RfqCell¶

A single RFQ (Radio-Frequency Quadrupole) cell — the building block of an RFQ buncher/accelerator that turns a continuous DC ion beam into a bunched, accelerated beam suitable for the downstream linac. Implements the Crandall 2-term potential expansion (M1 in HELIX nomenclature).

TL;DR¶

	TraceWin / Toutatis	HELIX
Keyword	`RFQ_CELL` (Toutatis-format `.dat`)	`RfqCell(...)`
Voltage	inter-vane voltage V (V)	same `voltage_V`
A₁₀	Crandall 2-term coefficient	same
Modulation m	vane modulation factor (m ≥ 1)	same
φ_s	synchronous phase (deg)	`phi_s_deg`
cell_type	±2 / ±3 / ±4	same

Conventions:

Voltage is in volts (not MV) — typical RFQs run 50-150 kV.
cell_type: ±2 = accelerating, ±3 = front-end / shaper, ±4 = transcell. The sign selects which neighbour cell the transverse model couples to.
Internally split into N substeps (auto-picked, ≤0.1 mm/substep, ≥20 substeps). See VaneRFQ for multi-cell.

Tutorial¶

An RFQ cell uses four electrodes (vanes) with a sinusoidally modulated tip profile to produce a transverse focusing potential that simultaneously bunches and accelerates.

The Crandall 2-term potential is

\[ U(r, \theta, z) = \frac{V}{2}\left[ A_{01}\left(\frac{r}{r_0}\right)^2 \cos(2\theta) + A_{10} I_0(kr) \cos(kz) \right] \]

where r₀ is the average radius, k = π/L (cell wavenumber), I₀ is the modified Bessel function, A₀₁ ≈ 1 (transverse focusing), A₁₀ encodes modulation strength (longitudinal acceleration).

Transfer matrix and per-substep integration¶

Like a FieldMap, an RFQ cell has no closed-form 6×6 transfer matrix — the 2-term potential mixes transverse position with z non-linearly. The production integrator in this codebase is the 2-term Strang Drift–Kick–Drift splitting: each substep applies a half-drift, the full AG transverse + longitudinal kick, then the second half-drift (TraceWin manual convention). The default field_model="2term" — A_quad = (1−A₁₀)/R₀² with S = −sign(Type) — is the path validated against TraceWin envelope output; three diagnostic-only variants (crand_x, crand_x_noflip, pdf_2term) are kept for comparison but blow up in envelope runs and must not be used for production.

A Boris time-stepper + Hybrid field source exploration exists in the separate rfqtrack subproject — it is not the integrator behind RfqCell in linac_gen.

For envelope tracking, the per-substep 6×6 Jacobian is built by finite differencing the pusher and chained over the cell.

Block	Effect
(x, x', y, y') 4×4	strong AG focusing from sin(2θ) potential term
(Δφ, ΔW) 2×2	bunching + acceleration from cos(kz) modulation
Cross blocks	(x, Δφ) and (y, Δφ) non-zero — RFQ deliberately couples transverse and longitudinal

The transverse-longitudinal coupling is intrinsic to the RFQ — it is what bunches a continuous beam. No purely-transverse subspace is invariant.

Validation status¶

The numbers below come from the rfqtrack subproject's Boris time-stepper + Hybrid field source exploration on PXIE NOSC (continuous beam, no SC) — not from the linac_gen RfqCell integrator documented on this page:

Quantity	Ratio (rfqtrack Boris+Hybrid) / TW
σ_x	0.83
σ_y	0.88
W (energy)	0.94
Transmission	92 %

In that study the 2-term Strang-splitting integrator showed σ_y blow-up by 3.1× at the M1 ceiling — the Boris/Hybrid path closed that gap in rfqtrack. Within linac_gen, the 2-term Strang DKD remains the production path (σ_x within ~30 % of the TraceWin reference at the whole-RFQ level, see VaneRFQ).

Higher-fidelity variants (M3-family laplace2d/3d/8-term) hit structural blockers; M1 is the production path.

API reference¶

linac_gen.elements.rfq_cell.RfqCell(
    name: str,
    voltage_V: float,             # inter-vane V (volts)
    r0_mm: float,                 # vane mean radius R₀ (mm)
    A10: float,                   # Crandall 2-term coefficient
    modulation: float,            # m
    length_mm: float,             # cell length L (mm)
    phi_s_deg: float,             # synchronous phase (deg)
    cell_type: int,               # ±2 / ±3 / ±4
    Tc_mm: float = 0.0,
    dP_deg: float = 0.0,
    n_steps: int | None = None,   # auto-picked if None
    type_prev: int | None = None,
    type_next: int | None = None,
    A_quad: float | None = None,
    aperture: float = 0.0,
    field_model: str = "2term",
)

Parameter	Default	Units	Notes
`name`	(required)	—	identifier
`voltage_V`	(required)	V	inter-vane voltage (typical 50-150 kV)
`r0_mm`	(required)	mm	vane mean radius R₀
`A10`	(required)	—	Crandall 2-term acceleration coefficient
`modulation`	(required)	—	tip modulation m (≥ 1); feeds the 2-term `A_quad` default
`length_mm`	(required)	mm	cell length L (no βλ/2 check enforced)
`phi_s_deg`	(required)	deg	synchronous phase
`cell_type`	(required)	int	±2 = accelerating, ±3 = front-end / shaper, ±4 = transcell
`Tc_mm`	0.0	mm	transverse curvature (TraceWin `Tc`) — accepted for parser compatibility, currently unused
`dP_deg`	0.0	deg	output-phase shift (TraceWin `dP`), applied at cell exit
`n_steps`	None	—	auto-picked: max(20, ceil(L/0.1 mm)) when None
`type_prev`, `type_next`	None	int	neighbouring cell types (S = −sign(type[n±1])); default to `cell_type`
`A_quad`	None	1/mm²	DC quadrupole coefficient override; None → `(1 − A₁₀)/R₀²`
`aperture`	0.0	mm	loss-tracking aperture radius; 0 = no check
`field_model`	`"2term"`	—	production `2term`; diagnostic-only `crand_x`, `crand_x_noflip`, `pdf_2term`

Source¶

linac_gen/elements/rfq_cell.py:135 (constructor)