... | ... | @@ -8,11 +8,8 @@ |
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Distribution Command
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--------------------
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|
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.Possible distribution types. Note that the `SURFACEEMISSION` and
|
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`SURFACERANDCREATE` distribution types will not be discussed in this
|
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chapter. Instead, refer to Chapter [femiss] on field emission for using
|
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these types.
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[cols="<,<",options="header",]
|
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.Possible distribution types. Note that the `SURFACEEMISSION` and `SURFACERANDCREATE` distribution types will not be discussed in this chapter. Instead, refer to Chapter [femiss] on field emission for using these types.
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[cols="<1,<5",options="header",]
|
|
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|=======================================================================
|
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|Distribution Type |Description
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|`FROMFILE` |Initial distribution read in from text file provided by
|
... | ... | @@ -79,18 +76,18 @@ used to input the momentum. This is controlled with the `INPUTMOUNITS` |
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attribute, defined in Table [distattrinputmounits].
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.Definition of `INPUTMOUNITS` attribute.
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[cols="<,^,<",options="header",]
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[cols="<1,^2,<4",options="header",]
|
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|=======================================================================
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|Attribute Name |Value |Description
|
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|`INPUTMOUNITS` |`NONE` (default for _OPAL-t_) |Use no units for the
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input momentum (e.g. latexmath:[$p_{x}$], latexmath:[$p_{y}$],
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latexmath:[$p_{z}$]). Momentum is given as
|
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latexmath:[$\beta_{x} \gamma$], latexmath:[$\beta_{y} \gamma$] and
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latexmath:[$\beta_{z} \gamma$], as in Section [variablesopalt].
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input momentum (e.g. latexmath:[p_{x}], latexmath:[p_{y}],
|
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latexmath:[p_{z}]). Momentum is given as
|
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latexmath:[\beta_{x} \gamma], latexmath:[\beta_{y} \gamma] and
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latexmath:[\beta_{z} \gamma], as in Section [variablesopalt].
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|`INPUTMOUNITS` |`EV` (default for _OPAL-cycl_) |Use the units eV for
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the input momentum (e.g. latexmath:[$p_{x}$], latexmath:[$p_{y}$],
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latexmath:[$p_{z}$]).
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the input momentum (e.g. latexmath:[p_{x}], latexmath:[p_{y}],
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latexmath:[p_{z}]).
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|=======================================================================
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[[sec:gendistattributes]]
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... | ... | @@ -108,7 +105,7 @@ supports _emitted_ distributions. The default is an _injected_ |
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distribution.
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.Definition of `EMITTED` attribute.
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[cols="<,^,<",options="header",]
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[cols="<1,^1,<5",options="header",]
|
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|=======================================================================
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|Attribute Name |Value |Description
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|`EMITTED` |`FALSE` (default) |The distribution is injected into the
|
... | ... | @@ -116,7 +113,7 @@ simulation in its entirety at the start of the simulation. The particle |
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coordinates for an injected distribution are defined as in
|
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Section [variablesopalt,variablesopalcycl]. Note that in _OPAL-t_ the
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entire distribution will automatically be shifted to ensure that the
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latexmath:[$z$] coordinate will be greater than zero for all particles.
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latexmath:[z] coordinate will be greater than zero for all particles.
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|`EMITTED` |`TRUE` |The distribution is emitted into the simulation over
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time as the simulation progresses. Currently only _OPAL-t_ supports this
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... | ... | @@ -135,10 +132,8 @@ in Table [distattruniversal,distattrinjected,distattrsemitted]. |
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Universal Attributes
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^^^^^^^^^^^^^^^^^^^^
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.Definition of universal distribution attributes. Any distribution type
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can use these and they are the same whether the beam is _injected_ or
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_emitted_.
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[cols="<,^,^,<",options="header",]
|
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.Definition of universal distribution attributes. Any distribution type can use these and they are the same whether the beam is _injected_ or _emitted_.
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[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
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|Attribute Name |Default Value |Units |Description
|
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|`WRITETOFILE` |`FALSE` |None |Echo initial distribution to text file
|
... | ... | @@ -154,48 +149,48 @@ list see Section [distlist]. |
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energy bins. This has consequences for the space charge solver
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see Section [FSENBINS].
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|`XMULT` |1.0 |None |Value used to scale the latexmath:[$x$] positions
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|`XMULT` |1.0 |None |Value used to scale the latexmath:[x] positions
|
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of the distribution particles. Applied after the distribution is
|
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generated (or read in).
|
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|`YMULT` |1.0 |None |Value used to scale the latexmath:[$y$] positions
|
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|`YMULT` |1.0 |None |Value used to scale the latexmath:[y] positions
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of the distribution particles. Applied after the distribution is
|
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generated (or read in).
|
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|`PXMULT` |1.0 |None |Value used to scale the x momentum,
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latexmath:[$p_{x}$], of the distribution particles. Applied after the
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latexmath:[p_{x}], of the distribution particles. Applied after the
|
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distribution is generated (or read in).
|
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|`PYMULT` |1.0 |None |Value used to scale the y momentum,
|
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latexmath:[$p_{y}$], of the distribution particles. Applied after the
|
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latexmath:[p_{y}], of the distribution particles. Applied after the
|
|
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distribution is generated (or read in).
|
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|`PZMULT` |1.0 |None |Value use to scale the z momentum,
|
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latexmath:[$p_{z}$], of the distribution particles. Applied after the
|
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latexmath:[p_{z}], of the distribution particles. Applied after the
|
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distribution is generated (or read in).
|
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|`OFFSETX` |0.0 |m |Distribution is shifted in latexmath:[$x$] by this
|
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|`OFFSETX` |0.0 |m |Distribution is shifted in latexmath:[x] by this
|
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amount after the distribution is generated (or read in). Same as the
|
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average latexmath:[$x$] position, latexmath:[$\bar{x}$].
