**Abstract: **Energetic particles (EPs) can destabilise a wide range of instabilities in tokamaks, which can significantly impact the plasma performance, either negatively by redistributing EPs out of the plasma core [1], or positively by mitigating thermal turbulent transport [2]. The nature of this impact depends strongly on the gradients of the EP distribution functions in phase space, which condition the type of modes that can be driven unstable by EPs. It is therefore essential to model precisely such distributions, to isolate the plasma scenarios that can maximise fusion performance in ITER burning plasmas. This modelling is however challenging as EPs are far from thermodynamic equilibrium, and therefore characterised by anisotropic non-Maxwellian distributions. Such distributions can be reconstructed numerically with Fokker-Planck codes or using inverse tomography diagnostics for experimental discharges. First-principles and stability codes cannot however operate with such numerical distributions due to their significant noise over the EP distribution gradients in phase space, and consequently require another kind of input for EPs.

In this work, a method is developed within the ITER Integrated Modelling Analysis Suite [3] (IMAS) to transform numerical EP distributions in arbitrary coordinates towards 3D constants of motions (CoM) distributions, ideal for first-principles and stability codes as they represent equilibrium distribution functions. Such a transformation is performed for a given experimental configuration by computing EP orbits on a 3D CoM grid [4], in order to calculate the Jacobian of the CoM change of variable, which depends on the EPs poloidal bounce/transit time. EP distributions in CoM space are then obtained using 3D C2 B-splines, to ensure high numerical precision for stability and nonlinear simulations with C1 CoM distribution gradients. The intrinsic singularities in 3D CoM space [4] are removed by splitting the EP distribution into co-going and counter-going components for both trapped and passing particles, in order to enforce the C2 condition across the trapped-passing boundary in particular. The precision of the CoM transformation is then successfully tested by performing back-and-forth transformations between CoM distributions and distributions obtained from Fokker-Planck simulations based on JET and ITER plasmas in energy-pitch-cylinder coordinates. Different techniques are then presented to initialize EP CoM distributions in codes using either \delta f or full-f methods. These schemes will be tested in another work using the \delta f gyrokinetic code GTC [5] and the full-f kinetic-MHD code XTOR-K [6].

The views and opinions expressed herein do not necessarily reflect those of the ITER organization.

[1] K. McGuire et al., Phys. Rev. Lett. 51, 1925 (1983).

[2] G. Brochard et al., Phys. Rev. Lett. 132 075101 (2024)

[3] S. D. Pinches et al., Proceedings of the 27th IAEA Fusion Energy Conference, Ahmedabad India (2018).

[4] A. Bierwage et al. Comput. Phys. Commun. 275, 108305 (2022).

[5] Z. Lin et al. Science 281, 1835 (1998).

[6] G. Brochard et al. Nucl. Fusion 60, 086002 (2020).