It is shown that the penetration of an oscillating electric field in a semi-infinite classical plasma obeys the standard exponential attenuation law e^−x/λ_e (besides oscillations), where x is the distance from the wall and λ_e is the extinction length (penetration depth, attenuation length). This solves the problem of various approximations and semi-empirical models of the surface sheath. The penetration depth λ_e is computed here explicitly; it is shown that it is of the order ${\lambda }_e\simeq {[\mid \epsilon \mid /(1-\epsilon )]}^{1/3}{v}_{\mathrm{th}}/\omega$, where ε is the dielectric function, ω is the frequency of the field and $v_{\mathrm{th}}=\sqrt{T/m}$ is the thermal velocity (T being the temperature and m the particle (electron) mass). The result is obtained by including explicitly the contribution of the surface term in the (linearized) Boltzmann (Vlasov) equation for the semi-infinite plasma. A key point in solving the problem is the observation that there exists a uniform (oscillating in time) component of the response electric field, besides the spatially decaying and oscillating component.

结果表明，一个振荡电场的半无限经典等离子体穿透服从标准指数衰减法ë ^{- X / λ _ë}（除了振荡），其中X是从所述壁的距离，并且λ _Ë是消光长度（穿透深度，衰减长度）。这解决了表面护套的各种近似和半经验模型的问题。穿透深度λ _è明确这里计算; 显示它是顺序的${\lambda }_{Ë}\simeq {[\mid \epsilon \mid /（\mathrm{1个}-\epsilon ）]}^{\mathrm{1个}/3}{v}_{日}/\omega$，其中ε是介电函数，ω是磁场频率，$v_{日}=\sqrt{Ť/米}$是热速度（T是温度，m是粒子（电子）的质量）。通过将表面项的贡献明确包含在半无限等离子的（线性化）Boltzmann（Vlasov）方程中，可以获得结果。解决该问题的关键是观察到，除了空间衰减和振荡分量外，响应电场还存在一个均匀的（时间振荡）分量。