Homework 5¶

due 10/17/2018 at 11:59pm

Problem 1¶

Using the binary collision function of HW03, plot the distribution function of 25 protons and 25 electrons locked inside a box of size 2mmx2mm, randomly distributed, for each of the following initial parameters:

1. $v_i=v_e=1000\,m/s$, all with random directions
2. $v_i=v_e/10=100\,m/s$, all with random directions

Note that we will suppose that there is no displacement along the Z-direction and that all particles reflect back inside the box when they hit the walls of the box.

Problem 2¶

Compute numerically the total number of particles for an infinitely large box where the particles inside have the following distribution function: $$f(\vec x,\vec v,t)=A_0\exp\Big(-\frac{x^2+y^2+z^2}{L_0^2}\Big)\exp\Big(-\frac{v_x^2+v_y^2+v_z^2}{v_0^2}\Big)$$ where $A_0=200\,particles/m^6s^3$, $L_0=2 m$ and $v_0=0.1\,m/s$. Compare the numerical answer with the analytical answer using the fact that $$\int_{-\infty}^{+\infty}\exp(-x^2)dx=\sqrt{\pi}.$$

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