\;z)$] with latexmath:[$y > 0.0$] the correct field
|
|
|
can then be derived from the latexmath:[$R(x,\;y,\;z)$].
|
|
|
latexmath:[R(x,\;-y,\;z)] with latexmath:[y > 0.0] the correct field
|
|
|
can then be derived from the latexmath:[R(x,\;y,\;z)].
|
|
|
|
|
|
.Layout of a `3DMagnetoStatic_Extended` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<",]
|
|
|
|=======================================================================
|
|
|
| |TRUE | FALSE (optional) |
|
|
|
| |TRUE \| FALSE (optional) |
|
|
|
|
|
|
|latexmath:[$x_{start}$] (in cm) |latexmath:[$x_{end}$] (in cm)
|
|
|
|latexmath:[$N_{x}$]
|
|
|
|latexmath:[x_{start}] (in cm) |latexmath:[x_{end}] (in cm)
|
|
|
|latexmath:[N_{x}]
|
|
|
|
|
|
|latexmath:[$y_{start}$] (in cm) |latexmath:[$y_{end}$] (in cm)
|
|
|
|latexmath:[$N_{y}$]
|
|
|
|latexmath:[y_{start}] (in cm) |latexmath:[y_{end}] (in cm)
|
|
|
|latexmath:[N_{y}]
|
|
|
|
|
|
|latexmath:[$z_{start}$] (in cm) |latexmath:[$z_{end}$] (in cm)
|
|
|
|latexmath:[$N_{z}$]
|
|
|
|latexmath:[z_{start}] (in cm) |latexmath:[z_{end}] (in cm)
|
|
|
|latexmath:[N_{z}]
|
|
|
|
|
|
|latexmath:[$B_{y,\,1}$] (T) | |
|
|
|
|latexmath:[B_{y,\,1}] (T) | |
|
|
|
|
|
|
|latexmath:[$B_{y,\,2}$] (T) | |
|
|
|
|latexmath:[B_{y,\,2}] (T) | |
|
|
|
|
|
|
|. | |
|
|
|
|
... | ... | @@ -1360,7 +1385,7 @@ can then be derived from the latexmath:[$R(x,\;y,\;z)$]. |
|
|
|
|
|
|. | |
|
|
|
|
|
|
|latexmath:[$B_{y,\,N}$] (T) | |
|
|
|
|latexmath:[B_{y,\,N}] (T) | |
|
|
|
|=======================================================================
|
|
|
|
|
|
A `3DMagnetoStatic_Extended` field map has the general form shown in
|
... | ... | @@ -1381,7 +1406,7 @@ Line 4:: |
|
|
there are in the fastest changing direction.
|
|
|
|
|
|
The lines following the header give the 3D field map grid values from
|
|
|
latexmath:[$1$] to latexmath:[$N= (N_{z} + 1) \times (N_{x} + 1)$]. The
|
|
|
latexmath:[1] to latexmath:[N= (N_{z} + 1) \times (N_{x} + 1)]. The
|
|
|
order of these depend on the field orientation
|
|
|
see Section [fieldorientation] and can currently only be the format
|
|
|
shown in Table [3DMagnetoStatic_Extended].
|
... | ... | @@ -1418,34 +1443,37 @@ The field is non-negligible between -3.0cm to 51.0cm relative to |
|
|
relative to the design path. The field values are ordered such that the
|
|
|
index in z-direction changes fastest, then the index in y-direction
|
|
|
while the index in x-direction changes slowest. The columns correspond
|
|
|
to latexmath:[$E_x$], latexmath:[$E_y$], latexmath:[$E_z$],
|
|
|
latexmath:[$H_x$], latexmath:[$H_y$] and latexmath:[$H_z$]. _OPAL-t_
|
|
|
to latexmath:[E_x], latexmath:[E_y], latexmath:[E_z],
|
|
|
latexmath:[H_x], latexmath:[H_y] and latexmath:[H_z]. _OPAL-t_
|
|
|
normalizes the field so that
|
|
|
latexmath:[$max(|E_{z,\text{ on axis}}|) = {1}{MVm^{-1}}$].
|
|
|
latexmath:[max(|E_{z,\text{ on axis}}|) = {1}{MVm^{-1}}].
|
|
|
|
|
|
.Layout of a `3DDynamic` field map file.
