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With the observations from \textit{Rossi X-ray Timing Explorer}, we searchand study the X-ray bursts of accreting millisecond X-ray pulsarSAX~J1748.9-2021 during its 2010 outburst. We find 13 X-ray bursts, including12 standard type-\uppercase\expandafter{\romannumeral1} X-ray bursts and anirregular X-ray burst which lacks cooling tail. During the outburst, thepersistent emission occurred at $\sim$(1-5)$\%\rm {\dot{M}_{Edd}}$. We use acombination model of a blackbody (BB), a powerlaw, and a line component to fitthe persistent emission spectra. Another BB is added into the combination modelto account for the emission of the X-ray bursts due to the thermonuclearburning on the surface of the neutron star. Finally, we modify the combinationmodel with a multiplicative factor $f_{\rm a}$, plus a BB to fit the spectraduring the X-ray bursts. It is found that the $f_{\rm a}$ is inverselycorrelated with the burst flux in some cases. Our analysis suggests that theignition depth of the irregular X-ray burst is obviously smaller than those ofthe type-\uppercase\expandafter{\romannumeral1} X-ray bursts. We argue that thedetected type-\uppercase\expandafter{\romannumeral1} X-ray bursts originatefrom helium-rich or pure-helium environment, while the irregular X-ray burstoriginates from the thermonuclear flash in a shallow ocean.

The X-ray bursts within the 2010 outburst of the accreting millisecond X-ray pulsar SAX J1748.9-2021