MATLAB [MatLab] Motion of Particle in a spatially varying electromagnetic field

[1Keenan]

I have to simulate the motion of particle in an electromagnetic device which deflects particle using electric and magnetic field.
Those field are arranged in such a way that the electric field is inside the magnetic one. Moreover the electrodes begin at the center of the magnetic field ad their end is a bit outside the coils.
The motion equations are:
1) d^2x(z)/dz^2 = qE/mv^2
2) d^2y(z)/dz^2 = qB/mv

The problem is that MatLab cannot solve second order differential equation, thus I have tried to use the code:

%%Initial drift
rhsE1=@(z,x)[x(2); 0];
[zaE1, xaE1] = ode45(rhsE1, [0 69], [0 0]);
%%inside E field
  E=1;
  rhsE =@(z,x)[x(2); (q/m)*(E/v^2)];
  [zaE, xaE] = ode45(rhsE, [70 130], [0 0]);

For the drift after the field I have calculated the derivative of the trajectory and used it as initial condition for solving the eqaution of motion in the drift sector.
I have also write a similar code for the magnetic field.
The problem is that solving the equation separately doesn't seem to me correct because one solution could be longer than the other...

I have also tryed to solve the lorentz force using the code:

%%%%
f = @(t,y) [y(4:6); (q_over_m).*cross(y(4:6),B)+(q_over_m).*E];
[t,y] = ode23t(f,tspan,y0);
%%%

and some "while" loop like:

%%%
while (z>= length at which B begins ||  z<= length atwhich the electric field begins)
     B=[1 0 0]';
     E = [0 0 0]';
   solve the equation
  z=y(end,3);
end
%%%%%

and so on...

The problem is that the code is incredibly slow and sometimes, I think, it cannot get out of a loop.

I think I have used bad approaches to solve the problem, someone can give me a clue?

 

[1Keenan]

more than 100 people have red this thread but I still get no answer.
Am I doing something wrong?
I really need some help because I am stuck with this simulation.

 

[AIR&SPACE]

Matlab CAN however solve a system of first order diff eqns... if only there was a way to take a system of 2nd order diff eqns to a system of 1st order eqns...

 

[1Keenan]

Matlab CAN however solve a system of first order diff eqns... if only there was a way to take a system of 2nd order diff eqns to a system of 1st order eqns...

Yes, that's what I did with the code:

%%%%
f = @(t,y) [y(4:6); (q_over_m).*cross(y(4:6),B)+(q_over_m).*E];
[t,y] = ode23t(f,tspan,y0);
%%%

It is supposed to solve the system
dx/dt=v_x
dy/dt=v_y
dz/dt=v_z
dv_x/dt= (Lorentz Force)_x
...

I have found what was wrong in my code, it is able to track a particle all the way long from the source to the detector and inside the field... I hope...
The trajectory seems to be reasonable, I would need someone to double check it for confirmation.
Is there someone available to test the code for me?
I can post it here or send in private, doesn't matter.

 

[1Keenan]

Ok, I have done with the code.
If the moderators want to close this thread for me it is ok.