Magic wavelengths for the 7s_(1/2)6d_(3/2,5/2)transitions in Ra~+

The dynamic polarizabilities of the 7s and 6d states of Ra⁺ are calculated using a relativistic core polarization potential method. The magic wavelengths of the 7s_1/2-6d_3/2,5/2 transitions are identified. Comparing to the common radio-frequency (RF) ion traps, using the laser field at the magic wavelength to trap the ion could suppress the frequency uncertainty caused by the micromotion of the ion, and would not affect the transition frequency measurements. The heating rates of the ion and the powers of the laser for the ion trapping are estimated, which would benefit the possible precision measurements based on all-optical trapped Ra⁺.