Cross-field electron transport and cross-field electric field induced by linearly or nonlinearly unstable localized electrostatic waves in an electron beam-plasma system were investigated theoretically and numerically on the basis of the transport equations and magnetohydrodynamic equations [1,2]. The transport equations are derived from the θ-dependent quasilinear velocity-space diffusion equation [1-3]. It was verified that the parallel and perpendicular electron transport generates a large and abrupt dip of the electron density and a strong peak of the electron temperature in the radial direction. At the same time the cross-field electric field is produced partially by the cross-field electron transport and partially by the perpendicular pressure gradient, that is, it is given by E_⊥= B₀×v_e⊥/c−(∇_⊥p_e)/en_e (p_e=n_ek_BT_e). The small cross-field electron transport is predited to create the strong cross-field electric field. On the other hand, the parallel electric field E_//=−(∇_//p_e)/en_e +m_eν_env_e///e is created by the parallel transport and pressure gradient. The radial and axial profiles of the electron density and temperature and the electrical potential were obtained numerically and they can explain well the experimental observation in an electron beam-plasma system qualitatively and quantitatively [4,5].

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