Fast forward modeling of neutral beam injection and halo formation including full Balmer-α emission prediction at W7-X

Abstract

A full collisional-radiative (CR) neutral beam injection model based on Gaussian pencil (Gausscil) beams and a diffusive CR neutral halo model are presented. The halo is a neutral cloud around the neutral beam forming due to multiple charge exchange (CX) reactions. Both models do not rely on Monte-Carlo techniques and are thereby orders of magnitude faster than commonly used models. To model the neutral halo a system of coupled diffusion equations is solved numerically, enforcing mixed boundary conditions. From the equilibrium hydrogen neutral densities in the second excited energy state (n = 3), the Balmer-α emission intensity is calculated and the full spectrum is predicted, including effects as Doppler shifts and broadening due to the complex neutral beam geometry and the motional Stark effect (MSE) from the magnetic field. All forward models are implemented in the Minerva [1] Bayesian analysis framework to enable detailed multivariant inference from Balmer-α spectroscopy data. The modeled neutral beam and halo densities are successfully verified against calculations with a validated Monte-Carlo code for the W7-X beam and plasma geometry, especially proving the validity of the halo diffusion ansatz. A comparison of the predicted emission spectra with the experimental data proves the accuracy of the implemented model. All important parameters defining the neutral beams are inferred and compared to available reference values.

Validation of a synthetic fast ion loss detector model for Wendelstein 7-X

“…We assume, for the halo neutrals, an average density of 1 × 10 15 m −3 and a full-width half-max of 0.125 m from the beam axis, both based on [51]. Taking the plasma circumference as 2π R 0 = 34.6 m, where R 0 , the major radius, is 5.5 m, and the two halo regions to be 0.25 m wide each, the fast ions are estimated to spend 1.4% of their time in the two beam halos.…”

Bayesian inference of electron density and ion temperature profiles from neutral beam and halo Balmer-α emission at Wendelstein 7-X

“…The halo formation and its Hα emission are computed by solving a coupled, ColRad CX diffusion equation with the beam-plasma CX reaction rate being the initial source term. A detailed description of the model and its verification can be found in [8]. A simplified graph diagram of the implemented beam and halo emission forward model described in [8] is shown in figure 2.…”

“…A detailed description of the model and its verification can be found in [8]. A simplified graph diagram of the implemented beam and halo emission forward model described in [8] is shown in figure 2. The free parameters which can be inferred by the model from the beam and halo emission data are drawn as blue ellipsoids.…”

“…To access the information on plasma density a full collisional-radiative (ColRad) model of the beam attenuation and the halo formation is needed. The beam and halo model used for the following analysis is described in detail in [8].…”

Turbulence-reduced high-performance scenarios in Wendelstein 7-X

“…The PyFidaSim source rate includes the ionisation rate of both beam neutrals and beam 'halo' neutrals, which are created by charge exchange and diffuse through the plasma before their eventual ionisation. The halo contribution is significant (around 50%) but in moderate or high density plasmas has a similar source profile to the direct ionisation due to the small diffusion length (∼10 cm) compared to the plasma radius (50 cm) [58]. It can therefore be assumed, as it is in Beams3D, that the source rate is locally equal to the sum of the ionisation and charge exchange rates (also known as the beam-stopping rate).…”