Beam Width ( \(1 / V_b \) )
The phenomenon of the two-stream instability occurs where plasma flows are moving in opposite directions. This instability arises from the transfer of energy between particles in the plasma and EM wave, leading to the exponential growth of certain wave modes, described by the dispersion relation: \[ 1 = \dfrac{\omega_p^2/2}{(\omega+\omega_D)^2} + \dfrac{\omega_p^2/2}{(\omega-\omega_D)^2}. \] (See blog post for more detail 
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