tokens: range of 1.58, 1.60, and 1.57, respectively. However, the power spectra have flattened in the dissipation range for the whole ICME and the previous AF-rich region, with the spectral indexes of 1.12 and 0.82, respectively, which may be aliased by the instrument noises. The power spectrum for the previous AF-lack region still has a steepening in the dissipation range, with the spectral index of 1.84. Similarly, the break frequencies are also comparable to the frequency corresponding to the ion inertial length. Figure 3. Power spectral density of magnetic fluctuations inside the ICME: (A) the whole ICME observed by Wind at 1.0 au; (B) the AF-rich region of the ICME at 1.0 au; (C) the AF-lack region of the ICME at 1.0 au; (D) the whole ICME observed by Ulysses at 5.4 au; (B) the AF-rich region of the ICME at 5.4 au; (C) the AF-lack region of the ICME at 5.4 au. The dashed colored lines are the power-law fitting results. The red ones are in the inertial range, while the green ones are in the dissipation range. The vertical dashed lines represent the proton gyro-frequency, f pc , the break frequency, f b , and the frequency corresponding to the ion inertial length, f di . The energy cascade rate then can be calculated from Equation ( 1 ). For the whole ICME, the energy cascade rates at 1.0 au are derived to be about 2688.6 J kg −1 s −1 , which is close to the lower limit (2970 ∼ 65,320) estimated by Vasquez et al. ( 2007 ) when the solar wind speed is between 350 and 400 km s −1 . When the ICME propagates to 5.4 au, this value reduces to 274.7 J kg −1 s −1 , suggesting that the capacity of turbulence cascade reduces as the ICME propagates outward. For the AF-rich region, the energy cascade rate drops from 3312.2 to 89.7 J kg −1 s −1 accompanied with the disappearance of AFs, when the ICME propagates from Wind to Ulysses . For comparison, the energy cascade rates for the AF-lack region can be maintained at a certain level, and the values at 1.0 and 5.4 au are 526.9 and 737.3 J kg −1 s −1 , respectively. In addition, Smith et al. ( 2006 ) have found the dependence of the dissipation range spectrum on the rate of energy cascade through the inertial range. Our results are also in agreement with their findings that the steeper spectral in the dissipation range forms from greater cascade rates. Liu et al. ( 2006 ) have taken into account the Coulomb energy transfer between protons and alphas, and derived the equations of the heating rate required for protons ( ε p ) and alphas ( ε α ) to produce the observed temperature profile. The specific expressions are as follows where k B is the Boltzmann constant, T p and T α are the temperature of protons and alphas, m α is the alpha mass, τ pα and τ αp are the Coulomb collision timescales and have a relationship of , n α is the alpha number density, and τ e is the expansion time of the plasma. For more details, please refer to Appendix A in Liu et al. ( 2006 ). The total required heating rate ( ε re ) is
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