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Fig. 2.

image

Influence of the beam density on the wave growth and fractional bandwidths, investigated by varying the beam-to-background density ratio rn from 10−4 to 1: Panel a: maximum growth rates ωi for different beam-to-background density ratios rn obtained by solving the linear dispersion relation (dots) and from simulations (crosses) with fit function (solid line). Panel b: integrated growth rates calculated from numerical solutions of the dispersion relation (dots) and from simulation results (crosses) with fit function (solid line). Panel c: fractional bandwidth Δωr at the point where ωi is at its maximum, normalised to the corresponding real part of the frequency ωr, obtained by linear theory (dots) and simulation (crosses). All three figures are for ρ0 = ρ1 = 1 and γb = 26. Details regarding the fit functions can be found in Table 1.

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