Anomalous skin effect for anisotropic electron velocity distribution function

We show that anomalous skin effect in a plasma with a highly anisotropic electron velocity distribution function (EVDF) is very different from skin effect in a plasma with the isotropic EVDF. We have derived an analytical solution for the electric field penetrated into plasma with the EVDF described as a Maxwellian with two temperatures T _x>>T _z, where x is the direction along plasma boundary and z is the direction perpendicular plasma boundary. In a recent Letter [1], it was shown that a highly anisotropic electron velocity distribution function (EVDF) yields a large skin-layer depth compared with the isotropic EVDF. The electromagnetic wave is assumed to propagate also along z-axis in vacuum. The skin layer was determined to be much longer than the skin layer in a plasma with isotropic EVDF. The authors of Ref. [l] showed that under conditions T _x>T _z; c/ω _p<V _Tx/ω; ω _p>ω where ω is the incident wave frequency, ω _p is the plasma frequency, V _Tx=√T _x/m the electric field profile is exponential E(z)̃exp(-z/l _x) where lx= _vTx/ω. In their analysis authors of Ref. l assumed from the beginning that skin depth is longer than v _Tz/ω, where v _Tz=√T _z/m We have performed kinetic analysis similar to Ref. 2 and obtained an analytical solution for the electric field. We show that skin layer actually consists of two distinctive regions of width of order v _Tx/ω and v _Tz/ω, the latter short region was missed in Ref. l.