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average latexmath:[x] position, latexmath:[\bar{x}].
|
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|`OFFSETY` |0.0 |m |Distribution is shifted in latexmath:[$y$] by this
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|`OFFSETY` |0.0 |m |Distribution is shifted in latexmath:[y] by this
|
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amount after the distribution is generated (or read in). Same as the
|
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average latexmath:[$y$] position, latexmath:[$\bar{y}$].
|
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average latexmath:[y] position, latexmath:[\bar{y}].
|
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|`OFFSETPX` |0.0 |Section [unitsdistattributes] |Distribution is shifted
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in latexmath:[$p_{x}$] by this amount after the distribution is
|
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|
generated (or read in). Same as the average latexmath:[$p_{x}$] value,
|
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|
latexmath:[$\bar{p}_{x}$].
|
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in latexmath:[p_{x}] by this amount after the distribution is
|
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generated (or read in). Same as the average latexmath:[p_{x}] value,
|
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latexmath:[\bar{p}_{x}].
|
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|`OFFSETPY` |0.0 |Section [unitsdistattributes] |Distribution is shifted
|
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in latexmath:[$p_{y}$] by this amount after the distribution is
|
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|
generated (or read in). Same as the average latexmath:[$p_{y}$] value,
|
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|
latexmath:[$\bar{p}_{y}$].
|
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|
in latexmath:[p_{y}] by this amount after the distribution is
|
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|
generated (or read in). Same as the average latexmath:[p_{y}] value,
|
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|
latexmath:[\bar{p}_{y}].
|
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|
|
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|`OFFSETPZ` |0.0 |Section [unitsdistattributes] |Distribution is shifted
|
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|
in latexmath:[$p_{z}$] by this amount after the distribution is
|
|
|
generated (or read in). Same as the average latexmath:[$p_{z}$] value,
|
|
|
latexmath:[$\bar{p}_{z}$].
|
|
|
in latexmath:[p_{z}] by this amount after the distribution is
|
|
|
generated (or read in). Same as the average latexmath:[p_{z}] value,
|
|
|
latexmath:[\bar{p}_{z}].
|
|
|
|
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|
|`ID1` |0.0 |Section [unitsdistattributes] |Tracer particle which is
|
|
|
written also into _data/track_orbit.dat_
|
... | ... | @@ -208,18 +203,17 @@ written also into _data/track_orbit.dat_ |
|
|
Injected Distribution Attributes
|
|
|
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
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|
|
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|
.Definition of distribution attributes that only affect _injected_
|
|
|
beams.
|
|
|
.Definition of distribution attributes that only affect _injected_ beams.
|
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|
[cols="<,^,^,<",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`ZMULT` |1.0 |None |Value used to scale the latexmath:[$z$] positions
|
|
|
|`ZMULT` |1.0 |None |Value used to scale the latexmath:[z] positions
|
|
|
of the distribution particles. Applied after the distribution is
|
|
|
generated (or read in).
|
|
|
|
|
|
|`OFFSETZ` |0.0 |m |Distribution is shifted in latexmath:[$z$] by this
|
|
|
|`OFFSETZ` |0.0 |m |Distribution is shifted in latexmath:[z] by this
|
|
|
amount relative to the reference particle. Same as the average
|
|
|
latexmath:[$z$] position, latexmath:[$\bar{z}$].
|
|
|
latexmath:[z] position, latexmath:[\bar{z}].
|
|
|
|=======================================================================
|
|
|
|
|
|
[[sec:emitteddistattributes]]
|
... | ... | @@ -227,10 +221,10 @@ Emitted Distribution Attributes |
|
|
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
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|
|
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|
.Definition of distribution attributes that only affect _emitted_ beams.
|
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|
[cols="<,^,^,<",options="header",]
|
|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`TMULT` |1.0 |None |Value used to scale the latexmath:[$t$] values of
|
|
|
|`TMULT` |1.0 |None |Value used to scale the latexmath:[t] values of
|
|
|
the distribution particles. Applied after the distribution is generated
|
|
|
(or read in).
|
|
|
|
... | ... | @@ -256,9 +250,8 @@ have it either _injected_ or _emitted_ into the simulation. In |
|
|
Table [distattrfromfile] we list the single attribute specific to this
|
|
|
type of distribution type.
|
|
|
|
|
|
.Definition of distribution attributes for a `FROMFILE` distribution
|
|
|
type.
|
|
|
[cols="<,^,^,<",options="header",]
|
|
|
.Definition of distribution attributes for a `FROMFILE` distribution type.
|
|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`FNAME` |None |None |File name for text file containing distribution
|
... | ... | @@ -287,53 +280,48 @@ be _injected_ or _emitted_. The _injected_ file format is defined in |
|
|
Table [fromfileinjfileformat]. The _emitted_ file format is defined in
|
|
|
Table [fromfileemitfileformat].
|
|
|
|
|
|
.File format for _injected_ `FROMFILE` distribution type. N is the
|
|
|
number of particles in the file. The particle coordinates are defined in
|
|
|
Section [variablesopalt,variablesopalcycl].
|
|
|
.File format for _injected_ `FROMFILE` distribution type. N is the number of particles in the file. The particle coordinates are defined in Section [variablesopalt,variablesopalcycl].
|
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|
[cols="<,<,<,<,<,<",]
|
|
|
|=======================================================================
|
|
|
|N | | | | |
|
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|
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|
|latexmath:[$x_{1}$] |latexmath:[$p_{x1}$] |latexmath:[$y_{1}$]
|
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|latexmath:[$p_{y1}$] |latexmath:[$z_{1}$] |latexmath:[$p_{z1}$]
|
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|
|latexmath:[x_{1}] |latexmath:[p_{x1}] |latexmath:[y_{1}]
|
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|
|latexmath:[p_{y1}] |latexmath:[z_{1}] |latexmath:[p_{z1}]
|
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|
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|
|latexmath:[$x_{2}$] |latexmath:[$p_{x2}$] |latexmath:[$y_{2}$]
|
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|
|latexmath:[$p_{y2}$] |latexmath:[$z_{2}$] |latexmath:[$p_{z2}$]
|
|
|
|latexmath:[x_{2}] |latexmath:[p_{x2}] |latexmath:[y_{2}]
|
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|
|latexmath:[p_{y2}] |latexmath:[z_{2}] |latexmath:[p_{z2}]
|
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|
|
|
|
|. | | | | |
|
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|
|
|
|
|. | | | | |
|
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|latexmath:[$x_{N}$] |latexmath:[$p_{xN}$] |latexmath:[$y_{N}$]
|
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|
|latexmath:[$p_{yN}$] |latexmath:[$z_{N}$] |latexmath:[$p_{zN}$]
|
|
|
|latexmath:[x_{N}] |latexmath:[p_{xN}] |latexmath:[y_{N}]
|
|
|
|latexmath:[p_{yN}] |latexmath:[z_{N}] |latexmath:[p_{zN}]
|
|
|
|=======================================================================
|
|
|
|
|
|
.File format for _emitted_ `FROMFILE` distribution type. N is the number
|
|
|
of particles in the file. The particle coordinates are defined in
|
|
|
Section [variablesopalt] except that latexmath:[$z$], in meters, is
|
|
|
replaced by latexmath:[$t$] in seconds.
