# Beam Transmission (BTR) Software for Efficient Neutral Beam Injector Design and Tokamak Operation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}, and hence, the source beam and beamline elements need to be adjusted with extremely high precision so that the intercepted power is minimized, and no surface is damaged due to insufficient cooling. Further, due to the tight space constraints of the main device (e.g., tokamak) configuration, a beamline design is made as compact as possible. The available space considerations result in a very long multi-parametrical optimization procedure, while NB design specifications with an account of cooling requirements tend to be increasingly complex. To minimize the efforts for NBI optimization and to reduce the beam losses and heat loads along the beamline, dedicated numerical tools are required. At present, the BTR code [3,4,5] is one of the most popular tools for NBI design and analysis [6,7,8,9,10,11,12,13,14,15,16].

- NBI purposes, general structure, and efficiency concerns are brought up in Section 2.
- BTR code basic features and GUI capabilities are represented in Section 3.
- BTR scope and methods are discussed in Section 4.
- Verification and validation (V&V) issues are considered in Section 5.
- The software applications in various NBI designs are illustrated in Section 6.
- The main conclusions and plans are manifested in the final Section 7.

## 2. NBI Purpose, Scheme and Structure

#### 2.1. Neutral Injection Purpose

#### 2.2. Neutral Injection Principles and Scheme

#### 2.3. Neutral Beamline Losses and Efficiency

^{−}) core divergence: 3 mrad, 5 mrad, and 7 mrad; further, according to experiments, the beam core (85% of extracted current) is accompanied by a higher divergent (~30 mrad) current fraction— ‘halo’, which carry ~15% of current. The beamline geometrical transmission for 3–7 mrad beams can vary from 70% to 90%, leading to the total beamline efficiency of 35–50%.

#### 2.4. Neutral Beamline Geometry in BTR

- -
- the beam source grounded grid (GG),
- -
- multi-channel (can be single channel) neutralizer,
- -
- residual ion dump, RID (multi- or single channel),
- -
- neutral beam dump, or calorimeter,
- -
- beam transmission line, or duct, which consists of multiple modules (scrapers, FEC, liners, blanket sections, etc.).

## 3. BTR Basic Features and GUI

#### 3.1. BTR General Info

#### 3.2. BTR User Interface

- “Config plot”, main view with NBI geometry and beam layout.
- “Green panel” tool—BTR interactive input data processor.
- “Loads Summary”/“Map” view switch.
- “Running Status”/“Profiles” view switch.

- -
- Update/Save/Import data.
- -
- Call dialogs for input by categories (i.e., alternative direct input way).
- -
- Define specific ‘Tasks’ and output options.
- -
- Add/Edit gas or field input profiles.
- -
- Select/manage visualization categories and many others.

## 4. BTR Models and Tasks

#### 4.1. Beam Shape and the Injected Power

_{c}and Δ

_{h}—the angular width of core и halo. Note: The Gaussian width in BTR notation is not the same as standard deviation σ for normal distribution.

^{2}NBI window, the calculated beam transmission efficiency is ~76%, with the injected power of 3.5 MW. If the beam focusing has small errors (misaligned) of about ±4 mrad in the horizontal and ±6 mrad in a vertical plane, the injected power to plasma reduces to 3.3 MW (with the beam transmission ~71%), and the effect is illustrated in Figure 8a,b.

^{2}, which is comparable with the tokamak camera size. If the NB port is reduced to 20 × 40 cm

^{2}, the injected power drops from 3.5 MW to ~2.3 MW, or by ~30% from nominal NB power. The beam misalignment additionally reduces the NB power (down to ~2 MW). If we consider the neutralization efficiency (~50% for the beam energy adopted), the overall NBI performance would be about 25%, so the NBI total performance is quite low. Further, for the reduced port size design, the beam power intercepted by the beamline components becomes too high, and the entire NBI design revision is needed to address the overheating issue.

^{2}). The main feature that distinguishes the BTR approach from the existing NBI models is that BTR calculates the injected beam statistics not only with a detailed account of the source beamlet structure but also including the effects of background conditions (fields and gas); as a result, BTR generally provides a complete and more ‘realistic’ beam losses and transmission through the injector as compared to the NBI models which typically ignore all these minor effects. However, the combination of these effects tends to be far from negligible, so during the experiments, the need for a more realistic simulation becomes more evident [30,31].

