Based on the Kharzeev-McLerran-Warringa (KMW) model that estimates strong electromagnetic (EM) fields generated in relativistic heavy-ion collisions, we generalize the formulas of EM fields in the vacuum by incorporating the longitudinal position dependence, the generalized charge distributions and retardation correction. We further generalize the formulas of EM fields in the pure quark-gluon plasma (QGP) medium by incorporating a constant Ohm electric conductivity and also during the realistic early-time stages QGP evolution by using a time-dependent electric conductivity. Using the extended KMW model, we observe a slower time evolution and a more reasonable impact parameter b dependence of the magnetic field strength than those from the original KMW model in the vacuum. The inclusion of medium effects by using the lattice data helps to further prolong the time evolution of magnetic field, such that the magnetic field strength during the realistic QGP evolution at thermal freeze-out time can meet the 1σ bound constrained from experimentally measured difference in global polarizations of Λ and $\overline{\mathrm{\Lambda }}$ hyperons in Au+Au collisions at top RHIC energy. These generalized formulations in the extended KMW model will be potentially useful for many EM fields relevant studies in heavy-ion collisions, especially at lower colliding energies and for various species of colliding nuclei.

基于Kharzeev-McLerran-Warringa（KMW）模型，该模型估算了相对论重离子碰撞中产生的强电磁场，我们通过结合纵向位置依赖性，广义电荷分布和延迟校正。我们通过结合恒定的欧姆电导率以及在现实的早期QGP演化过程中，通过使用随时间变化的电导率，来进一步推广纯夸克-胶子等离子体（QGP）介质中的EM场公式。使用扩展的KMW模型，我们观察到较慢的时间演化和更合理的影响参数b磁场强度的依赖性比真空中原始KMW模型的强。通过使用晶格数据包含介质效应有助于进一步延长磁场的时间演化，从而使热冻结时间下实际QGP演化过程中的磁场强度可以满足受实验测量的差异限制的1σ界。和的全局极化$\overline{\mathrm{\Lambda }}$RHIC能量最高的Au + Au中的超子碰撞。扩展的KMW模型中的这些广义公式对于重离子碰撞中的许多EM领域的相关研究，尤其是在较低碰撞能量和各种碰撞核物种中的潜在研究中，可能是有用的。