  We present a cold atomic beam source based on a two-dimensional (2D)+
magneto-optical trap (MOT), capable of generating a continuous cold beam of
87Rb atoms with a flux up to 4.3*10^9 atoms/s, a mean velocity of 10.96(2.20)
m/s, and a transverse temperature of 16.90(1.56) uK. Investigating the
influence of high cooling laser intensity, we observe a significant population
loss of atoms to hyperfine-level dark states. To account for this, we employ a
multiple hyperfine level model to calculate the cooling efficiency associated
with the population in dark states, subsequently modifying the scattering
force. Simulations of beam flux at different cooling and repumping laser
intensities using the modified scattering force are in agreement with
experimental results. Optimizing repumping and cooling intensities enhances the
flux by 50%. The influence of phase modulation on both the pushing and cooling
lasers is experimentally studied, revealing that the mean velocity of cold
atoms can be tuned from 9.5 m/s to 14.6 m/s with a phase-modulated pushing
laser. The versatility of this continuous beam source, featuring high flux,
controlled velocity, and narrow transverse temperature, renders it valuable for
applications in atom interferometers and clocks, ultimately enhancing
bandwidth, sensitivity, and signal contrast in these devices.