|
|
|
.File format for _emitted_ `FROMFILE` distribution type. N is the number of particles in the file. The particle coordinates are defined in Section [variablesopalt] except that latexmath:[z], in meters, is replaced by latexmath:[t] in seconds.
|
|
|
[cols="<,<,<,<,<,<",]
|
|
|
|=======================================================================
|
|
|
|N | | | | |
|
|
|
|
|
|
|latexmath:[$x_{1}$] |latexmath:[$p_{x1}$] |latexmath:[$y_{1}$]
|
|
|
|latexmath:[$p_{y1}$] |latexmath:[$t_{1}$] |latexmath:[$p_{z1}$]
|
|
|
|latexmath:[x_{1}] |latexmath:[p_{x1}] |latexmath:[y_{1}]
|
|
|
|latexmath:[p_{y1}] |latexmath:[t_{1}] |latexmath:[p_{z1}]
|
|
|
|
|
|
|latexmath:[$x_{2}$] |latexmath:[$p_{x2}$] |latexmath:[$y_{2}$]
|
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|
|latexmath:[$p_{y2}$] |latexmath:[$t_{2}$] |latexmath:[$p_{z2}$]
|
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|
|latexmath:[x_{2}] |latexmath:[p_{x2}] |latexmath:[y_{2}]
|
|
|
|latexmath:[p_{y2}] |latexmath:[t_{2}] |latexmath:[p_{z2}]
|
|
|
|
|
|
|. | | | | |
|
|
|
|
|
|
|. | | | | |
|
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|latexmath:[$x_{N}$] |latexmath:[$p_{xN}$] |latexmath:[$y_{N}$]
|
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|
|latexmath:[$p_{yN}$] |latexmath:[$t_{N}$] |latexmath:[$p_{zN}$]
|
|
|
|latexmath:[x_{N}] |latexmath:[p_{xN}] |latexmath:[y_{N}]
|
|
|
|latexmath:[p_{yN}] |latexmath:[t_{N}] |latexmath:[p_{zN}]
|
|
|
|=======================================================================
|
|
|
|
|
|
Note that for an _emitted_ `FROMFILE` distribution, all of the
|
|
|
particle’s time, latexmath:[$t$], coordinates will be shifted to
|
|
|
particle’s time, latexmath:[t], coordinates will be shifted to
|
|
|
negative time (if they are not there already). The simulation clock will
|
|
|
then start at latexmath:[$t = 0$] and distribution particles will be
|
|
|
then start at latexmath:[t = 0] and distribution particles will be
|
|
|
emitted into the simulation as the simulation progresses. Also note
|
|
|
that, as the particles are emitted, they will be modified according to
|
|
|
the type of emission model used. This is defined by the attribute
|
... | ... | @@ -341,7 +329,7 @@ the type of emission model used. This is defined by the attribute |
|
|
of `NONE` for the `EMISSIONMODEL` (which is the default) can be defined
|
|
|
so as not to affect the distribution coordinates at all.
|
|
|
|
|
|
To maintain consistency latexmath:[$N$] and `NPART` from the `BEAM`
|
|
|
To maintain consistency latexmath:[N] and `NPART` from the `BEAM`
|
|
|
command in Chapter [beam] must be equal.
|
|
|
|
|
|
[[sec:gaussdisttype]]
|
... | ... | @@ -354,7 +342,7 @@ one-dimensional example): |
|
|
|
|
|
latexmath:[\[f(x) = \frac{1}{\sqrt{2 \pi}} e^{-\frac{(x - \bar{x})^{2}}{2 \sigma_{x}^{2}}}\]]
|
|
|
|
|
|
where latexmath:[$\bar{x}$] is the average value of latexmath:[$x$].
|
|
|
where latexmath:[\bar{x}] is the average value of latexmath:[x].
|
|
|
However, the `GAUSS` distribution can also be used to generate an
|
|
|
emitted beam with a flat top time profile. We will go over the various
|
|
|
options for the `GAUSS` distribution type in this section.
|
... | ... | @@ -367,68 +355,67 @@ We will begin by describing how to create a simple `GAUSS` distribution |
|
|
type. That is, a simple 6-dimensional distribution with a Gaussian
|
|
|
distribution in all dimensions.
|
|
|
|
|
|
.Definition of the basic distribution attributes for a `GAUSS`
|
|
|
distribution type.
|
|
|
[cols="<,^,^,<",options="header",]
|
|
|
.Definition of the basic distribution attributes for a `GAUSS` distribution type.
|
|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`SIGMAX` |0.0 |m |RMS width, latexmath:[$\sigma_{x}$], in transverse
|
|
|
latexmath:[$x$] direction.
|
|
|
|`SIGMAX` |0.0 |m |RMS width, latexmath:[\sigma_{x}], in transverse
|
|
|
latexmath:[x] direction.
|
|
|
|
|
|
|`SIGMAY` |0.0 |m |RMS width, latexmath:[$\sigma_{y}$], in transverse
|
|
|
latexmath:[$y$] direction.
|
|
|
|`SIGMAY` |0.0 |m |RMS width, latexmath:[\sigma_{y}], in transverse
|
|
|
latexmath:[y] direction.
|
|
|
|
|
|
|`SIGMAR` |0.0 |m |RMS radius, latexmath:[$\sigma_{r}$], in radial
|
|
|
|`SIGMAR` |0.0 |m |RMS radius, latexmath:[\sigma_{r}], in radial
|
|
|
direction. If nonzero `SIGMAR` overrides `SIGMAX` and `SIGMAY`.
