# Connection between the two branches of the quantum two-stream instability across the k space 

A. Bret 1 and F. Haas 2 

$^{1}$ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain 

Av. Unisinos 950, 93022-000 S˜ ao Leopoldo RS, Brazil 

$^{2}$Universidade do Vale do Rio dos Sinos, 

Abstract The stability of two quantum counter-streaming electron beams is investigated within the quan- tum plasma fluid equations for arbitrarily oriented wave vectors k . The analysis reveals that the two quantum two-stream unstable branches are indeed connected by a continuum of unstable modes with oblique wave vectors. Using the longitudinal approximation, the stability domain for any k is analytically explained, together with the growth rate. 

PACS numbers: 52.35.Qz, 41.75.-i, 03.65.-w 

