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

1. Feb 6, 2012

### 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:

Code (Text):

%%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:
Code (Text):

%%%%
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:

Code (Text):

%%%
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?

2. Feb 6, 2012

### 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.

3. Feb 6, 2012

### 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...

4. Feb 6, 2012

### 1Keenan

Yes, that's what I did with the code:
Code (Text):

%%%%
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=vx
dy/dt=vy
dz/dt=vz
dvx/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.

5. Feb 7, 2012

### 1Keenan

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