|
|
|
|
|
|
|`SIGMAZ` |0.0 |m |RMS length, latexmath:[$\sigma_{z}$], in longitudinal
|
|
|
|`SIGMAZ` |0.0 |m |RMS length, latexmath:[\sigma_{z}], in longitudinal
|
|
|
(z) direction. `SIGMAZ` is used for an _injected_ distribution.
|
|
|
|
|
|
|`SIGMAT` |0.0 |s |RMS width, latexmath:[$\sigma_{t}$], in time (t).
|
|
|
|`SIGMAT` |0.0 |s |RMS width, latexmath:[\sigma_{t}], in time (t).
|
|
|
`SIGMAT` is used for an _emitted_ distribution.
|
|
|
|
|
|
|`SIGMAPX` |0.0 |Section [unitsdistattributes] |Parameter
|
|
|
latexmath:[$\sigma_{px}$] for defining distribution.
|
|
|
latexmath:[\sigma_{px}] for defining distribution.
|
|
|
|
|
|
|`SIGMAPY` |0.0 |Section [unitsdistattributes] |Parameter
|
|
|
latexmath:[$\sigma_{py}$] for defining distribution.
|
|
|
latexmath:[\sigma_{py}] for defining distribution.
|
|
|
|
|
|
|`SIGMAPZ` |0.0 |Section [unitsdistattributes] |Parameter
|
|
|
latexmath:[$\sigma_{pz}$] for defining distribution.
|
|
|
latexmath:[\sigma_{pz}] for defining distribution.
|
|
|
|
|
|
|`CUTOFFX` |3.0 |None |Defines transverse distribution cutoff in the
|
|
|
latexmath:[$x$] direction in units of latexmath:[$\sigma_{x}$]. If
|
|
|
`CUTOFFX` latexmath:[$= 0$] then actual cutoff in latexmath:[$x$] is set
|
|
|
latexmath:[x] direction in units of latexmath:[\sigma_{x}]. If
|
|
|
`CUTOFFX` latexmath:[= 0] then actual cutoff in latexmath:[x] is set
|
|
|
to infinity.
|
|
|
|
|
|
|`CUTOFFY` |3.0 |None |Defines transverse distribution cutoff in the
|
|
|
latexmath:[$y$] direction in units of latexmath:[$\sigma_{y}$]. If
|
|
|
`CUTOFFY` latexmath:[$= 0$] then actual cutoff in latexmath:[$y$] is set
|
|
|
latexmath:[y] direction in units of latexmath:[\sigma_{y}]. If
|
|
|
`CUTOFFY` latexmath:[= 0] then actual cutoff in latexmath:[y] is set
|
|
|
to infinity.
|
|
|
|
|
|
|`CUTOFFR` |3.0 |None |Defines transverse distribution cutoff in the
|
|
|
latexmath:[$r$] direction in units of latexmath:[$\sigma_{r}$]. If
|
|
|
`CUTOFFR` latexmath:[$= 0$] then actual cutoff in latexmath:[$r$] is set
|
|
|
to infinity. `CUTOFFR` is only used if `SIGMAR` latexmath:[$>0$].
|
|
|
latexmath:[r] direction in units of latexmath:[\sigma_{r}]. If
|
|
|
`CUTOFFR` latexmath:[= 0] then actual cutoff in latexmath:[r] is set
|
|
|
to infinity. `CUTOFFR` is only used if `SIGMAR` latexmath:[>0].
|
|
|
|
|
|
|`CUTOFFLONG` |3.0 |None |Defines longitudinal distribution cutoff in
|
|
|
the latexmath:[$z$] or latexmath:[$t$] direction (_injected_ or
|
|
|
_emitted_) in units of latexmath:[$\sigma_{z}$] or
|
|
|
latexmath:[$\sigma_{t}$]. `CUTOFFLONG` is different from other
|
|
|
the latexmath:[z] or latexmath:[t] direction (_injected_ or
|
|
|
_emitted_) in units of latexmath:[\sigma_{z}] or
|
|
|
latexmath:[\sigma_{t}]. `CUTOFFLONG` is different from other
|
|
|
dimensions in that a value of 0.0 does not imply a cutoff value of
|
|
|
infinity.
|
|
|
|
|
|
|`CUTOFFPX` |3.0 |None |Defines cutoff in latexmath:[$p_{x}$] dimension
|
|
|
in units of latexmath:[$\sigma_{px}$]. If `CUTOFFPX` latexmath:[$= 0$]
|
|
|
then actual cutoff in latexmath:[$p_{x}$] is set to infinity.
|
|
|
|`CUTOFFPX` |3.0 |None |Defines cutoff in latexmath:[p_{x}] dimension
|
|
|
in units of latexmath:[\sigma_{px}]. If `CUTOFFPX` latexmath:[= 0]
|
|
|
then actual cutoff in latexmath:[p_{x}] is set to infinity.
|
|
|
|
|
|
|`CUTOFFPY` |3.0 |None |Defines cutoff in latexmath:[$p_{y}$] dimension
|
|
|
in units of latexmath:[$\sigma_{py}$]. If `CUTOFFPY` latexmath:[$= 0$]
|
|
|
then actual cutoff in latexmath:[$p_{y}$] is set to infinity.
|
|
|
|`CUTOFFPY` |3.0 |None |Defines cutoff in latexmath:[p_{y}] dimension
|
|
|
in units of latexmath:[\sigma_{py}]. If `CUTOFFPY` latexmath:[= 0]
|
|
|
then actual cutoff in latexmath:[p_{y}] is set to infinity.
|
|
|
|
|
|
|`CUTOFFPZ` |3.0 |None |Defines cutoff in latexmath:[$p_{z}$] dimension
|
|
|
in units of latexmath:[$\sigma_{pz}$]. If `CUTOFFPZ` latexmath:[$= 0$]
|
|
|
then actual cutoff is latexmath:[$p_{z}$] is set to infinity.
|
|
|
|`CUTOFFPZ` |3.0 |None |Defines cutoff in latexmath:[p_{z}] dimension
|
|
|
in units of latexmath:[\sigma_{pz}]. If `CUTOFFPZ` latexmath:[= 0]
|
|
|
then actual cutoff is latexmath:[p_{z}] is set to infinity.
