How to use 1D FDTD to simulate EMP attenuation in space?

The following code is a 1D FDTD pulse simulation. I want to simulate EMP attenuation in space and understand how far it can propagate without gain. However, I am not sure what attenuation factors need to be considered in a space environment.

And how can I incorporate the attenuation calculation into the following code?

clear;
ke = 100;
% Position of the source
ks = 1;
% Number of time steps
nsteps = 1000;
% Cell size and time stepping
c0 = 3.e8;
dx = 0.01;				
dt = dx / (2 * c0); 
% Constants
cc = c0 * dt / dx;
% Initialize vectors
ex = zeros(1, ke);
hy = zeros(1, ke);
% Gaussian pulse
t0 = 20;
spread = 8;
% Gaussian signal
for t = 1:nsteps
    time(t) = t;
    ex_source(t) = exp(- 0.5 * ((t - t0) / spread) ^ 2);
end
plot(time,ex_source)


% Create a directory to save frames
outputDir = 'frames';
if ~exist(outputDir, 'dir')
    mkdir(outputDir);
end

for t = 1:nsteps
    % E field loop
    for k = 2:ke - 1
        ex(k) = ex(k) + cc * (hy(k - 1) - hy(k));
    end

    % Source
    ex(ks) = exp(- 0.5 * ((t - t0) / spread) ^ 2);
    % H field loop
    for k = 1:ke - 1
        hy(k) = hy(k) + cc * (ex(k) - ex(k + 1));
    end

    plot(ex); axis([1 ke -2 2]);
    % plot(hy); axis([1 ke -2 2]);

    % Save each frame as an image file
    saveas(gcf, fullfile(outputDir, sprintf('frame_%04d.png', t)));
end

Answer 1

[Rahul]

Hi hui,

I understand you are working on simulating EMP propagation in MATLAB using a 1D FDTD (Finite-Difference Time-Domain) setup, where you are facing issues in incorporating attenuation to see how far the pulse can travel without external amplification.

In case you are looking to incorporate attenuation to model EMP propagation in space, one approach to do this in the current 1D setup could be by applying an attenuation factor directly to the electric field 'ex' as it propagates.

While space is idealized as a lossless vacuum in FDTD, you can introduce a decay manually to simulate signal weakening over distance. Here’s how you can modify your code to include the same:

% Set up an attenuation factor based on distance
distance = (1:ke) * dx;
attenuation_factor = 1 ./ distance;  % Or 1 ./ distance.^2 for faster decay
attenuation_factor(1) = 1;  % Prevent division by zero at source
for t = 1:nsteps
    % E field update   
    for k = 2:ke - 1
        ex(k) = ex(k) + cc * (hy(k - 1) - hy(k));
        ex(k) = ex(k) * attenuation_factor(k);  
        % Apply attenuation 
    end   
    % Source injection
    ex(ks) = exp(-0.5 * ((t - t0) / spread)^2);  
    % H field update  
    for k = 1:ke - 1
        hy(k) = hy(k) + cc * (ex(k) - ex(k + 1)); 
    end
    % Optional visualization
    plot(ex); axis([1 ke -2 2]);
    saveas(gcf, fullfile(outputDir, sprintf('frame_%04d.png', t)));
end

This causes the pulse amplitude to decrease with distance from the source, simulating basic range-based attenuation in the current 1D setup.

You can tweak the form of 'attenuation_factor' based on how strongly you want the signal to decay across the grid.

For more information on performing various operations on arrays and matrices in MATLAB, you can refer to the documentation link mentioned below:

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

Cheers!