particle in magnetic field
The motion of particles in an uniform magnetic. The relativity is taken into consideration.
Parameters
mass
m
\(kg\)
charge
q
\(c\)
magnet
B
\(T\)
Temperature
`T_bot`
\(eV\)
Electric Field
E
\(V/m\)
Electron
Temperature
`KT=1eV`
gamma `gamma`
`m_0 gamma c^2=E_k+m_0 c^2`
magnetic moment `mu`
`mu=E_{k bot}/B={mv_bot^2}/(2B)`
newton speed `v_bot`
`KT_bot=1/2 m_e v_bot^2`
relativity speed `v_bot`
`v=c sqrt(1-1/gamma^2)`
anger frequency `omega_{ce}`
\(\omega _{ce}=\frac{e B}{m_e}\)
frequency `f_{ce}`
\(f_{ce}=\frac{\omega}{2 \pi}\)
larmor radius `r_e`
\(r_e=\frac{v_{\bot}}{\omega_c}\)
period `T_{ce}`
\(T_{ce}=\frac{1}{f}\)
\(E \times B \) drift
\(\frac{E \times B}{B^2} \)
mass ratio
`m_i/m_e`
Ion
speed `v_bot`
`KT_bot=1/2 m_i v_bot^2`
anger frequency `omega_{ci}`
`omega_{ci}={q B}/m_i`
cyclotron frequency `f_{ci}`
`f_{ci}=omega_{ci}/{2pi}`
lamor radius `r_i`
`r_i=v_bot/omega_{ci}`
period `T_{ci}`
`T_{ci}=1/f_{ci}`