10.48 IONEFFECTS—Simulates ionization of residual gas and interaction with the beam.

Simulates ionization of residual gas and interaction with the beam.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no

Simulates ionization of residual gas and interaction with the beam.

This element provides serial or parallel simulation of the interaction of residual gas ions with the electron beam. It must be used in concert with the ion_effects command, described in 7.34.

Modeling of residual ions has these features:

• s-dependent gas pressure profiles for any number of species.
• Arbitrary ion species, specified by a user-provided file that includes the cross sections.
• User-defined locations for ion generation. Each IONEFFECTS element represents the ions present in a segment of the accelerator. The segments start and end half way between successive IONEFFECTS elements. The segment for the first element starts at the beginning of the ring, and the last element covers the end of the ring. By default, the pressure used is an average over this region. If use_local_pressure = 1, the pressure at the IONEFFECTS element is used.
• Arbitrary fill patterns. Uniform fills can be set up using the bunched_beam command, while custom fills can be set up by generating the beam externally and using the sdds_beam command.
• Multiple ionization of trapped ions. For example, a CO+ ion could multiply ionize into CO++, or dissociate into C+.

Some limitations of the model include:

• Fields from electron bunches are computed based on gaussian parameters, which is a reasonably good approximation.
• By default, fields from ions are computed based on gaussian parameters, which is often a somewhat poor approximation. Alternatively, a bi-gaussian form may be used, which uses a sum of two gaussians. This is a much better approximation to the typical distribution, which often has a hot core and long tails. One can also use a tri-gaussian, bi-lorentzian, or tri-lorentzian fit. For the best accuracy and speed, the Poisson method is recommended.
• Ions move only transversely and exist only outside of magnets.

Performing ion simulations involves the following steps

1. Prepare file describing the ion properties, as described in 7.34. Each ion is generated by either a source gas or source ion.
2. Prepare file giving gas pressure vs s for the source gases described in the ion properties file.
3. Insert IONEFFECTS elements in the lattice. This can be performed using the insert_elements command (described in 7.32), or manually by editing the lattice file.
4. Insert ion_effects command after the run_setup command. See 7.34 for syntax. Note that certain properties of the individual IONEFFECTS elements can override the global settings given by in the ion_effects command.
5. Generate a bunched beam, using either the bunched_beam command or providing an externally-generated beam to the sdds_beam command. Section 6 gives more information about bunched beams in elegant.

For each bunch passage, the IONEFFECTS element does the following:

1. Advance existing ions during bunch gap
2. Eliminate ions that are outside of given boundaries
3. Generate ions
4. Apply kick from beam to ions
5. Apply kick from ions to beam

The line density of ions generated by a single bunch in a single pass is:

(59)

where σ_ion is the ionization cross section, P is the pressure, k_B is the Boltzmann constant, T is the temperature, and N_b is the bunch population.

The resulting macroparticle charge is:

(60)

Here σ_ion has units of Mb, P has units of Torr, k_B = 1.38 × 10^-23 J/K, e is the electron charge, L_eff is the effective length of the ion element (in m), and n_macro is the number of macroparticles generated. The initial ion distribution follows the bunch distribution (assumed to be Gaussian).

The IONEFFECTS element also supports multiple ionization. In the ion_properties file, one can define the SourceName for a given IonName to be another ion. In this case, each macro-ion of type SourceName has a chance of being multiply ionized into type IonName. The calculation is done every multiple_ionization_interval bunch passes. The probability of multiple ionization depends on the cross section and local beam density.

The kick on the ions from the beam is calculated using the Basetti-Erskine formula [52], which assumes the beam is Gaussian in both transverse dimensions. By default, this assumption is also used for the ion distribution. The parameter gaussian_ion_range gives the range (in beam sigma) over which ions are counted, for calculating the ion-beam kicks.

The Gaussian method may be a poor assumption for the ions, in which case the field_calculation_method parameter can be set to bigaussian, which uses a sum of two gaussians. This provides a much better model for the actual distribution, at the expense of a considerable increase in run time. One can also use a trigaussian fit, as well as a bilorentzian or trilorentzian. The ion_bin_divisor and ion_range_multiplier parameters can be used to control the bin size and range, respectively, of the histogram used to approximate the ion charge distribution. The ion_bin_divisor gives the ratio of the rms size of the electron bunch in the plane in question to the bin size.

The ion_range_multiplier parameter is used to determine the range of the histogram. If positive, a rough histogram of the ion distribution (with ten times the desired bin size) is used to estimate the range required to encompass 80% of the ions; half this value is multiplied by the absolute value of ion_range_multiplier to get the half range of the full histogram; a value of 1.5 is is suggested. If zero, the histogram encompasses all of the ions, which may result in a sparse histogram when a few ions have large coordinates. If negative gives the range of the binned coordinates in units of the rms size of the ion distribution.

The ion_histogram_output parameter and related parameters can be used to request output of the ion distribution and the multi-function fit, which is advisable when setting the binning parameters.

For the Poisson method, the number of bins used in each plane is given by ion_poisson_bins. By default, the Poisson equation is solved over the full ion_span, but a smaller region can be defined with the parameter ion_poisson_span.

The change in momentum of an ion due to the bunch passage is:

(61)

where c is the speed of light, N_b is the bunch population, r_e is the classical electron radius (2.82 × 10^-15 m), m_e is the electron mass, γ is the relativistic factor (~ 1 for the ions), σ_x,y are the horizontal and vertical beam sizes, w is the complex error function, and x and y are the distance from the ion to the bunch center.