Setting Units for Constants And Particle Functions using @APCdef

@APCdef Description

@APCdef must be called during package initialization. It sets the units for physical constants, species mass, and charge. The macro also defines physical constants in the appropriate units and creates getter functions for species mass and charge with appropriate units and data. See the Species page for more details. Note @APCdef can only be called once.

Users can choose their preferred units for mass, length, time, energy, and charge using predefined unit systems: ACCELERATOR (default), MKS, or CGS.

Users can also specify whether constants should be of type Float64 (default), Unitful, or Dynamic Quantities for easier unit calculations.

All constants are stored in a named tuple, whose name can be customized (defaults to APC). For example, the default name for the speed of light is APC.C_LIGHT.

@APCdef Syntax

@APCdef(name = APC, unitsystem = ACCELERATOR, unittype = Float)

Keyword Parameters

• name specifies the named tuple that stores the constants (default: APC).
• unitsystem sets the unit system for constants: ACCELERATOR (default), MKS, or CGS.
• unittype sets the constant type: Float (default), Unitful, or DynamicQuantities.

This also determines the return type of both the named tuple and the massof() and chargeof() functions. See the DynamicQuantities.jl documentation for a discussion of the difference between how Unitful and DynamicQuatities handle units. Note: setting the unit type to DynamicQuantities will return quantities only in SI units.

Unit Systems

• ACCELERATOR units:
  • mass: eV/c^2
  • length: m
  • time: s
  • energy: eV
  • charge: elementary charge
• MKS units:
  • mass: kg
  • length: m
  • time: s
  • energy: J
  • charge: C
• CGS units:
  • mass: g
  • length: cm
  • time: s
  • energy: J
  • charge: C
• Users can also define their own units by creating a tuple of Unitful units.
  • The tuple must be using the types in Unitful
  • The tuple must have 5 elements
  • The elements must be ordered in “mass unit”, “length unit”, “time unit”, “energy unit”, and “charge unit”.

Example

julia> @APCdef  # Sets unit system to ACCELERATOR (default). define constants with type Float64.

julia> APC.C_LIGHT  # Access the constant within the named tuple `APC`.
2.99792458e8        # Now the constant is defined with units m/s and type Float64.

Unitful

Unitful.jl is a powerful package for managing physical units. This package uses Unitful internally to store constants.

Units

Unitful uses the macro @u_str to create units.

julia> kg = u"kg"

The variable kg represents the unit kilogram.

Creating constants with units is straightforward—simply write the number before the unit.

julia> M = 1u"kg"

Now M represents 1 kilogram.

Conversion to Float

To convert a Unitful object to Float64, access the .val field.

julia> a = 1.5u"kg"
julia> a.val
1.5

Unit Conversions

Unitful provides a convenient way to create new units with expressions. You can also add prefixes directly.

julia> m = 0.511u"MeV/c^2"

To convert between units, use the uconvert() function with the target unit as the first parameter and the variable as the second.

julia> uconvert(u"kg",m)
9.109402419518556e-31 kg

@APCdef returning Unitful type

To use Unitful-typed constants, set unittype to Unitful.

julia> @APCdef unittype = Unitful 

julia> APC.C_LIGHT 
2.99792458e8 m s⁻¹ # Now the constant is a Unitful quantity.

Package-specific Unitful Units

AtomicAndPhysicalConstants defines three custom units not found in the Unitful package. Users can access these units with the @u_str macro, just like standard Unitful units.

• amu: It represents the atomic mass unit.
• e: It represents the elementary charge.
• h_bar: It represents the reduced Planck's constant. It is used as the unit for spin.

@APCdef returning DynamicQuantities.jl type

DynamicQuantities.jl is another popular package for managing units. We also support returning constants in DynamicQuantities type.

julia> @APCdef unittype = DynamicQuantities

julia> APC.C_LIGHT 
2.99792458e8 m s⁻¹ # Now the constant is a DynamicQuantities quantity.

Note: setting the unit type to DynamicQuantities will return quantities only in SI units.