A theory is presented for a two-stream free-electron laser (FEL) with a background plasma. A dispersion relation (DR) for the unstable couplings of wave modes is derived using fluid formulation. This DR is solved numerically to find the unstable modes and their growth rate. The effect of the velocity difference of the two electron beams as well as the background plasma on the FEL resonance and the two-stream instability is studied. It is shown that their separate as well as combined effects can increase the growth rates.
二流自由電子レーザー（FEL）と背景プラズマを伴う場合の理論を提示する。流体定式化を用いて、波動モードの不安定結合に対する分散関係（DR）を導出する。このDRを数値的に解いて、不安定モードとその成長率を求める。2つの電子ビームの速度差および背景プラズマが、FEL共鳴と二流不安定性に及ぼす影響を調べる。それらの個別の効果および複合的な効果が成長率を増大させ得ることが示される。