System of Units

Because the simulation involves inconveniently small values, such as the charge of an electron, Coulombs, or the mass of a Mg ion, kg, numbers were expressed in ``reduced units'' which scale values to easier-to-deal-with magnitudes. Simulation values were expressed in the following system of units:

• 1 mass unit = mass of one ion- this eliminates calculations converting force to acceleration and velocity expressions to kinetic energy, since

  

• 1 length unit = = m=m for traps whose dimensions are on the order of m.
• 1 energy unit = where is the charge of one electron and is the permittivity constant, F/m. This unit of energy simplified calculations involving the Coulomb interaction (see Eq. 5).

All other units- e.g, for expressions of force, velocity, etc.- are derivable from the units above.