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Appendix C — Glossary

Domain terms used throughout the manual.

A

  • Adiabatic damping — divergences x', y' shrink during acceleration as p_in/p_out. Geometric ε shrinks; normalised ε_n is invariant.
  • Aperture — the local maximum allowed transverse extent. Particles outside are lost.
  • AGS — Alternating Gradient Synchrotron focusing: pair a focusing quad with a defocusing quad, net is focusing.

B

  • Beam pipe — the vacuum chamber the beam travels in. Sets the aperture.
  • Bend / dipole — magnet that bends the beam trajectory.
  • Boris pusher — symplectic time-step integrator for charged-particle motion in EM fields.

C

  • CIC — Cloud-In-Cell, the 8-corner trilinear particle-mesh shape function (1st order).
  • Continuous beam — DC, unbunched. No longitudinal structure. Pre-RFQ.
  • Crandall 2-term — RFQ field expansion; HELIX's M1.

D

  • Drift — field-free propagation.
  • DC mode — continuous-beam tracking; HELIX's continuous=True flag.
  • Dispersion — D_x = ∂x/∂(Δp/p₀); off-momentum particles take different paths.
  • DKD — Drift-Kick-Drift, second-order symplectic field-map integrator (velocity-Verlet).

E

  • Eigenemittance — symplectic-eigenvalue invariant emittance; 4-D (ε₁, ε₂) or 6-D (ε_E1, ε_E2, ε_E3).
  • Emittance — phase-space ellipse area / π. Geometric (mm·mrad) or normalised (β·γ·ε).
  • Envelope solver — propagates the σ-matrix instead of individual particles.

F

  • Field map — tabulated electromagnetic field on a regular grid, integrated by RK4.
  • FODO — Focusing-Drift-Defocusing-Drift cell.
  • FREQ jump — RF frequency boundary in a multi-section linac.

G

  • Geometric emittance — ε in mm·mrad, untouched by βγ conversion.

H

  • H⁻ — singly-negative hydrogen ion; PIP-II's particle. Has a loosely-bound second electron prone to stripping.
  • Halo — beam-tail population beyond the Gaussian core. HELIX records the kurtosis halo parameter h = ⟨x⁴⟩/⟨x²⟩² − 1 (Gaussian ⇒ 2, KV ⇒ 1; values noticeably above 2 indicate halo).
  • HEBT — High-Energy Beam Transport (downstream of linac).
  • HWR — Half-Wave Resonator, a low-β SRF cavity type.

I

  • IBS — IntraBeam Stripping; H⁻ losing electron via in-bunch collisions.
  • IGF — Integrated Green Function; HELIX's PIC Poisson kernel.
  • Image charge — charge on the beam-pipe wall that mirrors the bunch. Not modelled in HELIX.

J

(none)

K

  • KV — Kapchinskij-Vladimirskij, the uniform-charge-density analytic distribution. Self-consistent with linear envelope dynamics.

L

  • Larmor — angular frequency of cyclotron motion in a B-field.
  • LB650 — Low-Beta 650 MHz; one of PIP-II's SRF cavity types.
  • LEBT — Low-Energy Beam Transport (between source and RFQ).
  • Levenberg-Marquardt — non-linear least-squares solver used by the matcher.

M

  • MEBT — Medium-Energy Beam Transport (between RFQ and first SRF cavity).
  • Mismatch — ε scaled by a factor != 1; tests Twiss-tolerance.
  • Multipole — sextupole, octupole, decapole, dodecapole — thin kicks.

N

  • Normalised emittance — ε_n = β·γ·ε, invariant under acceleration.

P

  • Partran — TraceWin's multi-particle tracker; HELIX's validation reference.
  • PIC — Particle-In-Cell; the 3-D space-charge solver method.
  • PIP-II — Proton Improvement Plan II, a Fermilab linac; HELIX's reference benchmark.
  • PMQ — Permanent Magnet Quadrupole.

Q

  • Quadrupole — alternating-gradient focusing magnet.

R

  • RFQ — Radio-Frequency Quadrupole; bunches and accelerates the DC beam. PIP-II's first accelerating element.
  • RK4 — fourth-order Runge-Kutta integrator.

S

  • Sacherer ODE — DC-beam envelope equation.
  • SC — Space Charge.
  • Sigma matrix — 6×6 second-moment matrix of the beam.
  • Skew quadrupole — quad with magnetic axes rotated about z; couples (x, x') with (y, y').
  • SRF — Superconducting RF (cavity).
  • Solenoid — axial-B-field magnet, focuses both planes.
  • SSR — Single Spoke Resonator, mid-β SRF cavity type.
  • σ — RMS standard deviation; e.g. σ_x.

T

  • TraceWin — Saclay's commercial linac code; HELIX's validation benchmark.
  • TSC — Triangular-Shaped Cloud, 27-cell quadratic particle-mesh shape (2nd order).
  • Twiss — α, β, γ Courant-Snyder parameters describing the phase-space ellipse.

V

  • VaneRFQ — HELIX's whole-RFQ wrapper around RfqCell instances.

W

  • Waterbag — uniform-distribution-in-6D-ellipsoid; textbook-benchmark distribution.
  • Wangler halo parameter — kurtosis-style halo measure; HELIX's halo_x/halo_y implement h = ⟨x⁴⟩/⟨x²⟩² − 1 (Gaussian ⇒ 2, KV ⇒ 1).

Z

  • z — longitudinal coordinate; in HELIX's reduced phase space, represented by Δφ.

Symbols

  • α, β, γ — Twiss parameters (or β = v/c, γ = Lorentz factor).
  • ε — emittance.
  • σ — RMS beam size.
  • Σ — full 6×6 σ-matrix.
  • κ(s) — focusing function (envelope ODE coefficient).
  • K — generalised perveance K = qI / (2πε₀mc³(βγ)³).

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