|
|
|
[grid=none]
|
|
|
[frame=topbot]
|
|
|
[options=noheader]
|
|
|
[cols="<,<,<,<,<,<",]
|
|
|
|=======================================================================
|
|
|
|3DDynamic |TRUE | FALSE (optional) | | | |
|
|
|
|3DDynamic |TRUE \| FALSE (optional) | | | |
|
|
|
|
|
|
|latexmath:[$Frequency$] (in MHz) | | | | |
|
|
|
|latexmath:[Frequency] (in MHz) | | | | |
|
|
|
|
|
|
|latexmath:[$x_{start}$] (in cm) |latexmath:[$x_{end}$] (in cm)
|
|
|
|latexmath:[$N_{x}$] | | |
|
|
|
|latexmath:[x_{start}] (in cm) |latexmath:[x_{end}] (in cm)
|
|
|
|latexmath:[N_{x}] | | |
|
|
|
|
|
|
|latexmath:[$y_{start}$] (in cm) |latexmath:[$y_{end}$] (in cm)
|
|
|
|latexmath:[$N_{y}$] | | |
|
|
|
|latexmath:[y_{start}] (in cm) |latexmath:[y_{end}] (in cm)
|
|
|
|latexmath:[N_{y}] | | |
|
|
|
|
|
|
|latexmath:[$z_{start}$] (in cm) |latexmath:[$z_{end}$] (in cm)
|
|
|
|latexmath:[$N_{z}$] | | |
|
|
|
|latexmath:[z_{start}] (in cm) |latexmath:[z_{end}] (in cm)
|
|
|
|latexmath:[N_{z}] | | |
|
|
|
|
|
|
|latexmath:[$E_{x,\,1}$] (MV/m)) |latexmath:[$E_{y,\,1}$] (MV/m)
|
|
|
|latexmath:[$E_{z,\,1}$] (MV/m) |latexmath:[$H_{x,\,1}$] (A/m)
|
|
|
|latexmath:[$H_{y,\,1}$] (A/m) |latexmath:[$H_{z,\,1}$] (A/m)
|
|
|
|latexmath:[E_{x,\,1}] (MV/m)) |latexmath:[E_{y,\,1}] (MV/m)
|
|
|
|latexmath:[E_{z,\,1}] (MV/m) |latexmath:[H_{x,\,1}] (A/m)
|
|
|
|latexmath:[H_{y,\,1}] (A/m) |latexmath:[H_{z,\,1}] (A/m)
|
|
|
|
|
|
|latexmath:[$E_{x,\,2}$] (MV/m)) |latexmath:[$E_{y,\,2}$] (MV/m)
|
|
|
|latexmath:[$E_{z,\,2}$] (MV/m) |latexmath:[$H_{x,\,2}$] (A/m)
|
|
|
|latexmath:[$H_{y,\,2}$] (A/m) |latexmath:[$H_{z,\,2}$] (A/m)
|
|
|
|latexmath:[E_{x,\,2}] (MV/m)) |latexmath:[E_{y,\,2}] (MV/m)
|
|
|
|latexmath:[E_{z,\,2}] (MV/m) |latexmath:[H_{x,\,2}] (A/m)
|
|
|
|latexmath:[H_{y,\,2}] (A/m) |latexmath:[H_{z,\,2}] (A/m)
|
|
|
|
|
|
|. | | | | |
|
|
|
|
... | ... | @@ -1453,9 +1481,9 @@ latexmath:[$max(|E_{z,\text{ on axis}}|) = {1}{MVm^{-1}}$]. |
|
|
|
|
|
|. | | | | |
|
|
|
|
|
|
|latexmath:[$E_{x,\,N}$] (MV/m)) |latexmath:[$E_{y,\,N}$] (MV/m)
|
|
|
|latexmath:[$E_{z,\,N}$] (MV/m) |latexmath:[$H_{x,\,N}$] (A/m)
|
|
|
|latexmath:[$H_{y,\,N}$] (A/m) |latexmath:[$H_{z,\,N}$] (A/m)
|
|
|
|latexmath:[E_{x,\,N}] (MV/m)) |latexmath:[E_{y,\,N}] (MV/m)
|
|
|
|latexmath:[E_{z,\,N}] (MV/m) |latexmath:[H_{x,\,N}] (A/m)
|
|
|
|latexmath:[H_{y,\,N}] (A/m) |latexmath:[H_{z,\,N}] (A/m)
|
|
|
|=======================================================================
|
|
|
|
|
|
A `3DDynamic` field map has the general form shown in Table [3DDynamic].
|
... | ... | @@ -1477,6 +1505,6 @@ Line 5:: |
|
|
there are in the fastest changing index direction.
|
|
|
|
|
|
The lines following the header give the 3D field map grid values from
|
|
|
latexmath:[$1$] to
|
|
|
latexmath:[$N= (N_{z} + 1) \times (N_{y} + 1) \times (N_{x} + 1)$].
|
|
|
latexmath:[1] to
|
|
|
latexmath:[N= (N_{z} + 1) \times (N_{y} + 1) \times (N_{x} + 1)].
|
|
|
Figure [3DDynamic] gives an example of a `3DDynamic` field file. |