Ideal Crab Cavity
Four-dimensional simulation of collision geometry, crab crossing, bunch-length asymmetry and the hourglass effect.
Scientific objective
ILUMI4D describes a bunch crossing as a four-dimensional interaction process. The two colliding bunches are represented by three-dimensional particle-density distributions evolving in time. Their overlap determines not only the integrated luminosity produced during the crossing, but also the spatial and temporal distribution of the resulting interaction vertices.
The objective of Study 01 is to investigate this four-dimensional collision structure for an ideal crab-crossing configuration and to determine how the geometry of the crossing is reflected in the position and time of the interaction vertices.
Physical configuration
Two bunches approach the interaction point with a finite crossing angle. Crab rotation changes the orientation of the bunch distributions and modifies their effective collision geometry.
Study 01 starts from an idealized configuration in which the transverse beam size is independent of the longitudinal position. This provides a well-defined reference case before introducing the hourglass effect.
The study subsequently compares symmetric and asymmetric crab configurations, together with different combinations of bunch lengths. This allows effects arising from the crossing geometry to be separated from effects associated with longitudinal bunch-length asymmetry.
Collision geometry
Study of the spatial overlap of the two bunches during the crossing process, including the effects of the crossing angle and crab rotation.
Space-time structure
Investigation of the relationship between collision time and vertex position, including the motion of the mean interaction point through the detector.
Bunch-length asymmetry
Comparison of symmetric and asymmetric bunch-length configurations and their influence on the longitudinal interaction region.
Hourglass effect
Comparison of the idealized collision geometry with configurations in which the transverse beam size varies along the interaction region.
Reference configuration
The following parameters define the baseline configuration used as the reference for Study 01. Subsequent simulation cases modify selected parameters in order to investigate the corresponding physical effects.
Beam parameters
| Parameter | Beam 1 | Beam 2 | Unit / setting |
|---|---|---|---|
| Beam energy | 7000 | 7000 | GeV |
| Normalized emittance, x | 2.1 | 2.1 | µm |
| Normalized emittance, y | 2.1 | 2.1 | µm |
| βx | 0.1 | 0.1 | m |
| βy | 0.1 | 0.1 | m |
| Bunch length | 1.2 | 1.2 | ns (4σ) |
| Protons per bunch | 0.94 × 1011 | 0.94 × 1011 | protons |
| Crab angle | +250 | +250 | µrad |
Collision and simulation parameters
| Parameter | Value | Unit / setting |
|---|---|---|
| Half crossing angle | 250 | µrad |
| Particles in bunch cloud | 10,000 | simulation particles |
| Interaction cross section | 80.0 | mb |
| Crab cavity | Yes | True |
| Hourglass | No | False |
Selected results
Selected simulation results for the reference configuration with symmetric crab crossing, equal bunch lengths and no hourglass effect.
The selected results summarize the spatial and temporal structure of the interaction region, the motion of the luminous region and the correlation between the central vertex position and the Roman Pot arrival time.
Dynamic 4D visualization
The following animations illustrate the four-dimensional collision process from three complementary views. The evolution of the interaction vertices is shown together with the outgoing protons produced during the simulated bunch crossing.
Crossing-plane view
View in the transverse plane containing the crossing angle. The animation shows the spatial evolution of the interaction region during the bunch crossing.
Side view
View along the direction perpendicular to the crossing plane, showing the longitudinal structure of the interaction region and the motion of the outgoing protons.
Three-dimensional view
Three-dimensional visualization of the simulated bunch crossing, showing the spatial evolution of the interaction region and outgoing protons.
Study structure
The study is organized by physical configuration rather than by individual plots or simulations. This allows different geometries and beam parameters to be compared consistently within the same scientific framework.
Each configuration can contain its own simulations, numerical results, figures and videos. The same structure will be used consistently for subsequent ILUMI4D studies.
Results
The numerical results of Study 01 will be presented here, together with the corresponding figures, parameter sets and four-dimensional visualizations.
Figures and numerical results
This section will contain the main quantitative results obtained from the ILUMI4D simulations, including vertex distributions, luminosity-related observables and space-time correlations.
Four-dimensional visualization
Dynamic visualizations will illustrate the evolution of the collision region and the resulting interaction vertices during the bunch crossing.
Simulation parameters
The relevant beam, crossing-angle, crab-cavity and bunch-length parameters will be documented together with each simulation case.
ILUMI4D
Study 01 is part of the broader ILUMI4D program investigating four-dimensional luminosity and interaction-region phenomena.
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