Motion in electric and magnetic fields
I spent about an hour writing code that computes the trajectory of a particle in constant electric or constant magnetic fields, the first of which is available here and the second here. I apologize for the incomplete code that computes the motion of a particle in a magnetic field, I am still trying to figure out how to plot two different data sets with different x and y ranges on the same figure. There are convenience functions to duplicate the x axis or the y axis but not both, which is what I'm looking for.
Either way, the codes are still rough, in the sense that I used euler's method to do solve the differential equation that governs the motion, which is known to be errenous. I will have to implement one of the Runge-Kutta methods if I want better accuracy in position and velocity measurements. Moving further, it's a bit harder to solve the case of a particle in a magnetic field as there are cross terms i.e the force in the x direction depends on the velocity in the y direction and vice versa, assuming the magnetic field to be in the z direction! Again, I am not updating the force mid iteration, which is probably why it is giving my such erroneous results. If you don't understand, the trajectory should be a perfect circle and not a flattened spiral! I'll have to read up on this, maybe I'm not even on the right track.
Otherwise, the day was spent writing notes on ultrafast lasers and making small visualizations there as well, related to how a zeroth and first order phase factor would influence a pulse shape, that can be found here.
And one of these days, I'll have to sit down and add the relevant theory to the ipynb files. I've been thinking about this for over a month now and I've written it down multiple times in my to-do list but I just don't seem to be able to bring myself to doing it. Sigh...
Either way, the codes are still rough, in the sense that I used euler's method to do solve the differential equation that governs the motion, which is known to be errenous. I will have to implement one of the Runge-Kutta methods if I want better accuracy in position and velocity measurements. Moving further, it's a bit harder to solve the case of a particle in a magnetic field as there are cross terms i.e the force in the x direction depends on the velocity in the y direction and vice versa, assuming the magnetic field to be in the z direction! Again, I am not updating the force mid iteration, which is probably why it is giving my such erroneous results. If you don't understand, the trajectory should be a perfect circle and not a flattened spiral! I'll have to read up on this, maybe I'm not even on the right track.
Otherwise, the day was spent writing notes on ultrafast lasers and making small visualizations there as well, related to how a zeroth and first order phase factor would influence a pulse shape, that can be found here.
And one of these days, I'll have to sit down and add the relevant theory to the ipynb files. I've been thinking about this for over a month now and I've written it down multiple times in my to-do list but I just don't seem to be able to bring myself to doing it. Sigh...
