Element

This module introduces the various beamline elements supported in PASS.

CrossingAngle, CrabCavity and FloatWaister are described in Beam-Beam Interaction (BeamBeam).

• Element errors
  • Field errors
  • Alignment errors
• Magnet ramping
  • Strength convention
  • Current strength state
  • Configuration
  • TFS format
  • Entry sampling and frozen-element tracking
  • Evaluation and diagnostics
  • Creating files
• Marker
  • Interface Parameters
  • Usage Examples
  • Physical Description
  • Application Scenarios
• Drift
  • Interface Parameters
  • Usage Examples
  • Physical Derivation
  • Application Scenarios
  • Internal Space Charge
• Dipole (SBend)
  • Parameter List
  • Usage Examples
  • Small-angle numerical stability
  • Coordinate Convention
  • Overall Tracking Flow
  • Body: DKD-exact Model
  • Body model selection
  • Entrance Edge: YRotation
  • Entrance Edge: Fringe Field
  • Entrance Edge: Wedge (Edge Angle)
  • Edge Angle Sign Convention
  • References
  • Internal Space Charge
• Quadrupole
  • Interface Parameters
  • Physical entrance and exit fringe maps
  • Usage Examples
  • Coordinate Convention
  • Quadrupole Field and Normalized Strength
  • Overall Tracking Flow
  • Physical Derivation
  • Chromaticity Effects
  • Tracking Model Comparison
  • Application Scenarios
  • References
  • Internal Space Charge
• Sextupole
  • Interface Parameters
  • Usage Examples
  • Coordinate Convention
  • Sextupole Field and Normalized Strength
  • Overall Tracking Flow
  • Physical Derivation
  • Chromaticity Correction
  • Naturally Included Higher-Order Effects
  • Application Scenarios
  • References
  • Internal Space Charge
• Octupole
  • Interface Parameters
  • Usage Examples
  • Coordinate Convention
  • Octupole Field and Normalized Strength
  • Overall Tracking Flow
  • Physical Derivation
  • Amplitude-Dependent Tune Shift
  • Naturally Included Higher-Order Effects
  • Application Scenarios
  • References
  • Internal Space Charge
• Multipole
  • Interface Parameters
  • Usage Examples
  • Coordinate Convention
  • Multipole Field and Normalized Strength
  • Overall Tracking Flow
  • Physical Derivation
  • Horner Nested Evaluation
  • Exact Drift Map
  • Symplectic Integrators
  • Naturally Included Effects
  • Reference-orbit scope
  • Application Scenarios
  • References
  • Internal Space Charge
• Solenoid
  • Interface Parameters
  • Usage Examples
  • Coordinate Convention
  • Solenoid Field and Normalized Strength
  • Physical Derivation
  • Why the Solenoid Has No Thin Lens Mode
  • Multipole Field Overlay and SKS Integrator
  • Overall Tracking Flow
  • Chromaticity Effects
  • Application Scenarios
  • Internal Space Charge
• ElectronCooler
  • Collision models
  • Python example
  • Element interface
  • Electron reservoir interface
  • Collision equations
  • Transport, timing and smooth fields
  • Diagnostics, component state and IBS
  • References
• Kicker
  • Interface Parameters
  • Turn Window
  • Usage Examples
  • Coordinate Convention
  • Physical Derivation
  • Overall Tracking Flow
  • Exact Drift Map
  • Symplectic Integrators
  • Application Scenarios
  • References
  • Internal Space Charge
• Bump
  • Transport and loss handling
  • Waveform boundaries
• ElSeparator
  • Input parameters
  • Input configuration
  • Length, orientation and time
  • Geometry and voltage
  • Propagation and collisions
  • Drift and approximation limits
• Exciter
  • Parameter List
  • Usage Examples
  • Kick Convention
  • Particle Arrival Time and Excitation Mode
  • Frequency Input Modes
  • Waveform Modes
  • Complete Formulas for Each Mode
  • Kick Application
• ACDipole
  • Physics convention
  • Input interface
  • Excitation operating mode
  • Time tables and phase
  • CPU batch size
  • Fixed-frequency optics example
  • Comparison with MAD-X
• RFCavity
  • Input interface
  • Energy kick and reference update
  • Stable weak kicks
  • Numerical precision
  • Files and synchronous programs
  • Physical scope

Integration precision

The symmetric fourth-order composition uses

\[S_4(h) = S_2(w_1 h) S_2(w_0 h) S_2(w_1 h), \qquad w_1 = \frac{1}{2-2^{1/3}}, \quad w_0 = 1-2w_1.\]

CPU and GPU use the same double-precision composition coefficients. GPU split maps retain double precision for element lengths, substep lengths and accumulated multipole momentum increments, including transport between internal space-charge nodes.

This applies to the split maps of bends, quadrupoles, sextupoles, octupoles, multipoles, kickers and solenoids with superposed multipole fields. A pure uniform solenoid uses its exact uniform-field map. These changes preserve the maps, field normalization and integration order.

Particle Precision still controls the stored six-dimensional coordinates. FP32 therefore denotes storage precision, not exclusively FP32 arithmetic. Remaining intermediate types depend on the element: for example, static RKR bends use binary64 working coordinates, whereas CPU FP32 RKR transport with internal space-charge nodes still rounds its submaps into the live FP32 arrays. CPU/GPU results are not required to be bit-identical. Binary64 step coefficients reduce an avoidable source of error, but do not remove coordinate rounding or integrator truncation error; more slices need not improve FP32 accuracy.