# 3D Plot of particle trajectory in E and B field

66 views (last 30 days)
Lujain Almarhabi on 3 Feb 2021
I have the following code that solves Lorents equation using Boris method time integrator and it calculates the gyro radius and frequency asw well. The code works for me now and it provides a 2D plot, however I am trying to plot a 3D plot of the particle trajectory. So an example would be like this:
Do you have sugesstions to do this in MATLAB? Thanks
Code:
%HW1: Problem 2: Boris Solver for 1) E = 0 and B =/ 0 2) E =/0 ande B =/0
%Start setting up constants
dt = 1e-2; % time step
mass = 1.0; % mass of particle
charge = 1.0; % charge of particle
n = 500; % number of time steps
%Initial parameters:
v = [0, 1, 0]; % initial velocity
x = [0, 0, 0]; % initial position
B = [0, 0, 10]; % initial mag. field along z directions
E = [0, 0, 0]; % initial E field, for case 1) E = 0 and B =/ 0
omega = (charge .*B(3)) ./mass;
rL = v(2) ./omega; % try v(2) as well since initial v is the perp velocity to B
fprintf('Cyclotron frequency is %4.2f \n',omega); %Test
X = zeros(n,3); % initialize an array of zeros with size nx3 for positions
V = zeros(n,3);
for time = 1:1:n
t = (charge./mass) .*(B .*0.5 .*dt); %compute the t vector
s = (2 .*t) ./(1+ t.*t); %compute the s vector
% start the Boris algorithm:
v_minus = v + (charge./mass) .*(E .*0.5 .*dt); % First half E acceleration: generally for E =/0 ande B =/0
v_prime = v_minus + cross(v_minus,t); % First half B rotation
v_plus = v_minus + cross(v_prime,s); % Second hald B rotation
v = v_plus + (charge./mass) .*(E .*0.5 .*dt); % Second half E acceleration
% Finally update position
x = x + v .*dt;
X(time,:) = x;
V(time,:) = v;
end
% plotting
figure;
plot(X(:,1),X(:,2),'k','Linewidth',2); hold on;
set(gca,'TickLabelInterpreter','Latex','Fontsize',14)
ylabel('$y / d_{\rm p}$','Interpreter','Latex','Fontsize',14);
xlabel('$x / d_{\rm p}$','Interpreter','Latex','Fontsize',14);

David Goodmanson on 3 Feb 2021
Edited: David Goodmanson on 3 Feb 2021
Hi Lujain,
After setting v = [0 1 1] to provide some initial z velocity,
figure(2)
plot3(X(:,1),X(:,2),X(:,3))
grid on
and note that if you put the mouse cursor inside the window and click on the symbol with the circle enclosing the cube, you can rotate the plot with a click-hold mouse.
Lujain Almarhabi on 3 Feb 2021
Hello David!
Thanks a lot, this does work!