Normalization

This code was normalized with plasma normalization with:

$$E'=eE/mc\omega; B'=eB/mc\omega; x' = kx; t' = \omega t; v' = \beta = v /c;$$

$$p'=p/m_ec; E'=E/m_ec^2; M' = M / m_e;$$

$$\nabla' = 1/k \nabla, \partial/\partial t' = 1/\omega \partial/\partial t;$$

$$\rho' = \rho /(n_c e); J' = J / (n_c e c);$$

with $n_c = \frac{m\omega^2}{4\pi e^2}$

Now maxwell equation becomes

$$\nabla \cdot E = \rho$$

$$\nabla \cdot B = 0$$

$$\nabla \times E = -\frac{\partial B}{\partial t}$$

$$\nabla \times B = \frac{\partial E}{\partial t} + J$$

$$\partial_t \rho + \nabla \cdot J = 0$$

Assuming we are using a new laser with frequency $\omega' = n \omega_0$, which means

$$\frac{\omega'^2}{\omega^2} = \frac{n_c'}{n_c}$$

Thus the new $n_c'$ will be:

$$n_c' = \omega' \frac{n_c}{\omega^2} = \omega'^2 \frac{m}{4\pi e^2}$$

This means, when you use new frequency $\omega' \neq 1$, then, the critical density will be $\omega'^2$

It's better to use $\omega = 1$, then you only need to worry about the $n$. Then the intensity of field is still a standard normalization.