7.33 insert_sceffects

• type: setup command.
• function: set up for transverse space charge calculation by inserting special elements into the lattice.
• sequence: must precede run_setup.
• Notes:
  • This command is intended only for simulation of space-charge kicks in rings.
  • If multiple commands are given, the calculation settings from the last command are used for all insertion points.
• Command syntax, including use of equations and subcommands, is discussed in 7.2.

• name — Possibily wild-card containing string specifying the name of the elements after which to insert the space charge kick element.
• type — Possibily wild-card containing string specifying the type of the elements after which to insert the space charge kick element.
• exclude — Possibily wild-card containing string specifying the name of elements to be excluded from the insertion of the space charge kick element.
• disable — If nonzero, the command is ignored.
• clear — If nonzero, all prior space charge insertions are deleted.
• element_prefix — Name under which the space charge kick will appear in the beamline.
• skip — If nonzero, the given number of insertion locations are skipped. If zero, only one space charge kick is inserted at the end of beamline.
• vertical, horizontal, longitudinal — If non-zero, then space charge is included in the plane in question. Longituidinal is not, in fact, supported at present; the LSCDRIFT element can be used for this.
• nonlinear — If zero, use linear approximation, otherwise not. See details below.
• uniform_distribution — Used for bi-Gaussian distributed beam (coasting beam), i.e., beam that is uniform in z but gaussian in x and y.
• verbosity — Larger non-zero values request greater amounts of detail in printouts.
• averaging_factor — For nonlinear space charge mode only, this parameter allows applying an infinite-impulse-response (IIR) filter to the turn-by-turn beam size data in order to reduce the effects of noise. A value of 1 means that only data from the present turn is used, while values approaching 0 will tend to use the initial beam sizes only. In more detail, the effective rms beam size used in the calculation of the kicks for the i^th turn is

  (6)

  where σ_i is the actual rms beam size. N.B.: strictly speaking, simulations performed with f≠1 are invalid, as the effect of strong space charge could be understated. However, judicious use of this parameter may allow valid simulations with fewer particles. The user should vary the parameter to ensure that results are insenstive to the value.

• slice_duration — The length, in seconds, of slices into which to divide the beam for computations. Space charge kicks are computed slice-by-slice assuming each slice is independent and has a uniform longitudinal distribution.
• slice_threshold — The minimum number of particles in a slice, below which slice-based computations of the centroids and beam sizes will replaced with whole-beam values. If this value is too small, numerical instabilities may be encountered.
• slice_interpolation — If non-zero, the charge, centroid, and beam size values used to compute the kicks are interpolated linearly within each slice.

Important notes:

• By default skip=0, which results in only one SCMULT element at the end of the beamline, regardless of whether values are given for the name or type fields.
• This element is not designed for space charge calculations in guns or linacs. It is only intended for simulating space charge in rings.
• This command can not work with concatenation-based matrix tracking.
• Some users use matched_to_cell in the bunched_beam command. This will erase SCMULT assignments along the beamline. In this case, issue another twiss_output command just before tracking.

This element simulates transverse space charge (SC) kicks using K.Y. Ng’s formula [24].

The linear SC force is given by:

(7)

where K_sc = , L is the integrating length, σ_x,y,z are rms beam size.

The non-linear SC force is given by:

(8)

where w(z) is the complex error function

(9)

These expressions appear to diverge when σ_x = σ_y. In fact, this is not true, because the expressions inside the square brackets will provide zero too at σ_x = σ_y to cancel the poles outside. In our code, we calculate this equation at 1.01σ_x and 0.99σ_x, and average the total effects.