#### 4.2. Beam Neutralization

_{−10}(electron stripping), σ

_{−11}(double electron stripping), σ

_{10}(positive ion neutralization), and σ

_{01}(atom ionization). A positive ion neutralization process is defined by the ratio σ

_{10}/σ

_{01}. There are two options (models) available in BTR for beam neutralization—‘thick’ and ‘thin’. The thin model is less accurate: the total gas volume is “pushed” to a thin layer at the neutralizer exit, causing an overestimated beam deflection at the device output. However, it is by many orders of magnitude faster and finds much wider use than a thick model, which takes the real gas target distribution and produces a reduced beam deflection and, in fact, a wider test-particle divergence. The thick model (Figure 9a–c) solves balance equations for beam species:

^{k}is the k-th species flux, n is background gas density.

#### 4.3. Residuals Deflection and Dumping

^{3}–10

^{4}ions per single BS beamlet, or 10

^{6}–10

^{7}total particles) and each ion track calculation guided by the Lorenz force until the ions stop or escape from the calculation area. BTR helps to choose the optimum configuration and magnitude of the field by scanning several NBI parameters across the nominal operation range; typically, the following values are to be scanned: neutralization output, beam tilting and focusing, beam initial divergence, and magnetic field profile in the neutralization region. When the optimal deflecting field is found, the expected power density maps are calculated for RID thermal cooling circuit design.

#### 4.4. Re-Ionization on Gas

_{01}(atom ionization) and σ

_{10}(ion neutralization), both depending on the atom specific energy. In BTR, each test neutral particle (‘super-atom) produces as many secondary ions as needed to be given by the step of re-ionization, and the secondary positive ions are next traced until their interception by a solid surface or escape from the area (Figure 11); this is like residual ions tracking in RID area. The governing system for the process is.

#### 4.5. Penetration to Tokamak Plasma

_{s}for fast atom ionization in plasma. The effective cross-section comprises all the main channels of beam ionization on plasma species, including the cascade (multi-step) processes of atom ionization. Thus, the neutral beam intensity (I) decay along the trajectory is written as:

_{e}—the plasma target density; σ

_{s}—the effective beam stopping cross-section due to ionization represented as:

_{ie}, σ

_{ip}, σ

_{iz}—are ionization cross sections of atoms in collisions with electrons, protons, and impurities of charge Z, respectively; σ

_{cx}is the charge exchange cross section on hydrogen ions, brackets mean averaging over the Maxwell distribution of electron velocities. The plots showing the σ

_{s}dependence on the atom energy and plasma density are shown in Figure 12a–c. When the neutral beam energy is less than E

_{b}~140 keV, the NB is produced more efficiently with positive ion beam sources, so after the source ion neutralization and dissociation, the beam consists of three energy fractions. From Figure 12b, for the lowest energy fraction (Е

_{1/3}), the stopping cross-section is up to 3 times higher than σ

_{s}value for the full (maximum) energy fraction Е

_{full}; in fact, this results in more intense ionization of low-energy beam fractions (Е

_{1/2}and Е

_{1/3}) at plasma periphery reducing the total NBI efficiency output in the plasma. Important note: Janev model is valid for beam energy above 60 keV/amu.

^{12}test particles) from BTR calculation produce the most accurate fast ion source distribution in space and angle, which makes essential data for fast ion numerical studies and experimental plasma scenario control. Examples of beam ionization distributions in DEMO-FNS plasma are shown in Figure 13. The fast ion source imprints are shown in two orthogonal planes—vertical and horizontal—along the neutral beam axis direction and obtained with the beam particle statistics ~10

^{6}test-atoms, which is much smaller than BTR regular capacity. The decay of each test atom and the produced fast ion density are calculated with (6).

#### 4.6. Shine-Through Power at Tokamak Chamber Wall

_{b}/E

_{c}= 2 − 5 [5]. For example, NB optimum energy for plasma temperature about T

_{e}= 5 keV corresponds to the values of 200–500 keV, but the latter would be unacceptable from the point of the direct shine-through power faced by the FNS-ST device first wall.

