Laser-sustained plasma (LSP) sources have applications in wafer defect detection, near-field imaging, spectroscopic analysis, and endoscopy. A smaller-size and higher-temperature plasma can be generated through LSP to result in high-brightness, incoherent broadband emission. With the development of high-power fiber lasers in the mid-infrared, fiber lasers are widely used in LSP sources. Fiber lasers with excellent beam quality contribute to a lower LSP threshold and thereby further promote the application of LSP sources. Source stability is crucial in LSP source applications. However, LSP is characterized by spatial and temporal instabilities. The results of a study conducted by Yakimov et al. show that LSP first exhibits spatial and temporal instabilities when the f-number of the focusing objective increases to certain values. The spatial instability of the LSP can be avoided by reducing the f-number of the focusing objective. The temporal instability of the LSP is driven by the convective plume pulsation of the plasma. The inhibition of the convective plume pulsation of the plasma is key to solving the temporal instability of the LSP source.

In our study, we use an orthogonal laser to sustain the plasma. The plasma size and temperature of orthogonal LSP are shown in Fig. 4, and orthogonal LSPs can realize plasmas with smaller size and higher temperatures. When the laser power increases, the frequency of the convective plume pulsation of the plasma gradually decreases. When the laser power increases to a specific point, the convective plume pulsation of the plasma suddenly disappears.

This phenomenon is similar to the laminar flame combustion instability during fuel combustion processes. In flame combustion, there are three types of combustion: steady, transition, and pulsation combustion. The research in Refs. [24-25] shows that the laminar flame combustion gradually switches from pulsation combustion to transitional combustion and steady combustion as the Froude number decreases. In LSP, as the Froude number decreases, there should also be a switch between steady convective plume and convective plume pulsation. The Froude number, given by $F_{\mathrm{r}}=\sqrt[]{v^{\mathrm{2}}/\left(gr\right)}$, where $v$ is the velocity of the object motion, $g$ is the acceleration of gravity, and $r$ is the characteristic length of the object, is a dimensionless parameter in hydrodynamics that characterizes the relative magnitudes of the inertial force and the gravitational force of a fluid. The Froude number is inversely proportional to the diameter of the plasma convection plume. An increasing laser power leads to an enlarged diameter of the convective plume. Therefore, the Froude number decreases as the laser power increases, and it can be assumed that the convective plume pulsation of the plasma disappears when the Froude number decreases below the critical point for the steady convective plume. Determining the critical Froude number for the steady convective plume is the key to enhancing LSP temporal stability. According to the Froude number formula, increasing the velocity of the object motion and decreasing the characteristic length of the object increase the Froude number. A high Froude number helps LSP switch from convective plume pulsation to a steady convective plume. Orthogonal laser sustains a hotter plasma, which increases the velocity of the plasma convection plume. Therefore, orthogonal laser-sustained plasma reduces the Froude number, which overcomes the temporal instability of the LSP source.

In this study, a plasma with a smaller size and higher temperature is realized using orthogonal laser-sustained plasma. In the orthogonal laser-sustained plasma, the convective plume pulsation frequency of the plasma gradually decreases and disappears with an increase in the laser power, and the convective plume is converted from a pulsation state to a stable state. A stable plasma convection plume helps improve the time stability of the laser-sustained plasma, which is crucial for the application of laser-sustained plasma light sources. This study is analogous to switching between pulsation combustion and steady combustion in laminar combustion. It is proposed that a reduction in the Froude number is the key to realizing the conversion of a plasma convection plume from a pulsation state to a steady state. The key to reducing the Froude number is to reduce the expansion rate of the convective plume, which can help the plasma convective plume transition from the pulsation state to the steady state. Orthogonal laser-sustained plasma helps increase the plasma temperature and overcome the temporal instability of laser-sustained plasma. However, the critical Froude number of the plasma convective plume in the pulsation and steady states has not been quantitatively described. Therefore, the critical Froude number of the plasma convective plume will be thoroughly investigated in a subsequent study to further clarify the physical connotations of laser-sustained plasma time instability.