Energy supply sources for the heating process in the slow solar wind remain unknown. The Parker Solar Probe (PSP) mission provides a good opportunity to study this issue. Recently, PSP observations have found that the slow solar wind experiences stronger heating inside 0.24 au. Here for the first time we measure in the slow solar wind the radial gradient of the low-frequency breaks on the magnetic trace power spectra and evaluate the associated energy supply rate. We find that the energy supply rate is consistent with the observed perpendicular heating rate calculated based on the gradient of the magnetic moment. Based on this finding, one could explain why the slow solar wind is strongly heated inside 0.25 au but expands nearly adiabatically outside 0.25 au. This finding supports the concept that the energy added from the energy-containing range is transferred by an energy cascade process to the dissipation range, and then dissipates to heat the slow solar wind. The related issues for further study are discussed.

在缓慢的太阳风中用于加热过程的能源供应来源仍然未知。派克太阳探测器（PSP）任务为研究此问题提供了一个很好的机会。最近，PSP观测发现，缓慢的太阳风在0.24 au内经历了更强的加热。在这里，我们第一次在慢速的太阳风中测量磁迹功率谱上低频突变的径向梯度，并评估相关的能量供应率。我们发现能量供应速率与基于磁矩梯度计算的观测到的垂直加热速率一致。根据这一发现，可以解释为什么缓慢的太阳风在0.25 au内被强烈加热，而在0.25 au之外几乎绝热地膨胀。该发现支持以下概念：从能量包含范围添加的能量通过能量级联过程转移到耗散范围，然后耗散以加热慢速的太阳风。讨论了需要进一步研究的相关问题。