ParticleBinning units

When using happi to post-process the output from ParticleBinning diagnostics, the raw data is converted to more convenient units.

In a first step, happi divides the raw data in each bin by the size of the bin. For instance, if the axes of the diagnostic are x and ekin, the raw data is divided by a bin size that has units \(L_r K_r\).

A second, more subtle conversion is done by happi. The raw quantity stored in the output file has the units of the deposited_quantity. Let us take the most common example: deposited_quantity is a sum of macro-particle weights. As those weights are not in units of density, but of density multiplied by hypervolume, the raw data is in units of \(N_r L_r^D\), where \(D\) is the dimension of the simulation. The correction applied by happi is to divides the data by an hypervolume. The choice of this hypervolume depends on the axes of the diagnostic: for each direction x, y or z, if this direction was not already accounted for in the first step, then divide by the length of the box in that direction.

To be clearer, let us take an example of a 3D simulation with a ParticleBinning diagnostic that has axes x and ekin, and deposited_quantity="weight". Happi will first divide the raw data by the bin size, which can be written \(\Delta x \Delta K\). Then, it divides by the hypervolume, which is \(L_y L_z\) (the length of the box along \(x\) is already accounted for when dividing by the bin size). Finally, the units of the results will be \(N_r L_r^3/(L_r K_r L_r^2) = N_r/K_r\): a density per unit energy.