Unit definitions and conversions.
All physical quantities have both a numerical value and a unit. For the computations we always choose a particular unit so we only need to consider the numerical values as such. The chosen base unit for a particular physical quantity, e.g. length, time, or energy, within this code base is called the native unit. Here, the following native units are used:
Length is expressed in mm.
Time is expressed in [speed-of-light * time] == mm. A consequence of this choice is that the speed-of-light expressed in native units is 1.
Angles are expressed in radian.
Energy, mass, and momentum are all expressed in GeV (consistent with a speed-of-light == 1).
Electric charge is expressed in e, i.e. units of the elementary charge.
The magnetic field is expressed in GeV/(e*mm). The magnetic field connects momentum to length, e.g. in SI units the radius of a charged particle trajectory in a constant magnetic field is given by radius = - (momentum / charge) / magnetic-field
With the chosen magnetic field unit the expression above stays the
same and no additional conversion factors are necessary.
Amount of substance is expressed in mol.
To ensure consistent computations and results the following guidelines must be followed when handling physical quantities with units:
All unqualified numerical values, i.e. without a unit, are assumed to be expressed in the relevant native unit, e.g. mm for lengths or GeV for energy/momentum.
If a variable stores a physical quantity in a specific unit that is not the native unit, clearly mark this in the variable, i.e. double momentum = 100.0; // momentum is stored as native unit GeV
double momentumInMeV = 10.0; // would be 0.01 in native units
All input values must be given as
numerical_value * unit_constantor equivalently using the unit literals as
value_unit. The resulting unqualified numerical value will be automatically converted to the native unit.
To output an unqualified numerical value in the native units as a numerical value in a specific unit divide by the unit constants as
numerical_value / unit_constantor using the unit literals as
value / 1_unit.
Examples: #include “Acts/include/Definitions/Units.hpp” using namespace Acts::UnitLiterals;
// define input values w/ units (via unit constants) double width = 12 * Acts::UnitConstants::mm; double mmuon = 105.7 * Acts::UnitConstants::MeV; // define input values w/ units (via unit user literals) double length = 23_cm; double time = 1214.2_ns; double angle = 123_degree; double momentum = 2.5_TeV; double mass = 511_keV; double velocity = 345_m / 1_s; double bfield = 3.9_T; double density = 1_mol / 1_cm3;
// convert output values (via unit constants)
doube t_in_ns = trackPars.time() / Acts::UnitConstants::ns;
// convert output values (via unit user literals)
double x_in_mm = trackPars.position()[ePos0] / 1_mm;
double p_in_TeV = trackPars.absoluteMomentum() / 1_TeV; A helper script is available in
Core/scripts/print_units_physical_constants.py to validate some of the numerical values.