Electrostatic linear and nonlinear response functions for magnetized plasmas derived under the forward-scattering method

The present paper is a sequel to the prior paper [Yoon et al., AIP Adv. (to be published) (2026)], where the equivalence of the forward-scattering vs the Vlasov methods in computing the linear and nonlinear susceptibilities of plasmas was investigated. For the sake of simplicity, the prior paper considered the simplest situation, namely, the electrostatic plasma susceptibilities in unmagnetized plasma. It was shown that both methods led to the same linear and second-order nonlinear susceptibilities, but discrepancy was found for the third-order nonlinear susceptibility. The present paper extends the calculation to magnetized plasmas under the same electrostatic formalism by employing the forward-scattering method. The computation is, however, limited to the linear and second-order nonlinear response functions, as it was shown that the third-order susceptibility did not enjoy the equivalence with the Vlasov method. As such, the third-order nonlinear response function for magnetized plasmas is left out of consideration in the present paper.