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Worked example: DC LEBT

A pre-RFQ Low-Energy Beam Transport (LEBT) operating on a continuous H⁻ beam from the source. Demonstrates HELIX's DC-mode handling: continuous=True, 2-D analytic SC kick, no longitudinal physics.

Source

Mirrors examples/lebt_dc_demo.py:

python examples/lebt_dc_demo.py

The setup

A 30 keV H⁻ beam through two solenoids:

from linac_gen.core.particle import H_MINUS
from linac_gen.core.reference import ReferenceParticle
from linac_gen.core.config import BeamConfig, SpaceChargeConfig
from linac_gen.distributions.factory import create_beam
from linac_gen.elements.solenoid import Solenoid
from linac_gen.elements.drift import Drift
from linac_gen.core.lattice import Lattice
from linac_gen.core.simulation import Simulation

beam_cfg = BeamConfig(
    species="H-",
    energy=0.030,                   # 30 keV (LEBT entrance)
    frequency=162.5,                # downstream RFQ frequency
    current=5.0,
    n_particles=10_000,
    distribution="gaussian", cutoff=4.0,
    emit_nx=0.20, emit_ny=0.20,
    alpha_x=0.0, beta_x=0.10,
    alpha_y=0.0, beta_y=0.10,
    emit_z=0.0,                     # no longitudinal structure
    alpha_z=0.0, beta_z=1.0,
    continuous=True,                # ← critical
)
beam = create_beam(beam_cfg, seed=42)

lat = Lattice()
lat.add(Drift(name="D0", length=200.0))
lat.add(Solenoid(name="SOL1", length=300.0, field=0.20))
lat.add(Drift(name="D1", length=400.0))
lat.add(Solenoid(name="SOL2", length=300.0, field=0.20))
lat.add(Drift(name="D2", length=200.0))

# DC SC: 2-D analytic kick
sc = SpaceChargeConfig(dc_kernel="gaussian")
sim = Simulation(lat, beam, space_charge=sc)
results = sim.run()

What's special

  1. continuous=True in BeamConfig — turns on DC-aware physics throughout.
  2. emit_z=0 — DC beams have no longitudinal Twiss.
  3. dc_kernel="gaussian" in SpaceChargeConfig — Bassetti-Erskine 2-D analytic SC kick instead of 3-D PIC.
  4. σ_φ, σ_W, ε_z are not physical in the recorder — flagged by results.continuous_at[i] == True.

ε oscillates through solenoids

Plot results.emit_x vs s — you'll see big oscillations through each solenoid, because the projected ε is not invariant under solenoid rotation. Compare to results.emit_n1 (the eigenemittance) which stays smooth — that's the real invariant.

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
ax.plot(results.s, results.emit_x, label="ε_x (projected)")
ax.plot(results.s, results.emit_n1, label="ε₁ (eigen)")
ax.legend(); ax.set_xlabel("s [mm]"); ax.set_ylabel("ε [mm·mrad]")

Cross-references

← Envelope demo · Continue to LEBT + RFQ →