## 5. BTR Verification

- Neutral particle tracks
- Charged particle motion in a magnetic field.
- Charged particle motion in an electric field.
- Charged particle motion in a combined field.
- Beamlet current simplified profile (2D Gaussian distribution)
- Beamlet current complex profile (core and halo fractions)
- Positive beam source ion neutralization (H
^{+}/D^{+}) - Negative beam source ion neutralization (H
^{−}/D^{−}) - Neutral particle ionization on gas target (beam ducts volume)
- Neutral particle ionization in plasma (tokamak volume)
- Neutral beam power/particle balance after the neutralizer
- Accelerated source beam power/particle balance without re-ionization losses
- Accelerated source beam power/particle full balance (all processes included)

- Cut-off current input parameter effect
- Magnetic field magnitude effect
- Angular misfocusing effects
- Atomic cross-sections and target density effects
- The effects of the geometry representation accuracy, meshing and time steps, etc.

## 6. BTR Applications

#### 6.1. Beamline Transmission and Power Losses

#### 6.2. Neutral Injection Port Optimization

_{inj}) by 20–30%. When the NB window width is reduced by 5 cm only, the power losses along the beam transmission become unacceptable.

#### 6.3. Neutral Beam Shine-Through

^{12}test particles) are more than sufficient for the most accurate fast ion distributions both in space and angle, which is essential for beam-driven plasma scenario studies. The beam imprints shown in Figure 13 are calculated in the vertical and horizontal planes along the beam axis direction, with the beam statistics reduced to ~10

^{6}test atoms. The decay of each test atom is calculated with expression (6). The comparative analysis of the beam imprints has proved the shape effect to be essential for the beam deposition and resulting beam-driven quantities. The effect is clearly observed in Figure 12, where two characteristic beam geometries are compared: a rectangular beam shape (a bunch of parallel rays) and a Gaussian beam shape of 1280 beamlets with realistic focusing and 7 mrad divergence, with 15% halo (30 mrad).

#### 6.4. Benchmark of Different Numerical Tools for NBI Simulation

## 7. Conclusions and Outlook

^{10}beam test particles in a few hours maximum on humble old Windows systems, although its power is more evident in multi-thread execution on at least 4–8 cores. BTR numerical models are light and flexible, the calculation results are consistent and stable, and the methods can be verified analytically. BTR is still evolving; basic support is available to all BTR users. The information on BTR upgrades and code manuals can be found online [3]. Starting in 2024, the BTR Verification Manual will also become available online.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**(

**a**) The beam source particles statistical distribution before neutralization, left to right: (X, Y), (ϴx, ϴy), (X, ϴx), (Y, ϴy), where X, Y—horizontal and vertical position in the plane, ϴx, ϴy—horizontal and vertical angle from the beam main axis. The beam source spatial dimensions (shown in the left plot) correspond to the plasma emitter rectangle W × H = 18 × 115 cm

^{2}. (

**b**) The neutral beam distribution in the NBI port plane: (X, Y), (ϴx, ϴy), (X, ϴx), (Y, ϴy), where X, Y—horizontal and vertical position in the plane, ϴx, ϴy—horizontal and vertical angle from the beam main axis.

**Figure 5.**BTR screen with beamline standard ITER-like geometry and beamlets’ axes (X, Y, and Z units are [m]).

**Figure 7.**BTR plots with neutral beam power density at virtual planes: upper—along the beamline; lower—across the beamline (taken at different distances from BS GG).

**Figure 8.**Power density (PD) maps of the injected NB footprint (maximum value is coded white, minimum—black, background area is shown olive), and correspondent power density profiles (FNS-ST, port with size 30 × 60 cm

^{2}). The beamlets’ focus is on a horizontal plane at 10.5 m: (

**a**) ideal alignment, total power—3.49 MW, maximum PD—43.3 MW/m

^{2}; (

**b**) beam misalignment 4/−6 mrad, total power—3.27 MW, maximum PD—43.1 MW/m

^{2}. The maps are shown in local coordinates.

**Figure 9.**BTR subplots with gas target and beam fractions in the neutralizer (ITER NBI): (

**a**) gas local density and thickness; (

**b**) species source/loss rates; (

**c**) species integral output.

**Figure 10.**Residual ions deflection and dumping in ERID channel (DEMO-FNS): (

**a**) positive/negative ions trajectories; (

**b**) power density map and profiles at the dumping panel.

**Figure 11.**BTR screen with re-ionized particles (red) downstream of the neutralizer (DEMO-FNS). Atoms are shown in blue, negative source ions—in green color.

