ITER Heating Neutral Beam Simulator

Physics Model

This ITER Heating Neutral Beam simulator models the acceleration and transport of a H⁻ ion beam through a multi-gap electrostatic accelerator and a 25 m beamline. The beam is extracted from a multi-aperture plasma source with 1280 beamlets, each with a circular aperture of 14 mm diameter. The target for the beam source is 330 A/m², 870 keV in hydrogen, while the neutralized beam power transmitted to ITER shall be of 16.7 MW. See for the design description R Hemsworth et al. New J. Phys. 19 (2017) 025005.

Beam Optics and Perveance

The quality of beam extraction is governed by the reduced perveance Π~ = J / V_ext^3/2, where J is the extracted current density and V_ext is the extraction voltage.
When Π~ matches the optimal value Π~_opt = 5×10⁻⁴ A m⁻² V⁻¹·⁵, the beam is well-focused and losses on the accelerator grids are minimized.
Deviations from the optimal perveance increase beam divergence ω and reduce the beam interception efficiency η_interception. For the accelerator physics, see H.P.L. de Esch et al (2015) Nucl. Fusion 55 096001.

Accelerator Transmission

The total accelerator transmission is η_acc = η_interception · η_stripping.
The stripping loss L = 1 − η_stripping accounts for the neutralization of H⁻ ions through collisions with residual gas molecules inside the accelerator, which removes particles from the accelerated beam. See for instance Pimazzoni et al. Fus Eng Des 192 (2023) 113621 and references therein.

Neutralization and Re-ionization

After the accelerator, the beam enters a gas cell where H⁻ ions are neutralized through single electron detachment:
H⁻ + H₂ → H⁰ + e + H₂,
characterized by the cross-section σ₋₁₀. The evolution of the negative and neutral beam fractions along the beamline is governed by the system of ordinary differential equations:
dI⁻/dx = −σ₋₁₀ · n(x) · I⁻
dI⁰/dx = +σ₋₁₀ · n(x) · I⁻ − σ₀₁ · n(x) · I⁰
where σ₀₁ is the re-ionization cross-section for H⁰ + H₂ → H⁺ + e + H₂. The analytical solution gives the neutralization efficiency η_neut.
Beyond the gas cell, only re-ionization acts on the neutral beam, giving
η_reioniz = exp(−σ₀₁ ∫₅²⁵ n(x) dx).
The total neutralization efficiency is η = η_neut · η_reioniz. See for neutral beam neutralization and transmission G Serianni et al. New J. Phys. 19 (2017) 045003.

Beamline Transport

A transverse electric field deflects residual ions inside the Residual Ion Dump downstream of the gas cell, so only the neutral fraction reaches the target.
The beamline transmission due to beam divergence is F = erf(0.007 / ω), and the final beam power delivered to the target is:
P_end = P_out · F · η