Beamline

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The pieces of beamtracer.beamline in a row, from the grid to the port: a group of aimed beamlets, the charge states the neutralizer leaves, the residual-ion dump, the duct with its gas and the stray field, and where the power goes. At the end the neutrals at the port are written out as a dataset, in the tokamak’s frame, for the deposition in the plasma (freeofcharge).

The numbers are illustrative: a group of 5 by 16 beamlets of 1 MeV deuterium, 5 mrad each, curved to 7 m; the cross sections are placeholders, as plasmacoll holds no beam stripping data.

import matplotlib.pyplot as plt
import numpy as np
import plasma_plots as pp
from plasmacoll import ChargeStateTransitions
from scipy import constants
from simgeometry import Cuboid

from beamtracer.beamline import (
    ApertureGrid,
    Duct,
    FieldRegion,
    Markers,
    beamline_summary,
    box_field,
    gaussian_beam,
    profile_field,
)

mass = 2.014 * constants.atomic_mass
speed = np.sqrt(2 * 1e6 * constants.e / mass)
beamlet = gaussian_beam(1500, power=2e5, speed=speed, width=2e-3, divergence=5e-3)
grid = ApertureGrid.regular(16, 5, (0.020, 0.022), focal_length=(7.0, 7.0))
beam = grid.markers(beamlet)

# the neutralizer: 60 % neutrals, 20 % each of D- and D+
beam.state = np.random.default_rng(0).choice(3, size=len(beam), p=[0.2, 0.6, 0.2])
print(f"{len(beam)} markers, {beam.total_power / 1e6:.0f} MW")

120000 markers, 16 MW

The dump and the duct

The dump: two plates 0.12 m apart from 0.5 to 2.3 m, 20 kV between them, across the narrow side of the group. The duct: a rectangular channel of four plates from 2.3 to 6 m, its bore 0.12 by 0.24 m, with 1e18 m⁻³ of D $_2$ and a vertical stray field rising from 5 to 50 mT towards the port at 6 m.

dump_start, dump_end, gap = 0.5, 2.3, 0.12
dump_length = dump_end - dump_start
plates = [
    Cuboid(
        ((dump_start + dump_end) / 2, s * (gap / 2 + 0.005), 0),
        (dump_length, 0.01, 0.5),
    )
    for s in (1, -1)
]
dump = FieldRegion(
    plates,
    exit=dump_end,
    mass=mass,
    electric=box_field(
        (0, 20e3 / gap, 0), (dump_start, -gap / 2, -0.25), (dump_end, gap / 2, 0.25)
    ),
    step=2e-3,
).trace(beam)

port, half_y, half_z, wall = 6.0, 0.06, 0.12, 0.05
middle, duct_length = (dump_end + port) / 2, port - dump_end
duct_walls = [
    Cuboid(
        (middle, s * (half_y + wall / 2), 0), (duct_length, wall, 2 * (half_z + wall))
    )
    for s in (1, -1)
] + [
    Cuboid((middle, 0, s * (half_z + wall / 2)), (duct_length, 2 * half_y, wall))
    for s in (1, -1)
]
transitions = ChargeStateTransitions({"D2": {("0", "+"): 1.5e-20}})
duct = Duct(duct_walls, port=port, transitions=transitions, gas={"D2": 1e18}).trace(
    dump.exit
)
stray = profile_field([dump_end, port], [[0, 0], [0, 0], [0.005, 0.05]])
bent = FieldRegion(duct_walls, exit=port, mass=mass, magnetic=stray).trace(
    duct.reionized
)

summary = beamline_summary(
    Markers.concatenate([duct.port, bent.exit]),
    {"dump": dump.wall, "duct": duct.wall, "duct, reionized": bent.wall},
    power=beam.total_power,
    work=dump.work + bent.work,  # what the dump field gave the ions
    halo_radius=0.05,
    footprint_extent=(-0.1, 0.1, -0.15, 0.15),
    bins=50,
)
summary

Where the power goes

parts = ["port"] + list(summary.part.values)
values = [float(summary.power_port)] + list(summary.power_on.values)
with pp.figure(figsize=(7, 3.2)) as fig:
    ax = fig[0]
    ax.barh(parts[::-1], np.array(values[::-1]) / 1e6, color="#2a78d6")
    for k, v in enumerate(values[::-1]):
        ax.text(
            v / 1e6,
            k,
            f" {v / 1e6:.1f} MW ({v / float(summary.power_in):.0%})",
            va="center",
        )
    ax.set_xlabel("power [MW]")
    ax.set_xlim(0, 1.3 * max(values) / 1e6)

The dump takes the 40 % of the beam that left the neutralizer charged. Of the neutrals the duct walls take the tails of the beam, the gas reionizes a few percent, and the stray field turns those onto the walls near the port. The rest, about half the beam, reaches the port.

The footprint at the port

The group converges towards its focus at 7 m, 1 m behind the port. The power density at the port, clipped at $y = \pm 0.06$ m by the duct, with a circle of 5 cm round the beam’s centre; the power beyond it is power_halo. Here that is the Gaussian tail of the beamlets: the halo the experiments see, a broad component of some 30 mrad, appears only if the beamlet carries one.

footprint = (summary.footprint / 1e6).assign_attrs(units="MW/m²")
result = footprint.plasma.plot.slice(
    x="y", y="z", equal_aspect=True, colorbar_label="MW/m²"
)
ax = plt.gca()
ax.add_patch(plt.Circle((0, 0), 0.05, fill=False, color="white", ls="--"))
print(
    f"beyond 5 cm: {float(summary.power_halo) / float(summary.power_port):.1%} of the port power"
)

beyond 5 cm: 23.1% of the port power

Handing the neutrals on

The neutrals through the port, placed in the tokamak’s frame (here the port at $R = 9$ m, the beam aimed at a tangency radius of 5.3 m, horizontal), as a dataset with their weight in atoms per second, which freeofcharge’s NeutralBeam.from_dataset reads:

at_port = Markers.concatenate([duct.port, bent.exit]).drift_to(port)
neutral = at_port.subset(at_port.state == at_port.states.index("0"))
tangency, start = 5.3, 9.0
along = np.sqrt(start**2 - tangency**2)
origin = (tangency, -along, 0.0)
direction = (0.0, 1.0, 0.0)
markers = neutral.placed(origin, direction, x=port).to_dataset(mass)
markers