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 $(n_{0b}\ge n_0)$, 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.

在平板几何中发展了通过等离子通道传播的相对论电子束的威贝尔不稳定性的非局部理论。对于束密度大于等离子体密度的情况$（{ñ}_{0b}\ge {ñ}_0）$，光点大小有限的束将等离子电子推出束区域，并向外部区域的等离子电子赋予返回速度。内部区域束电子与外部区域等离子体电子之间的相对漂移以与束的光斑尺寸相当的横向标度长度来驱动电磁扰动。增长率随着平行波数增加而趋于饱和。对于典型参数，$v_{Øb}/C=0.9$， $v_0/C=0.3$， ${\omega }_{pb}/{\omega }_p=\mathrm{1个}，1.20，0.5，0.75，\mathrm{一种}{\omega }_p/C=3$，不稳定性的增长速率获得的值可与完全和部分电子抽空的等离子体通道中的等离子体频率的一部分相媲美。