|
|
|
|=======================================================================
|
|
|
|
|
|
In Table [distattrgauss] we list the basic attributes available for a
|
... | ... | @@ -454,27 +441,25 @@ Name:DISTRIBUTION, TYPE = GAUSS, |
|
|
....
|
|
|
|
|
|
This creates a Gaussian shaped distribution with zero transverse
|
|
|
emittance, zero energy spread, latexmath:[$\sigma_{x} = {1.0}{mm}$],
|
|
|
latexmath:[$\sigma_{y} = {3.0}{mm}$],
|
|
|
latexmath:[$\sigma_{z} = {2.0}{mm}$] and an average energy of:
|
|
|
emittance, zero energy spread, latexmath:[\sigma_{x} = {1.0}{mm}],
|
|
|
latexmath:[\sigma_{y} = {3.0}{mm}],
|
|
|
latexmath:[\sigma_{z} = {2.0}{mm}] and an average energy of:
|
|
|
|
|
|
latexmath:[\[W = {1.2}{MeV}\]]
|
|
|
|
|
|
In the latexmath:[$x$] direction, the Gaussian distribution is cutoff at
|
|
|
latexmath:[$x = 2.0 \times \sigma_{x} = {2.0}{mm}$]. In the
|
|
|
latexmath:[$y$] direction it is cutoff at
|
|
|
latexmath:[$y = 2.0 \times \sigma_{y} = {6.0}{mm}$]. This distribution
|
|
|
In the latexmath:[x] direction, the Gaussian distribution is cutoff at
|
|
|
latexmath:[x = 2.0 \times \sigma_{x} = {2.0}{mm}]. In the
|
|
|
latexmath:[y] direction it is cutoff at
|
|
|
latexmath:[y = 2.0 \times \sigma_{y} = {6.0}{mm}]. This distribution
|
|
|
is _injected_ into the simulation at an average position of
|
|
|
latexmath:[$(\bar{x},\bar{y},\bar{z})=({1.0}{mm}, {-2.0}{mm}, {10.0}{mm})$].
|
|
|
latexmath:[(\bar{x},\bar{y},\bar{z})=({1.0}{mm}, {-2.0}{mm}, {10.0}{mm})].
|
|
|
|
|
|
[[sec:gaussdisttypephotoinjector]]
|
|
|
`GAUSS` Distribution for Photoinjector
|
|
|
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
|
|
|
|
|
.Definition of additional distribution attributes for an _emitted_
|
|
|
`GAUSS` distribution type. These are used to generate a distribution
|
|
|
with a time profile as illustrated in Figure [flattop].
|
|
|
[cols="<,^,^,<",options="header",]
|
|
|
.Definition of additional distribution attributes for an _emitted_ `GAUSS` distribution type. These are used to generate a distribution with a time profile as illustrated in Figure [flattop].
|
|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`TPULSEFWHM` |0.0 |s |Flat top time see Figure [flattop].
|
... | ... | @@ -490,7 +475,7 @@ flat top in Figure [flattop]. This defines the amplitude of those |
|
|
oscillations in percent of the average flat top amplitude.
|
|
|
|
|
|
|`FTOSCPERIODS` |0 |None |Defines the number of oscillation periods
|
|
|
imposed on the flat top, latexmath:[$t_\mathrm{flattop}$], in
|
|
|
imposed on the flat top, latexmath:[t_\mathrm{flattop}], in
|
|
|
Figure [flattop].
|
|
|
|=======================================================================
|
|
|
|
... | ... | @@ -513,13 +498,13 @@ latexmath:[\[\begin{aligned} |
|
|
\texttt{TFALL} = t_{F} &= \left(\sqrt{2 \ln(10)} - \sqrt{2 \ln \left(\frac{10}{9} \right)} \right) \sigma_{F}\\
|
|
|
& = 1.6869 \sigma_{F}\end{aligned}\]]
|
|
|
|
|
|
where latexmath:[$\sigma_{R}$] and latexmath:[$\sigma_{F}$] are the
|
|
|
where latexmath:[\sigma_{R}] and latexmath:[\sigma_{F}] are the
|
|
|
Gaussian, RMS rise and fall times respectively. The flat-top portion of
|
|
|
the profile, `TPULSEFWHM`, is defined as (See also Figure [flattop]):
|
|
|
|
|
|
latexmath:[\[\texttt{TPULSEFWHM} = \mathrm{FWHM}_{P} = t_\mathrm{flattop} + \sqrt{2 \ln 2} \left( \sigma_{R} + \sigma_{F} \right)\]]
|
|
|
|
|
|
Total emission time, latexmath:[$t_{E}$], of this distribution, is a
|
|
|
Total emission time, latexmath:[t_{E}], of this distribution, is a
|
|
|
function of the longitudinal cutoff, `CUTOFFLONG`
|
|
|
see Table [distattrgauss], and is given by:
|
|
|
|
... | ... | @@ -529,63 +514,62 @@ latexmath:[\[\begin{aligned} |
|
|
&= \mathrm{FWHM}_{P} + \frac{\texttt{CUTOFFLONG} - \sqrt{2 \ln 2}}{1.6869} (\texttt{TRISE} + \texttt{TFALL})\end{aligned}\]]
|
|
|
|
|
|
Finally, we can also impose oscillations over the flat-top portion of
|
|
|
the laser pulse in Figure [flattop], latexmath:[$t_\mathrm{flattop}$].
|
|
|
the laser pulse in Figure [flattop], latexmath:[t_\mathrm{flattop}].
|
|
|
This is defined by the attributes `FTOSCAMPLITUDE` and `FTOSCPERIODS`
|
|
|
from Table [distattremittedgauss]. `FTOSCPERIODS` defines how many
|
|
|
oscillation periods will be present during the
|
|
|
latexmath:[$t_\mathrm{flattop}$] portion of the pulse. `FTOSCAMPLITUDE`
|
|
|
latexmath:[t_\mathrm{flattop}] portion of the pulse. `FTOSCAMPLITUDE`
|
|
|
defines the amplitude of those oscillations in percentage of the average
|
|
|
profile amplitude during latexmath:[$t_\mathrm{flattop}$]. So, for
|
|
|
example, if we set latexmath:[$\texttt{FTOSCAMPLITUDE} = 5$], and the
|
|
|
amplitude of the profile is equal to latexmath:[$1.0$] during
|
|
|
latexmath:[$t_\mathrm{flattop}$], the amplitude of the oscillation will
|
|
|
be latexmath:[$0.05$].