**Figure 12.**Neutral beam stopping calculation: (

**a**) stopping cross-section (${\mathsf{\sigma}}_{\mathrm{S}}$, 10

^{−16}cm

^{2}) vs. beam energy and plasma density; (

**b**) stopping cross-section (${\mathsf{\sigma}}_{\mathrm{S}}$, 10

^{−16}cm

^{2}) for varied temperature (T

_{e}) and plasma density (n

_{e}); (

**c**) stopping cross-section (${\mathsf{\sigma}}_{\mathrm{S}}$, 10

^{−16}cm

^{2}) for H/D/T beams, T

_{e}= 5 keV, n

_{e}= 0.3 × 10

^{20}m

^{−3}; (

**d**) neutral beam current attenuation (green) and ion birth rate (red) along NB passage through plasma.

**Figure 13.**BTR subplots with neutral beam spatial deposition (ionization rate intensity) in DEMO-FNS plasma (BTR plots) along the injected neutral beam axis (NB enters from the left): (

**a**,

**b**) vertical cross-section plane, (

**c**,

**d**) horizontal cross-section plane; (

**a**,

**c**) correspond to rectangular beam shape; (

**b**,

**d**) refer to the realistic beam shape—with divergence and beamlet focusing.

**Figure 14.**BTR plots with NB shine-through PD at FNS-ST first wall (NBI port size 0.3 × 0.6 m

^{2}) for two operation cases: (

**a**) ideal beam focus, total power—0.147 MW, peak PD—1.65 MW/m

^{2}; (

**b**) beam misalignment 4/−6 mrad in horizontal and vertical planes, total power—0.167 MW, peak PD—2.43 MW/m

^{2}.

**Figure 15.**DEMO-FNS NBI efficiency as a function of vertical magnetic field (B

_{z}): (

**a**) total neutral power (P

_{Neutr}) at the Neutralizer exit; (

**b**) beamline geometry transmission (P

_{inj}/P

_{Neutr}) and total power efficiency (P

_{inj}/P

_{0}) shown in %.

**Figure 16.**DEMO-FNS NBI efficiency as a function of beam misalignment in horizontal and vertical planes: (

**a**) total injected power (Pinj) at the duct exit; (

**b**) beamline geometry transmission (P

_{inj}/P

_{Neutr}) and total power efficiency (P

_{inj}/P

_{0}).

**Figure 17.**Total power deposition at DEMO-FNS NBI major components during the beam injection to tokamak (with calorimeter in open position).

**Figure 18.**BTR subplots showing the injected beam footprints in NB port plane illustrating the effect of the beam misfocusing and/or magnetic field on injected beam power in DEMO-FNS tokamak: (

**a**) source beam misalignment values in horizontal and vertical directions 1 mrad and 4 mrad (17.5% lost); (

**b**) misalignment values 2 mrad and 4 mrad (20% lost); (

**c**) ideal beam focusing with vertical magnetic field 3 G (33% lost).

**Figure 19.**BTR plots with injected neutral beam stopping in DEMO-FNS tokamak for two values of plasma density: (

**a**) n

_{e}= 10

^{20}m

^{−3}; (

**b**) n

_{e}= 0.5 × 10

^{20}m

^{−3}.

**Figure 20.**BTR plots with the injected neutral beam shine-through power footprints at the first wall in DEMO-FNS tokamak: (

**a**) rectangular beam shape; (

**b**) gauss beam shape.

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## Share and Cite

**MDPI and ACS Style**

Dlougach, E.; Kichik, M.
Beam Transmission (BTR) Software for Efficient Neutral Beam Injector Design and Tokamak Operation. *Software* **2023**, *2*, 476-503.
https://doi.org/10.3390/software2040022

**AMA Style**

Dlougach E, Kichik M.
Beam Transmission (BTR) Software for Efficient Neutral Beam Injector Design and Tokamak Operation. *Software*. 2023; 2(4):476-503.
https://doi.org/10.3390/software2040022

**Chicago/Turabian Style**

Dlougach, Eugenia, and Margarita Kichik.
2023. "Beam Transmission (BTR) Software for Efficient Neutral Beam Injector Design and Tokamak Operation" *Software* 2, no. 4: 476-503.
https://doi.org/10.3390/software2040022