The evolution of a relativistic blastwave is usually delineated under the
assumption of pressure balance between forward- and reverse-shocked regions.
However, such a treatment usually violates the energy conservation law, and is
inconsistent with existing MHD numerical simulation results. A mechanical model
of non-magnetized blastwaves was proposed in previous work to solve the
problem. In this paper, we generalize the mechanical model to the case of a
blastwave driven by an ejecta with an arbitrary magnetization parameter
Οejβ. We test our modified mechanical model by considering a
long-lasting magnetized ejecta and found that it is much better than the
pressure-balance treatment in terms of energy conservation. For a constant
central engine wind luminosity Lejβ=1047ergΒ sβ1 and
Οejβ<10, the deviation from energy conservation is negligibly
small at small radii, but only reaches less than 25% even at 1019cm from the central engine. For a finite life time of the central engine, the
reverse shock crosses the magnetized ejecta earlier for the ejecta with a
higher Οejβ, which is consistent with previous analytical and
numerical results. In general, the mechanical model is more precise than the
traditional analytical models with results closer to those of numerical
simulations.Comment: Accepted for publication in MNRAS; 8 pages, 2 figure