Simulating Particle Trajectories

This article discusses numerical simulations of particle trajectories in the "silver" permanent magnet.

Description of Code

The general problem of modeling relativistic particle trajectories in electromagnetic fields boils down to solving the following system of six differential equations: [math]\frac{d\vec{x}}{dt}=\vec{v}=\frac{1}{\gamma m_0}\vec{p}[/math] [math]\frac{d\vec{p}}{dt}=q\left(\vec{E}+\frac{1}{\gamma m_0}\vec{p}\times\vec{B}\right)[/math] where [math]\vec{x}\lt \math\gt is the position of the particle, \lt math\gt \vec{p}[/math] is the momentum of the particle, [math]m_0[/math] is the rest energy of the particle, and [math]\gamma[/math] is the usual relativistic factor.

subject to the appropriate boundary conditions.

Results of parameter space scans

"Ideal" orientation of magnet for 5 MeV photons

Pairs produced elsewhere on the beam