  The aim of this paper is to present the implementation of two new CME models
in the space weather forecasting tool, EUHFORIA. We introduce the two toroidal
CME models analytically, along with their numerical implementation in EUHFORIA.
One model is based on the modified Miller-Turner (mMT) solution, while the
other is derived from the Soloviev equilibrium, a specific solution of the
Grad-Shafranov equation. The magnetic field distribution in both models is
provided in analytic formulae, enabling a swift numerical computation. After
detailing the differences between the two models, we present a collection of
thermodynamic and magnetic profiles obtained at Earth using these CME solutions
in EUHFORIA with a realistic solar wind background. Subsequently, we explore
the influence of their initial parameters on the time profiles at L1. In
particular, we examine the impact of the initial density, magnetic field
strength, velocity, and minor radius. In EUHFORIA, we obtained different
thermodynamic and magnetic profiles depending on the CME model used. We found
that changing the initial parameters affects both the amplitude and the trend
of the time profiles. For example, using a high initial speed results in a fast
evolving and compressed magnetic structure. The speed of the CME is also linked
to the strength of the initial magnetic field due to the contribution of the
Lorentz force on the CME expansion. However, increasing the initial magnetic
field also increases the computation time. Finally, the expansion and integrity
of the magnetic structure can be controlled via the initial density of the CME.
Both toroidal CME models are successfully implemented in EUHFORIA and can be
utilized to predict the geo-effectiveness of the impact of real CME events.
Moreover, the current implementation could be easily modified to model other
toroidal magnetic configurations.
