Fulai, thank you for the question!

In general, GALPROP solves the time-dependent CR propagation equation. However, for most CR studies, the Galaxy is assumed to be in a steady state. In order to derive a steady state solution, GALPROP can be configured to solve the CR transport equation for a long enough period of time. With constant sources and constant losses, the solution of the CR propagation equation asymptotically approaches the steady state as time approaches infinity.

There are two methods of achieving the steady state solution:

1) The constant small time step ("CSS") solution, which makes time steps shorter than the electron energy loss time (~100 years), but makes enough of them to span the highest energy proton diffusion time (~10^9 years).

2) The "accelerated" solution, which starts with a very large time step (~10^9 years) and then gradually reduces the time step down to the smallest time scales (~10^2).

Andy Strong has made a comparison of the two methods in the Explanatory Supplement, Section 11.1

http://galprop.stanford.edu/code.php?option=manualIn order to implement the CSS solution, set, for example,

start_timestep=end_timestep=1e2

timestep_repeat=1e7

timestep_factor=0.99

(

**the values are just an example! the values you need to use depend on the problem you are solving**).

This will make 1e7 time steps, 1e2 years each. timestep_factor may be any number less than 1.

In order to implement the accelerated solution (default in WebRun), set (

**for example**)

start_timestep=1e9

end_timestep=1e2

timestep_repeat=100

timestep_factor=0.5

This will start with the time step equal to 1e9 years, repeat it 100 times, then set reduce the time step by 2 (i.e., multiply by timestep_factor) and repeat it 100 times, reduce it by 2 again, etc., until it is down to the time step equal to 1e2.