|
|
|
profile amplitude during latexmath:[t_\mathrm{flattop}]. So, for
|
|
|
example, if we set latexmath:[\texttt{FTOSCAMPLITUDE} = 5], and the
|
|
|
amplitude of the profile is equal to latexmath:[1.0] during
|
|
|
latexmath:[t_\mathrm{flattop}], the amplitude of the oscillation will
|
|
|
be latexmath:[0.05].
|
|
|
|
|
|
[[correlations-for-gauss-distribution-experimental]]
|
|
|
Correlations for `GAUSS` Distribution (Experimental)
|
|
|
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
|
|
|
|
|
.Definition of additional distribution attributes for a `GAUSS`
|
|
|
distribution type for generating correlations in the beam.
|
|
|
[cols="<,^,^,<",options="header",]
|
|
|
.Definition of additional distribution attributes for a `GAUSS` distribution type for generating correlations in the beam.
|
|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`CORRX` |0.0 |Section [unitsdistattributes] |latexmath:[$x$],
|
|
|
latexmath:[$p_x$] correlation. (latexmath:[$R_{12}$] in transport
|
|
|
|`CORRX` |0.0 |Section [unitsdistattributes] |latexmath:[x],
|
|
|
latexmath:[p_x] correlation. (latexmath:[R_{12}] in transport
|
|
|
notation.)
|
|
|
|
|
|
|`CORRY` |0.0 |Section [unitsdistattributes] |latexmath:[$y$],
|
|
|
latexmath:[$p_y$] correlation. (latexmath:[$R_{34}$] in transport
|
|
|
|`CORRY` |0.0 |Section [unitsdistattributes] |latexmath:[y],
|
|
|
latexmath:[p_y] correlation. (latexmath:[R_{34}] in transport
|
|
|
notation.)
|
|
|
|
|
|
|`CORRZ` |0.0 |Section [unitsdistattributes] |latexmath:[$z$],
|
|
|
latexmath:[$p_z$] correlation. (latexmath:[$R_{56}$] in transport
|
|
|
|`CORRZ` |0.0 |Section [unitsdistattributes] |latexmath:[z],
|
|
|
latexmath:[p_z] correlation. (latexmath:[R_{56}] in transport
|
|
|
notation.)
|
|
|
|
|
|
|`R51` |0.0 |Section [unitsdistattributes] |latexmath:[$x$],
|
|
|
latexmath:[$z$] correlation. (latexmath:[$R_{51}$] in transport
|
|
|
|`R51` |0.0 |Section [unitsdistattributes] |latexmath:[x],
|
|
|
latexmath:[z] correlation. (latexmath:[R_{51}] in transport
|
|
|
notation.)
|
|
|
|
|
|
|`R52` |0.0 |Section [unitsdistattributes] |latexmath:[$p_x$],
|
|
|
latexmath:[$z$] correlation. (latexmath:[$R_{52}$] in transport
|
|
|
|`R52` |0.0 |Section [unitsdistattributes] |latexmath:[p_x],
|
|
|
latexmath:[z] correlation. (latexmath:[R_{52}] in transport
|
|
|
notation.)
|
|
|
|
|
|
|`R61` |0.0 |Section [unitsdistattributes] |latexmath:[$x$],
|
|
|
latexmath:[$p_z$] correlation. (latexmath:[$R_{61}$] in transport
|
|
|
|`R61` |0.0 |Section [unitsdistattributes] |latexmath:[x],
|
|
|
latexmath:[p_z] correlation. (latexmath:[R_{61}] in transport
|
|
|
notation.)
|
|
|
|
|
|
|`R62` |0.0 |Section [unitsdistattributes] |latexmath:[$p_x$],
|
|
|
latexmath:[$p_z$] correlation. (latexmath:[$R_{62}$] in transport
|
|
|
|`R62` |0.0 |Section [unitsdistattributes] |latexmath:[p_x],
|
|
|
latexmath:[p_z] correlation. (latexmath:[R_{62}] in transport
|
|
|
notation.)
|
|
|
|=======================================================================
|
|
|
|
|
|
To generate Gaussian initial distribution with dispersion, first we
|
|
|
generate the uncorrelated Gaussian inputs matrix
|
|
|
latexmath:[$R=(R1,...,R_n)$]. The mean of latexmath:[$R_i$] is
|
|
|
latexmath:[$0$] and the standard deviation squared is 1. Then we
|
|
|
correlate latexmath:[$R$]. The correlation coefficient matrix
|
|
|
latexmath:[$\sigma$] in latexmath:[$x$], latexmath:[$p_x$],
|
|
|
latexmath:[$z$], latexmath:[$p_z$] phase space reads:
|
|
|
latexmath:[R=(R1,...,R_n)]. The mean of latexmath:[R_i] is
|
|
|
latexmath:[0] and the standard deviation squared is 1. Then we
|
|
|
correlate latexmath:[R]. The correlation coefficient matrix
|
|
|
latexmath:[\sigma] in latexmath:[x], latexmath:[p_x],
|
|
|
latexmath:[z], latexmath:[p_z] phase space reads:
|
|
|
|
|
|
latexmath:[\[\sigma= \left[
|
|
|
\begin{array}{cccc}
|
... | ... | @@ -597,14 +581,14 @@ r61 &r62 &c_t &1\\ |
|
|
\right] \\\]]
|
|
|
|
|
|
The Cholesky decomposition of the symmetric positive-definite matrix
|
|
|
latexmath:[$\sigma$] is latexmath:[$\sigma=C^{\mathbf{T}}C$], then the
|
|
|
correlated distribution is latexmath:[$\transpose{C}R$].
|
|
|
latexmath:[\sigma] is latexmath:[\sigma=C^{\mathbf{T}}C], then the
|
|
|
correlated distribution is latexmath:[\transpose{C}R].
