particle keV to velocity
The energy of the particles is always given in keV. Sometimes the speed and the parameters from the relativity is interesting. This app calculates the speed and the relativity parameters.
constants:c e me mi
mass \(m_0\)
charge
Temperature T
speed ratio \(\alpha=v_{\bot}/v_z\)
Magnetic field \(B_0\)
energy in Joule
1000(keV)e
newtonian velocity
\(E=\frac{1} {2} m_0 v^2\)
lorentz factory
\(\gamma=\frac{1}{\sqrt{1-\frac{v^2} {c^2}}}, mc^2=\gamma m_0 c^2=m_0c^2+E_k\)
relativity mass
\(m=m_0 \gamma\)
relativity velocity
\(v=c \sqrt{1-\frac{1} {\gamma^2}}\)
speed ratio
\(\beta=\frac{v}{c}\)
momentum
\(p=\gamma m_0 v\)
dimensionless speed
\(u=\gamma v/c=\gamma \beta\,\,\, p=\gamma m_0 v=m_0 c u\)
maximum efficiency
\(\eta_{max}=\frac{\alpha^2}{1+\alpha^2}\)
z-axial speed
\(v_z=\frac{v}{\sqrt{1+\alpha^2}}\)
traverse speed
\(v_{\bot}=\alpha v_z\)
cyclotron anguar frequency
\(\omega_c=\frac{q B_0}{m_0 \gamma}=\frac{\Omega_0}{\gamma} \)
cyclotron frequency
\(f_c=\frac{\omega_c}{2 \pi}\)
cyclotron frequency newton
\(f_0=\frac{1}{2 \pi}\frac{q B_0}{m_0} \)
gyration radius
\(r_L=\frac{v_{\bot}}{\omega_c}=\frac{v_{\bot}}{\Omega_0}\gamma\)
speed vs Ek
`beta=sqrt(1-1/(1+x/(m_0c^2))^2)`