10.56 LRWAKE—Long-range (inter-bunch and inter-turn) longitudinal and transverse
wake
Long-range (inter-bunch and inter-turn) longitudinal and transverse wake
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no
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| Parameter Name | Units | Type | Default | Description |
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| INPUTFILE | | STRING | NULL | name of file giving Green
function |
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| TCOLUMN | | STRING | NULL | column in INPUTFILE
containing time data |
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| WXCOLUMN | | STRING | NULL | column in INPUTFILE
containing horizontal dipole
Green function |
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| WYCOLUMN | | STRING | NULL | column in INPUTFILE
containing vertical dipole
Green function |
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| WZCOLUMN | | STRING | NULL | column in INPUTFILE
containing longitudinal Green
function |
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| QXCOLUMN | | STRING | NULL | column in INPUTFILE
containing horizontal
quadrupole Green function |
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| QYCOLUMN | | STRING | NULL | column in INPUTFILE
containing vertical quadrupole
Green function |
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| FACTOR | | double | 1 | factor by which to multiply
wakes |
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| XFACTOR | | double | 1 | factor by which to multiply
horizontal dipole wake |
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| YFACTOR | | double | 1 | factor by which to multiply
vertical dipole wake |
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| ZFACTOR | | double | 1 | factor by which to multiply
longitudinal dipole wake |
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| QXFACTOR | | double | 1 | factor by which to multiply
horizontal quadrupole wake |
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| QYFACTOR | | double | 1 | factor by which to multiply
vertical quadrupole wake |
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| TURNS_TO_KEEP | | long | 128 | number of turns of data to
retain |
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| RAMP_PASSES | | long | 0 | Number of passes over which
to linearly ramp up the wake
to full strength. |
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Long-range (inter-bunch and inter-turn) longitudinal and transverse wake
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| Parameter Name | Units | Type | Default | Description |
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| GROUP | | string | NULL | Optionally used to assign an
element to a group, with
a user-defined name. Group
names will appear in the
parameter output file in the
column ElementGroup |
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This element provides serial and parallel modeling of long range, multi-bunch, multi-pass,
non-resonant wakes. Resonant wakes can be modeled using the *RFMODE elements, while short-range wakes
are modeled with WAKE, TRWAKE, ZLONGIT, ZTRANSVERSE, and RFCW.
For the LRWAKE element, the beam is assumed to be bunched and wakes are computed bunch-to-bunch.
The long-range wake is assumed to be constant within any single bunch.
To use this element, the beam has to be prepared in a special way so that elegant can recognize
which particles belong to which bunches. See Section 6 for details. Given a properly prepared beam, the
algorithm works as follows.
- Each processor uses arrays to record
- How many particles are in each of B bunches,
- The sum of the arrival times t at the LRWAKE element for the particles in each bunch,
and
- The sum of x and y at the LRWAKE element for the particles in each bunch.
- These arrays are summed across all the processors and used to compute the moments ⟨t⟩, ⟨x⟩, and
⟨y⟩ for each bunch, as well as the charge in each bunch.
- Arrays of length B from N prior turns are kept in a buffer
- Buffer for turns N - 1 to 1 is copied to slots N through 2, thus overwriting the data for
the oldest turn.
- The data for latest turn is copied into slot 1.
- For each bunch, sums are performed over all prior bunches/turns to compute the voltage. For the
longitudinal wake, we have
 | (67) |
A positive value decelerates the particle. For the horizontal dipole wake we have
 | (68) |
with the vertical wake being similar. In both cases, a positive value deflects the particle toward
positive x or y for a positive offset of the driving particle.
- The quadrupole wakes may also be included. In this case, the contribution to the horizontal wake
is
 | (69) |
where xp is the coordinate of the probe particle. The vertical wake is similar.
To use LRWAKE, the user provides the wakes (functions of t) in an SDDS file. These wakes may
extend over an arbitrary number of turns, with the user declaring how many turns to actually use as part
of the element definition. However, they should be zero within the region occupied by a single bunch, to
avoid double-counting with the true short-range wake. (Note that the above sums include
the self-wake.) Similarly, the short-range should be zero for times comparable to the bunch
spacing.
Note that the quadrupole wakes are in some cases related to the dipole wakes by constant numerical
factors [48]. In such a case, one may name the same column for QXCOLUMN (QYCOLUMN) and WXCOLUMN
(WYCOLUMN) and then specify QXFACTOR (QYFACTOR) appropriately.