• ## Matlab终于出了像样的控制界面，Labview， 就问你怕不怕！？

Let’s assume that the reader has a basic knowledge of classical and relativistic mechanics.
Consier a particle of mass m and speed v. If c is the speed of light, it is customary to define a normalized velocity $\beta$ as $\beta =v/c$, and a relativistic mass factor $\gamma$, defined as $\gamma=1/\sqrt(1-\beta^2)$.

Some other important definitions include the relativistic momentum of a particle, $p=\gamma mv$, the kinetic energy, $W=(\gamma-1)mc^2$, the rest energy, $mc^2$, and the total energy, $U=W+mc^2=\gamma mc^2$. The nonrelativistic limit applied when $\beta <<1$.

It is often convenient to convert between velocity, energy, and momentum, and the following relationship are helpful. The conversion from velocity $\beta$ to kinetic energy W is
$\gamma=1/\sqrt(1-\beta^2), W=(\gamma-1)mc^2$

The inverse conversion is
$\gamma =(W+mc^2)/mc^2, \beta=\sqrt(1-1/\gamma^2)$

The following relationships between small differences are sometimes useful:
$\delta\gamma=\gamma^3\beta\delta\beta, \delta\gamma=\beta\delta(\beta\gamma), \delta W=mc^2\delta\gamma,\delta p=mc\delta(\beta\gamma)$.

Particle dynamics is obtained from Newton’s law relating the force and the rate of change of momentum:
$F=dp/dt=md(\gamma v)/dt$
For a particle of charge q in an electromagnetic ﬁeld, the Lorentz force on particle with charge q and velocity v in an electric ﬁeld E and a magnetic ﬁeld B, is given by
$F=q(E+v*B)$

From book of RF linear accelerators, second edition.

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Dr. Lu