Launching a plasma simulation with a trained network

Once the network is trained, we will now launch a plasma oscillation simulation with a trained network.

Plasma oscillation introduction

Plasmas tend to maintain electric charge neutrality at a macroscopic scale at equilibrium. When this macroscopic charge neutrality is changed, Coulomb forces try to restore the macroscopic charge neutrality. Ion motion is ignored since they are way heavier than electrons. Thus, the electron density evolves harmonically.

\[\frac{\partial^2n_e}{\partial t^2}+\omega_p^2 n_e = 0 ~~~~ {where} ~~~~ \omega_p = \sqrt{\frac{n_e e^2}{m_e\varepsilon_0}}\]

For further details about the plasma oscillation, please refer to [Cheng]

Launching plasma simulations

To launch a plasma simulation, we will first go to the folder path/to/plasmanet/CfdSolver/euler/poscill

Reference with linear solver

First, we will launch a plasma simulation with the linear solver. To do so, just modify the 101.yml file. As the linear solver will be used, we will only focus on the first block of the yaml file. First the physical parameters of the simulation are defined:

casename: 'runs/reference_oscillation/'                  # Set the casename

params:
   n_periods: 2.0                   # Number of oscillation periods we want to simulate
   geom: 'xy'
   dt: 1.0e-10                      # Fixed timestep
   nt_oscill: 5000

Then, we specify the initial profiles. We will start with a simple gaussian, but note that two two_gaussians or sinusoidal profiles can be used as well. The init_func argument can either be a string, in this case, the init_args argument needs to be declared, or instead it can be a list containing a string and a list with the arguments:

init:
   n_back: 1.0e+16
   n_pert: 1.0e+11
   init_func: ['gaussian', [0.5e-2, 0.5e-2, 1.0e-3, 1.0e-3]]      # Second argument corresponds to the gaussian center

init:
   n_back: 1.0e+16
   n_pert: 1.0e+11
   func: 'two_gaussians'                           # Choose between 'gaussian', 'two_gaussians', 'sin2D', ...
   args: [0.4e-2, 0.5e-2, 1.0e-3, 1.0e-3,          # Coordinates of the center of the gaussians
             0.6e-2, 0.5e-2, 1.0e-3, 1.0e-3]

Concerning the Poisson equation and the simulation mesh, we will define the spatial discretization and the resolution type:

poisson:
   type: 'lin_system'            # Choose between network, lin_system, analytical and hybrid
   mat: 'cart_dirichlet'         # Plasma oscillation for now only in cartesian coordinates with D BC
   nmax_fourier: 10              # For the analytical solution

mesh:
   xmin: 0
   ymin: 0
   xmax: 1.0e-2                  # Physical domain length in x direction
   ymax: 1.0e-2                  # Physical domain length in y direction
   nnx: 101                      # Number of points in x direction
   nny: 101                      # Number of points in y direction

BC: 'full_out'                   # Problem boundary conditions

output:
   save: 'plasma_period'         # Save for period intervals
   verbose: True                 # Useful information during inference
   period: 0.1                   # Saving every
   files: 'fig'                  # Saving options
   dl_save: 'no'                 # For training purposes
globals:
   fig: [1.0, 1.5]               # Reference plotting points for final plot
   vars: 'yes'                   # Save global variables

Once the yaml file is configured according to your needs, just perform:

plasma_euler -c 101.yml

Plasma oscillation with a CNN

Analogously, to launch a simulation with the network, just change:

poisson:
   type: 'network'               # Choose between network, lin_system, analytical and hybrid

And then we will focus on the remaining arguments of the config file. Please refer to the training section, as the config file is quite similar, with just several small modifications. Just specify the network used for the plasma simulation at the resume argument:

resume: '/path/to/trained/network/train/RF_study/Unet/5_scales/k_3/RF_200/models/random_8/model_best.pth'

If you don’t have any trained networks, you can use the predefined configuration with the pre-trained network found at path/to/trained/network/model_best.pth.