Dispersion relations for low-frequency waves in a warm, underdense, two-fluid plasma

Analytical forms of dispersion relations for three lower-frequency waves in a two-fluid plasma are presented. In underdense plasmas, omega(2)(p) less than or similar to Omega(2)(ce), that is, low density or strongly magnetized plasmas, where omega(p) and Omega(ce) are respectively the plasma frequency and the electron cyclotron frequency, the displacement current can become important in higher-frequency (non-magnetohydrodynamic) region. Focusing on only three branches that become magnetohydrodynamic waves in the low-frequency limit, we derive dispersion relations applicable to both underdense and overdense plasmas by the full set of equations of two-fluid plasmas including the displacement current. It is shown that our analytical results well agree with the exact numerical ones in all frequency ranges when the following conditions are satisfied: normal (i.e., not pair) plasma; low plasma beta, and not extremely small electron to ion temperature ratio, m(e)/m(i) << T-e/T-i, while more exact dispersion relations are needed to perform polarization analysis. (C) 2017 Author(s).