|
|
|
|
|
|
*Note*: Correlations work for the moment only with the Gaussian
|
|
|
distribution and are experimental, so there are no guarantees as to its
|
|
|
efficacy or accuracy. Also, these correlations will work, in principle,
|
|
|
for an _emitted_ beam. However, recall that in this case,
|
|
|
latexmath:[$z$] in meters is replaced by latexmath:[$t$] in seconds, so
|
|
|
latexmath:[z] in meters is replaced by latexmath:[t] in seconds, so
|
|
|
take care.
|
|
|
|
|
|
As an example of defining a correlated beam, let the initial correlation
|
... | ... | @@ -660,36 +644,34 @@ Table [distattrflattopinj,distattruniversal]. At the moment, we cannot |
|
|
define a spread in the beam momentum, so an _injected_ `FLATTOP`
|
|
|
distribution will currently have zero emittance. An _injected_ `FLATTOP`
|
|
|
will be a uniformly filled ellipse transversely with a uniform
|
|
|
distribution in latexmath:[$z$]. (Basically a cylinder with an
|
|
|
distribution in latexmath:[z]. (Basically a cylinder with an
|
|
|
elliptical cross section.)
|
|
|
|
|
|
.Definition of the basic distribution attributes for an _injected_
|
|
|
`FLATTOP` distribution type.
|
|
|
[cols="<,^,^,<",options="header",]
|
|
|
.Definition of the basic distribution attributes for an _injected_ `FLATTOP` distribution type.
|
|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`SIGMAX` |0.0 |m |Hard edge width in latexmath:[$x$] direction.
|
|
|
|`SIGMAX` |0.0 |m |Hard edge width in latexmath:[x] direction.
|
|
|
|
|
|
|`SIGMAY` |0.0 |m |Hard edge width in latexmath:[$y$] direction.
|
|
|
|`SIGMAY` |0.0 |m |Hard edge width in latexmath:[y] direction.
|
|
|
|
|
|
|`SIGMAR` |0.0 |m |Hard edge radius. If nonzero `SIGMAR` overrides
|
|
|
`SIGMAX` and `SIGMAY`.
|
|
|
|
|
|
|`SIGMAZ` |0.0 |m |Hard edge length in latexmath:[$z$] direction.
|
|
|
|`SIGMAZ` |0.0 |m |Hard edge length in latexmath:[z] direction.
|
|
|
|=======================================================================
|
|
|
|
|
|
[[emitted-flattop]]
|
|
|
Emitted `FLATTOP`
|
|
|
^^^^^^^^^^^^^^^^^
|
|
|
|
|
|
.Definition of the basic distribution attributes for an _emitted_
|
|
|
`FLATTOP` distribution type.
|
|
|
[cols="<,^,^,<",options="header",]
|
|
|
.Definition of the basic distribution attributes for an _emitted_ `FLATTOP` distribution type.
|
|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`SIGMAX` |0.0 |m |Hard edge width in latexmath:[$x$] direction.
|
|
|
|`SIGMAX` |0.0 |m |Hard edge width in latexmath:[x] direction.
|
|
|
|
|
|
|`SIGMAY` |0.0 |m |Hard edge width in latexmath:[$y$] direction.
|
|
|
|`SIGMAY` |0.0 |m |Hard edge width in latexmath:[y] direction.
|
|
|
|
|
|
|`SIGMAR` |0.0 |m |Hard edge radius. If nonzero `SIGMAR` overrides
|
|
|
`SIGMAX` and `SIGMAY`.
|
... | ... | @@ -710,7 +692,7 @@ flat top in Figure [flattop]. This defines the amplitude of those |
|
|
oscillations in percent of the average flat top amplitude.
|
|
|
|
|
|
|`FTOSCPERIODS` |0 |None |Defines the number of oscillation periods
|
|
|
imposed on the flat top, latexmath:[$t_\mathrm{flattop}$], in
|
|
|
imposed on the flat top, latexmath:[t_\mathrm{flattop}], in
|
|
|
Figure [flattop].
|
|
|
|
|
|
|`LASERPROFFN` | |None |File name containing measured laser image.
|
... | ... | @@ -726,13 +708,13 @@ intensity. |
|
|
|`FLIPY` |`FALSE` | |Flip the laser profile in vertical direction.
|
|
|
|
|
|
|`ROTATE90` |`FALSE` | |Rotate the laser profile
|
|
|
90latexmath:[$^{\circ}$] in counterclockwise direction.
|
|
|
90latexmath:[^{\circ}] in counterclockwise direction.
|
|
|
|
|
|
|`ROTATE180` |`FALSE` | |Rotate the laser profile
|
|
|
180latexmath:[$^{\circ}$].
|
|
|
180latexmath:[^{\circ}].
|
|
|
|
|
|
|`ROTATE270` |`FALSE` | |Rotate the laser profile
|
|
|
270latexmath:[$^{\circ}$] in counterclockwise direction.
|
|
|
270latexmath:[^{\circ}] in counterclockwise direction.
|
|
|
|=======================================================================
|
|
|
|
|
|
The attributes of an _emitted_ `FLATTOP` distribution are defined in
|
... | ... | @@ -796,33 +778,33 @@ the longitudinal time profile of the distribution is generated. |
|
|
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
|
|
|
|
|
The `BINOMIAL` type of distribution is based on [JohoDist]. The shape of
|
|
|
the binomial distribution is governed by one parameter latexmath:[$m$].
|
|
|
the binomial distribution is governed by one parameter latexmath:[m].
|
|
|
By varying this single parameter one obtains the most commonly used
|
|
|
distributions for our type of simulations, as listed in
|
|
|
Table [binomdist].
