# growth¶

Measure the growth rate in the time trace of a quantity, assuming that it is a squared quantity (e.g. $$\phi^2$$, $$|\mathbf{E}|^2$$). If one applies this to a non-squared quantity then the growth-rate would be off by a factor of two.

Command Docstrings

The command works by fitting $$A e^(2\gamma t)$$ to the data and returning $$\gamma$$.

## Command line¶

Command help
 \$ pgkyl growth --help
Usage: pgkyl growth [OPTIONS]

Attempts to compute growth rate (i.e. fit e^(2x)) from DynVector data,
typically an integrated quantity like electric or magnetic field energy.

Options:
-u, --use TEXT                Specify a 'tag' to apply to (default all
tags).

-g, --guess <FLOAT FLOAT>...  Specify initial guess
-p, --plot                    Plot the data and fit
--minn INTEGER                Set minimal number of points to fit
--maxn INTEGER                Set maximal number of points to fit
-i, --instantaneous           Plot instantaneous growth rate vs time
-h, --help                    Show this message and exit.


The two tream instability simulation produces a field energy time trace that can be plotted with

pgkyl two-stream_fieldEnergy.bp sel -c0 pl --logy We have selected the $$E_x$$ component because all other field components are essentially zero. We can then measure the growth rate in the field energy with the following command

pgkyl two-stream_fieldEnergy.bp sel -c0 growth


Such command produces the output below

fitGrowth: fitting region 100 -> 7916
gamma = +3.79836e-01 (current +5.814e-02 R^2=7.407e-01)    99.99% done [========= ]
gamma = +3.79836e-01


This output indicates that it made the measurement taking into account all the data between the 100th and the 7916th point (if you examine the file two-stram_fieldEnergy.bp you’d find that it has 7916 data points), and arrived at the growth rate $$\gamma=0.379836$$, the the $$R^2$$ of the fit being 0.7407.

The growth command also allows for specifying a window in which to perform the measurement via the --minn and --maxn flags. We could then limit the window between the 2000th and the 6000th point with

pgkyl two-stream_fieldEnergy.bp sel -c0 growth --minn 2000 --maxn 6000


and the output would be

fitGrowth: fitting region 2000 -> 6000
gamma = +3.79836e-01 (current +4.322e-01 R^2=9.998e-01)    99.98% done [========= ]
gamma = +3.79836e-01


giving the same result obtained above.

There is also an option for specifying a guess to $$A$$ and $$\gamma$$ in the fit, via the -g flag:

pgkyl two-stream_fieldEnergy.bp sel -c0 growth --minn 2000 --maxn 6000 -g 1. 0.36

fitGrowth: fitting region 2000 -> 6000
gamma = +3.79836e-01 (current +4.322e-01 R^2=9.998e-01)    99.98% done [========= ]
gamma = +3.79836e-01