10.52 LSRMDLTR—A non-symplectic numerically integrated planar undulator including optional co-propagating laser beam for laser modulation of the electron beam.

A non-symplectic numerically integrated planar undulator including optional co-propagating laser beam for laser modulation of the electron beam.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no






Parameter Name Units Type Default

Description






L M double 0.0

length






BU T double 0.0

Undulator peak field






TGU_GRADIENT 1∕M double 0.0

Transverse gradient divided by maximum on-axis field.






TGU_COMP_FACTOR NULLdouble 1

Use to adjust constant field component to reduce trajectory error.






PERIODS long 0

Number of undulator periods.






METHOD NULLSTRINGnon-adaptive runge-kutta

integration method (runge-kutta, bulirsch-stoer, modified-midpoint, two-pass modified-midpoint, leap-frog, non-adaptive runge-kutta)






FIELD_EXPANSION NULLSTRINGleading terms

ideal, exact, or ”leading terms”






ACCURACY NULLdouble 0.0

Integration accuracy for adaptive integration. (Not recommended)






N_STEPS long 0

Number of integration steps for non-adaptive integration.






POLE_FACTOR1 double 0.1557150345504

Strength factor for the first and last pole.






POLE_FACTOR2 double 0.380687012288581

Strength factor for the second and second-to-last pole.






POLE_FACTOR3 double 0.802829337348179

Strength factor for the third and third-to-last pole.






LASER_WAVELENGTHM double 0.0

Laser wavelength. If zero, the wavelength is calculated from the resonance condition.






LASER_PEAK_POWERW double 0.0

laser peak power






LASER_W0 M double 1

laser spot size at waist, w0 =   --
√ 2σx =   --
√ 2σy






LSRMDLTR continued

A non-symplectic numerically integrated planar undulator including optional co-propagating laser beam for laser modulation of the electron beam.






Parameter NameUnits Type Default

Description






LASER_PHASE RAD double 0.0

laser phase






LASER_X0 M double 0.0

laser horizontal offset at center of wiggler






LASER_Y0 M double 0.0

laser vertical offset at center of wiggler






LASER_Z0 M double 0.0

offset of waist position from center of wiggler






LASER_TILT RAD double 0.0

laser tilt






LASER_M short 0

laser horizontal mode number (<5)






LASER_N short 0

laser vertical mode number (<5)






SYNCH_RAD short 0

Include classical, single-particle synchrotron radiation?






ISR short 0

Include quantum excitation?






HELICAL short 0

If non-zero, simulate helical undulator.






TIME_PROFILENULLSTRINGNULL

<filename>=<x>+<y> form specification of input file giving time-dependent modulation of the laser electric and magnetic fields.






TIME_OFFSET S double 0.0

Time offset of the laser profile.






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






This element simulates a planar undulator, together with an optional co-propagating laser beam that can be used as a beam heater or modulator. The simulation is done by numerical integration of the Lorentz equation. It is not symplectic, and hence this element is not recommended for long-term tracking simulation of undulators in storage rings.

The fields in the undulator can be expressed in one of three ways. The FIELD_EXPANSION parameter is used to control which method is used.

If HELICAL is set to a nonzero value, a helical device is modeled by combining the fields of two planar devices, one of which is rotated 90 degrees and displaced one quarter wavelength. Again, the FIELD_EXPANSION parameter is used to control which method is used.

The expressions for the laser field used by this element are from A. Chao’s article “Laser Acceleration — Focussed Laser,” available on-line at
http://www.slac.stanford.edu/~achao/LaserAccelerationFocussed.pdf . The implementation covers laser modes TEMij, where 0 i 4 and 0 j 4.

By default, if the laser wavelength is not given, it is computed from the resonance condition:

      λu (    1   )
λl = --2- 1 + --K2  ,
     2γ       2
(88)

where γ is the relativistic factor for the beam and K is the undulator parameter.

The adaptive integrator doesn’t work well for this element, probably due to sudden changes in field derivatives in the first and last three poles (a result of the implementation of the undulator terminations). Hence, the default integrator is non-adaptive Runge-Kutta. The integration accuracy is controlled via the N_STEPS parameter. N_STEPS should be about 100 times the number of undulator periods.

The three pole factors are defined so that the trajectory is centered about x = 0 and x = 0 with zero dispersion. This wouldn’t be true with the standard two-pole termination, which might cause problems overlapping the laser with the electron beam.

The laser time profile can be specified using the TIME_PROFILE parameter to specify the name of an SDDS file containing the profile. If given, the electric and magnetic fields of the laser are multiplied by the profile P(t). Hence, the laser intensity is multiplied by P2(t). By default t = 0 in the profile is lined up with tin the electron bunch. This can be changed with the TIME_OFFSET parameter. A positive value of TIME_OFFSET moves the laser profile forward in time (toward the head of the bunch).

Explanation of <filename>=<x>+<y> format: Several elements in elegant make use of data from external files to provide input waveforms. The external files are SDDS files, which may have many columns. In order to provide a convenient way to specify both the filename and the columns to use, we frequently employ <filename>=<x>+<y> format for the parameter value. For example, if the parameter value is waveform.sdds=t+A, then it means that columns t and A will be taken from file waveform.sdds. The first column is always the independent variable (e.g., time, position, or frequency), while the second column is the dependent quantity.

LTHINLENS