7 Conventions
OPALX uses SI units internally. Input attributes that use another convention state it explicitly in their parameter tables.
7.1 Physical units
| Quantity | Input convention |
|---|---|
| Length | \(\mathrm{m}\) |
| Angle | \(\mathrm{rad}\) |
| Time | \(\mathrm{s}\) unless an attribute states otherwise |
| Quadrupole coefficient | \(\mathrm{T\,m^{-1}}\) |
| Multipole coefficient, \(2n\) poles | \(\mathrm{T\,m^{-n+1}}\) |
| Electric voltage | \(\mathrm{MV}\) |
| Electric field strength | \(\mathrm{MV\,m^{-1}}\) |
| Magnetic field strength | \(\mathrm{T}\) in current OPALX field output |
| Frequency | \(\mathrm{MHz}\) |
Charged-particle BEAM.ENERGY |
\(\mathrm{GeV}\) |
Photon BEAM.ENERGY |
\(\mathrm{eV}\), following the CAIN convention |
| Particle mass | \(\mathrm{GeV\,c^{-2}}\) in BEAM.MASS |
| Normalized momentum | \(\beta\gamma\) where explicitly stated |
| Beam current | \(\mathrm{A}\) |
| Particle charge | elementary-charge units |
| Normalized and geometric emittance | \(\mathrm{m\,rad}\) |
The analytic LASER definition uses WAVELENGTH, WAISTX, and WAISTY in meters, PULSEENERGY in joules, and PULSELENGTH in seconds. DIR and STOKES are dimensionless three-vectors.
7.2 Symbols
| Symbol | Definition |
|---|---|
| \(X\), \(Y\) | Ellipse axes in the transverse plane; \(X=Y=R\) for a circular beam. |
| \(R\) | Circular beam radius. |
| \(R^*\) | Effective elliptical radius, \((X+Y)/2\). |
| \(\sigma_x\), \(\sigma_y\), \(\sigma_z\) | RMS beam sizes in the respective coordinates. |
| \(\sigma_r\) | Circular-beam RMS radius, \(\langle r^2\rangle^{1/2}\). |
| \(\beta\), \(\gamma\) | Relativistic velocity and Lorentz factors. |
| \(p_0\) | Reference momentum. Input files commonly expose it as P0. |
| \(I\) | Beam current. |
| \(I_0\) | Species-dependent Alfvén current. |
| \(k_p\) | Generalized beam perveance. |
| \(q\), \(m\) | Particle charge and mass. |
Coordinate frames and transformations are defined in the Physics coordinate-system chapter.
7.3 Multipole conversion
When importing a normalized quadrupole strength \(k_1\) from codes such as Elegant, convert it to the magnetic gradient required by OPALX using the reference rigidity. In the historical convention,
\[ \frac{dB_y}{dx} = \frac{E[\mathrm{GeV}]}{0.29979}\,k_1, \]
with the sign fixed by the coordinate and charge conventions of the source code. A convenient conversion for energy in MeV is
def k1_to_gradient(k1, energy_mev):
return 3.33564095e-3 * energy_mev * k1Always verify the imported sign with a single-particle trajectory before using the result in a lattice study.