Electron beam
Electron beam parameters for klystrons.
constants:e me epsilon0 mu0
Parameters
beam voltage
V
\(kV\)
beam current
I
\(A\)
beam radius
`r_b`
\(mm\)
cavity radius
`r_c`
\(mm\)
Output
electron velocity \(u_0\)
\(\frac{1}{2}mu_0^2=eV_b\)
electron density \(\rho\)
\(I=\frac{Q}{t}=\frac{\rho\pi b^2l}{\frac{l}{u_0}}\)
current density J
\(J=I/\pi b^2\)
radial electric field Er(b)
\(\oint E_r \cdot ds=-\frac{\rho\pi r^2 l}{\epsilon_0}\)
potential V(b)
\(V(b)-V(a)=\int_a^b dV(r)=-\int_a^b E_r\cdot dr\)
potential V(0)
\(V(0)-V(a)=\int_a^0 dV(r)=-\int_a^0 E_r\cdot dr\)
Magnet field B(b)
\(\oint H \cdot dl=I, B=\mu H\)