OSIRIS units
Code Units and Normalization
OSIRIS simulations are done in normalized units. This has 2 distinct advantages: i) multiplication by several constants (like $m_e$, $e$, and $c$, for example) is avoided, resulting in a significant performance increase and ii) by expressing the simulation quantities in terms of the fundamental plasma quantities the results are general and not bound to some specific units we may choose.
In our case, we chose to normalize our quantities to $\omega_p$, $m_e$, $c$, and $e$, the electron plasma frequency, the electron rest mass, the speed of light, and the electron charge, respectively.
Simulation Units
| Quantity | Conversion |
|---|---|
| Time | $t’ = t \times \omega_p$ |
| Frequency | $\omega’ = \omega / \omega_p$ |
| Position | $\mathbf{x}’ = \frac{\omega_p}{c} \mathbf{x}$ |
| Momenta | $\mathbf{u’} = \frac{\mathbf{p}}{m_{sp} c} = \frac{\mathbf{\gamma v}}{c} = \frac{\mathbf{u}} {c}$ |
| Electric field | $\mathbf{E’} = e \frac{c / \omega_p}{m_e c^2} \mathbf{E}$ |
| Magnetic field | $\mathbf{B’} = e \frac{c / \omega_p}{m_e c^2} \mathbf{B}$ |
Where $m_{sp}$ is the mass of the species being considered. In this situation, the relativistic Lorentz factor $\gamma$ can be calculated as $\gamma = (1 + u’^2)^{1/2}$. Density will be normalized to the plasma density that yields the reference plasma frequency i.e. a plasma with a density of 1 in simulation units will have a plasma frequency $\omega_p$.
Laboratory Units
In practical units the physical quantities will relate to simulation quantities as:
| Quantity | Conversion |
|---|---|
| Position | $\mathbf{x} [\mathrm{cm}]= 2.998 \times 10^{10}\, \mathbf{x}’ \, \omega_p ^{-1} [\mathrm{rad / s}]$ |
| $\mathbf{x} [\mathrm{cm}]= 0.532 \times 10^{6}\, \mathbf{x}’ \, n_0^{-1/2} [\mathrm{cm} ^{-3}]$ | |
| Momenta | $\mathbf{p} [\mathrm{g \, cm / s}]= 2.731 \times 10^{-17}\, \frac{m_{sp}}{m_e} \mathbf{u}’$ |
| Electric field | $\mathbf{E} [\mathrm{GV/cm}] = 1.704 \times 10 ^{-14}\, \mathbf{E’} \, \omega_p [\mathrm{rad / s}]$ |
| $\mathbf{E} [\mathrm{GV/cm}] = 9.613 \times 10 ^{-10}\, \mathbf{E’} \, n_0 ^{1/2} [\mathrm{cm} ^{-3}]$ | |
| Magnetic Field | $\mathbf{B} [\mathrm{gauss}] = 5.681 \times 10 ^{-8}\, \mathbf{B’} \, \omega_p [\mathrm{rad / s}]$ |
| $\mathbf{B} [\mathrm{gauss}] = 3.204 \times 10 ^{-3}\, \mathbf{B’} \, n_0 ^{1/2} [\mathrm{cm} ^{-3}]$ |
Also note that for high kinetic energies, $p \gg m_{sp} c$, the relativistic energy is reduced to $W \simeq m_{sp} c^2 p’$, where $m_{sp} c^2$ is the rest mass energy for the species being considered.
Normalizing to another frequency
Alternatively, the user may choose another frequency such as the laser frequency, $\omega_0$ as the norm. In this case, just replace $\omega_p$ with $\omega_0$ in the above formulae. A simulation plasma density of 1.0 will correspond to the critical density.