1Keenan
Feb6-12, 02:32 AM
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?
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?