|
|
|
|
|
|
.Different distributions specified by a single parameter latexmath:[$m$]
|
|
|
[cols="<,<,<,<",options="header",]
|
|
|
.Different distributions specified by a single parameter latexmath:[m]
|
|
|
[cols="<1,<1,<3,<3",options="header",]
|
|
|
|=======================================================================
|
|
|
|latexmath:[$m$] |Distribution |Density |Profile
|
|
|
|0.0 |Hollow shell |latexmath:[$\frac{1}{\pi}\delta(1-r^2)$]
|
|
|
|latexmath:[$\frac{1}{\pi}(1-r^2)^{-0.5}$]
|
|
|
|latexmath:[m] |Distribution |Density |Profile
|
|
|
|0.0 |Hollow shell |latexmath:[\frac{1}{\pi}\delta(1-r^2)]
|
|
|
|latexmath:[\frac{1}{\pi}(1-r^2)^{-0.5}]
|
|
|
|
|
|
|0.5 |Flat profile |latexmath:[$\frac{1}{2\pi}(1-r^2)^{-0.5}$]
|
|
|
|latexmath:[$\frac{1}{2}$]
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|0.5 |Flat profile |latexmath:[\frac{1}{2\pi}(1-r^2)^{-0.5}]
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|latexmath:[\frac{1}{2}]
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|1.0 |Uniform |latexmath:[$\frac{1}{\pi}$]
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|latexmath:[$\frac{2}{\pi}(1-x^2)^{0.5}$]
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|1.0 |Uniform |latexmath:[\frac{1}{\pi}]
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|latexmath:[\frac{2}{\pi}(1-x^2)^{0.5}]
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|1.5 |Elliptical |latexmath:[$\frac{3}{2\pi}(1-r^2)^{0.5}$]
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|latexmath:[$\frac{1}{4}(1-x^2)$]
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|1.5 |Elliptical |latexmath:[\frac{3}{2\pi}(1-r^2)^{0.5}]
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|latexmath:[\frac{1}{4}(1-x^2)]
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|2.0 |Parabolic |latexmath:[$\frac{2}{\pi}(1-r^2)$]
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|latexmath:[$\frac{3}{8\pi}(1-x^2)^{1.5}$]
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|2.0 |Parabolic |latexmath:[\frac{2}{\pi}(1-r^2)]
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|latexmath:[\frac{3}{8\pi}(1-x^2)^{1.5}]
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|
|latexmath:[$\rightarrow \infty$] |Gaussian
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|latexmath:[$\frac{1}{2\pi\sigma_x\sigma_y}exp(-\frac{x^2}{2\sigma_x^2} -\frac{y^2}{2\sigma_y^2})$]
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|
|latexmath:[$\frac{1}{\sqrt{2\pi}*\sigma_x}exp(-\frac{x^2}{2\sigma_x^2}) $]
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|latexmath:[\rightarrow \infty] |Gaussian
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|latexmath:[\frac{1}{2\pi\sigma_x\sigma_y}exp(-\frac{x^2}{2\sigma_x^2} -\frac{y^2}{2\sigma_y^2})]
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|
|latexmath:[\frac{1}{\sqrt{2\pi}*\sigma_x}exp(-\frac{x^2}{2\sigma_x^2}) ]
|
|
|
|=======================================================================
|
|
|
|
|
|
[[sec:emissionmodel]]
|
... | ... | @@ -842,11 +824,11 @@ The emission model `NONE` is the default emission model used in |
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_OPAL-t_. It has a single attribute, listed in
|
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Table [distattremitmodelnoneastra]. The `NONE` emission model is very
|
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|
simplistic. It merely adds the amount of energy defined by the attribute
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|
`EKIN` to the longitudinal momentum, latexmath:[$p_{z}$], for each
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`EKIN` to the longitudinal momentum, latexmath:[p_{z}], for each
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|
particle in the distribution as it leaves the cathode.
|
|
|
|
|
|
.Attributes for the `NONE` and `ASTRA` emission models.
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|
[cols="<,^,^,<",options="header",]
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|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|==============================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`EKIN` |1.0 |eV |Thermal energy added to beam during emission.
|
... | ... | @@ -858,7 +840,7 @@ beams into our simulation. We must add some z momentum to ensure that |
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the particles drift into the simulation space. If in this example one
|
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|
were to specify `EKIN = 0`, then you would likely get strange results as
|
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|
the particles would not move off the cathode, causing all of the emitted
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|
|
charge to pile up at latexmath:[$z = 0$] in the first half time step
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|
charge to pile up at latexmath:[z = 0] in the first half time step
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|
before the beam space charge is calculated.
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|
|
|
|
|
....
|
... | ... | @@ -879,7 +861,7 @@ Dist:DISTRIBUTION, TYPE = FLATTOP, |
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|
One thing to note, it may be that if you are emitting your own
|
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|
distribution using the `TYPE = FROMFILE` option, you may want to set
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|
`EKIN = 0` if you have already added some amount of momentum,
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latexmath:[$p_{z}$], to the particles.
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latexmath:[p_{z}], to the particles.
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|
|
|
[[emission-model-astra]]
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|
|
Emission Model: `ASTRA`
|
... | ... | @@ -897,13 +879,13 @@ latexmath:[\[\begin{aligned} |
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|
p_{z} &= p_{total} |{\cos(\theta)}|
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|
\end{aligned}\]]
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|
|
|
|
where latexmath:[$\theta$] is a random angle between latexmath:[$0$] and
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|
latexmath:[$\pi$], and latexmath:[$\phi$] is given by
|
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where latexmath:[\theta] is a random angle between latexmath:[0] and
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|
latexmath:[\pi], and latexmath:[\phi] is given by
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|
|
latexmath:[\[\phi = 2.0 \arccos \left( \sqrt{x} \right)\]]
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with latexmath:[$x$] a random number between latexmath:[$0$] and
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latexmath:[$1$].
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with latexmath:[x] a random number between latexmath:[0] and
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|
latexmath:[1].
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|
|
[[emission-model-nonequil]]
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|
|
Emission Model: `NONEQUIL`
|
... | ... | @@ -915,7 +897,7 @@ attributes needed by this emission model are listed in |
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|
Table [distattremitmodelnonequil].
|
|
|
|
|
|
.Attributes for the `NONE` and `ASTRA` emission models.
|
|
|
[cols="<,^,^,<",options="header",]
|
|
|
[cols="<1,^1,^1,<4",options="header",]
|
|
|
|=======================================================================
|
|
|
|Attribute Name |Default Value |Units |Description
|
|
|
|`ELASER` |4.86 |eV |Photoinjector drive laser energy. (Default is 255nm
|
... | ... | |