To improve the directivity of source plasma ions supplied to the extraction gap of a laser-ablation ion source (LAIS), the behavior of a laser-produced dense plasma flow modulated by a divergent magnetic field was investigated in detail. A magnetic field having a "nozzle-like" structure was induced by a pulsed solenoid near the laser target in synchronization with laser irradiation. The waveforms of plasma ions passing through the magnetic field were observed by Faraday cups located at various directions and distances from the target. From the angular dependence of the waveforms, two different mechanisms were found to cause the enhancement of the plasma ion flux independently. The core part of the laser-produced plasma plume is compressed by the magnetic pressure, leading to an increase in the plasma ion flux. The ions in the peripheral part of the plume are gathered by the collective focusing effect, which also can contribute to the flux enhancement. The results indicate that the directivity of the plasma ions can be greatly improved by optimizing the structure and strength of the magnetic nozzle. The more detailed analyses using a Hybrid Particle-In-Cell code were also performed to find the optimum magnetic nozzle parameters, which well reproduced the experimental results.