9.1 Astra conventions

By definition the momentum $\v{p}$ is

$\displaystyle \v{p} = \gamma m_0 c \v{\beta} = \frac{\mathcal{E}}{c} \v{\beta}$

(9.1)

Astra uses another convention, such that the momentum defined in Astra, further written $\v{\tilde{p}}$ , is defined as:

$\displaystyle \v{\tilde{p}}= \frac{\v{p}}{m_0 c} = \gamma \v{\beta}$

(9.2)

As a result of this the calculation of $\gamma$ in Astra is performed by using the following relation ;

$\displaystyle \textsl{\textsc{gamma} } = \left[ \Vert \v{\tilde{p}} \Vert^2 +1\right]^{1/2} = \left[ \gamma \beta^2 +1 \right]^{1/2}$

(9.3)