Weibel instability of a relativistic electron beam in a plasma channel

A nonlocal theory of Weibel instability of a relativistic electron beam, propagating through a plasma channel, is developed in the slab geometry. For beam density greater than the plasma density (n(0b) >= n(0)), the beam of finite spot size pushes the plasma electrons out of the beam region and imparts return velocity to plasma electrons in the outer region. The relative drift between the inner region beam electrons and outer region plasma electrons drives the electromagnetic perturbation with transverse scale length comparable to the spot size of the beam. The growth rate increases with the parallel wave number and tends to saturate. For typical parameters, v(ob)/c = 0.9, v(0)/c = 0.3, omega(pb)/omega(p) = 1, 1.20, 0.5, 0.75, a omega(p)/c = 3, the growth rate of the instability acquires values comparable to a fraction of the plasma frequency in both fully and partially electron evacuated plasma channel.