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OPAL
Documentation
Manual
Commits
252c1487
Commit
252c1487
authored
Nov 26, 2020
by
albajacas_a
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Resolve "Documentation for new Undulator element"
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252c1487
...
...
@@ 2685,6 +2685,102 @@ bstp: BEAMSTRIPPING, PRESSURE=1E8, TEMPERATURE=300,
No
matter
what
the
value
of
STOP
is
,
the
particles
stripped
are
recorded
in
the
HDF5
file
_
<
elementname
>.
h5_
(
or
ASCII
if
link
:
control
#
sec
.
control
.
option
[`
ASCIIDUMP
`]
is
true
).
[[
sec
.
elements
.
undulator

opal

t
]]
===
Undulator
(
_OPAL

t_
)
_OPAL_
's undulator element comes with its own FiniteDifference TimeDomain fullwave solver, which
accounts for spacecharge and radiation effects in 3D.
It was implemented by means of the https://github.com/aryafallahi/mithra[MITHRA]
library, developed by Arya Fallahi.
To use the undulator element and its solver, one needs to compile _OPAL_ in the following way:
. install the https://github.com/aryafallahi/mithra[MITHRA 2.0] library,
. set the environment variable `MITHRA_PREFIX=directory/where/you/store/mithra`
. compile _OPAL_ with the option `cmake DENABLE_OPAL_FEL=yes ..`
When the head of the bunch crosses the start of an undulator in the beamline
(defined by `ELEMEDGE`), the solver changes automatically from
Poisson to fullwave, and changes back to Poisson once the bunch has passed through the
whole undulator and its fringe fields.
The length of the undulator is defined as
[latexmath]
++++
\begin{aligned}
&L = N\lambda + 2\,\text{fringe},\\
&\text{fringe} = 2\lambda,
\end{aligned}
++++
where latexmath:[\lambda] is the undulator period and latexmath:[N] its number of periods.
Since the element'
s
length
is
entirely
defined
by
the
undulator
periods
,
there
is
no
`
LENGTH
`
parameter
to
be
specified
for
the
undulator
element
.
The
magnetic
field
is
that
of
a
planar
undulator
with
flat
pole
faces
:
[
latexmath
]
++++
\
begin
{
aligned
}
&
B_x
=
B_0
\
cosh
(
kr
)\
sin
(
kz
)\
cos
(\
alpha
),\\
&
B_y
=
B_0
\
cosh
(
kr
)\
sin
(
kz
)\
sin
(\
alpha
),\\
&
B_z
=
B_0
\
sinh
(
kr
)\
cos
(
kz
),
\
end
{
aligned
}
++++
where
latexmath
:[
r
=
x
\
cos
(\
alpha
)
+
y
\
sin
(\
alpha
)]
is
the
radial
distance
from
the
undulator
axis
,
latexmath
:[
k
=
2
\
pi
/\
lambda
]
the
wave

number
,
latexmath
:[\
alpha
]
the
angle
between
the
magnetic
field
polarisation
and
the
x

axis
,
and
latexmath
:[
B_0
]
the
maximum
magnetic
field
value
.
The
fringe
fields
are
defined
as
:
[
latexmath
]
++++
\
begin
{
aligned
}
&
B_x
=
B_0
\
cosh
(
kr
)
kze
^{(
kz
)^
2
/
2
}\
cos
(\
alpha
),\\
&
B_y
=
B_0
\
cosh
(
kr
)
kze
^{(
kz
)^
2
/
2
}\
sin
(\
alpha
),\\
&
B_z
=
B_0
\
sinh
(
kr
)
e
^{(
kz
)^
2
/
2
}.
\
end
{
aligned
}
++++
The
parameters
that
describe
the
undulator
element
and
its
associated
full

wave
solver
are
as
follows
:
K
::
The
undulator
strength
parameter
.
LAMBDA
::
The
undulator
period
latexmath
:[\
lambda
]
[
m
].
NUMPERIODS
::
Number
of
periods
latexmath
:[
N
].
ANGLE
::
Angle
latexmath
:[\
alpha
]
between
the
magnetic
field
polarisation
and
the
x

axis
[
rad
]
(
default
:
0
).
MESHLENGTH
::
Size
in
three
dimensions
latexmath
:[(
L_x
,
L_y
,
L_z
)]
of
the
computational
grid
[
m
],
which
is
in
a
frame
of
reference
moving
at
the
average
speed
of
the
bunch
.
It
should
be
large
enough
to
contain
the
whole
bunch
,
as
particles
outside
of
it
will
not
perceive
any
fields
.
As
a
rule
of
thumb
,
the
grid
should
be
3
times
longer
than
the
bunch
,
since
the
bunch
will
slightly
shift
longitudinally
when
entering
and
exiting
the
undulator
,
and
10
times
wider
than
the
bunch
,
to
avoid
spurious
radiation
reflections
,
since
the
Absorbing
Boundary
Conditions
(
ABCs
)
cannot
correctly
absorb
obliquely
incident
waves
.
MESHRESOLUTION
::
Grid

spacing
latexmath
:[(\
Delta_x
,
\
Delta_y
,
\
Delta_z
)]
of
the
computational
domain
[
m
].
DTBUNCH
::
Time

step
for
the
particle
update
[
s
].
By
default
it
is
equal
to
the
field
update
time

step
,
which
is
automatically
chosen
by
the
algorithm
in
order
to
satisfy
the
stability
conditon
.
`
DTBUNCH
`
needs
to
be
equal
to
or
smaller
than
the
field
time

step
.
TRUNORDER
::
Truncation
order
of
the
ABCs
.
Can
be
1
or
2
(
default
:
2
).
TOTALTIME
::
Total
time
to
simulate
using
the
full

wave
solver
[
s
].
By
default
this
is
set
such
that
the
whole
passage
through
the
undulator
is
simulated
.
FNAME
::
File
specifying
which
output
the
full

wave
solver
should
provide
.
It
is
equivalent
to
the
job

file
in
https
://
github
.
com
/
aryafallahi
/
mithra
[
MITHRA
],
without
the
parameters
`
MESH
`,
`
bunch

initialization
`,
and
`
UNDULATOR
`.
This
file
is
optional
.
Example
of
the
wiggler
element
used
in
the
AWA
beamline
:

UND
:
UNDULATOR
,
ELEMEDGE
=
44.0e2
,
K
=
10.81
,
LAMBDA
=
8.5e2
,
NUMPERIODS
=
10
,
ANGLE
=
PI
/
2
,
MESHLENGTH
=
{
12e3
,
12e3
,
4e3
},
MESHRESOLUTION
=
{
1e5
,
1e5
,
8e6
},
FNAME
=
"wiggler_sims_July_2020/mithra_output.job"
;

[[
sec
.
elements
.
bibliography
]]
===
References
...
...
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