  In this paper, a generic self-similar flux rope model is proposed to probe
the internal state of CMEs in order to understand the thermodynamic process and
expansion of CMEs in interplanetary space. Using this model, three physical
parameters and their variations with heliocentric distance can be inferred
based on coronagraph observations of CMEs' propagation and expansion. One is
the polytropic index $\Gamma$ of the CME plasma, and the other two are the
average Lorentz force and the thermal pressure force inside CMEs. By applying
the model to the 2007 October 8 CME observed by STEREO/SECCHI, we find that (1)
the polytropic index of the CME plasma increased from initially 1.24 to more
than 1.35 quickly, and then slowly decreased to about 1.34; it suggests that
there be continuously heat injected/converted into the CME plasma and the value
of $\Gamma$ tends to be 4/3, a critical value inferred from the model for a
force-free flux rope; (2) the Lorentz force directed inward while the thermal
pressure force outward, and both of them decreased rapidly as the CME moved
out; the direction of the two forces reveals that the thermal pressure force is
the internal driver of the CME expansion whereas the Lorentz force prevented
the CME from expanding. Some limitations of the model and approximations are
discussed meanwhile.

Solar and Stellar Astrophysics