An Introduction to the Ion-Optics of Magnet Spectrometers

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Equivalence of Transport of ONE Ray ⇔ Ellipse Defining the σ Matrix representing a Beam
The 2-dimensional 2 case ( x, Θ ) Ellipse Area = π(det σ) 1/2 Emittance ε = (det σ) 1/2 is constant for fixed energy & conservative forces (Liouville’s Theorem) Note: ε shrinks (increases) with acceleration (deceleration); Dissipative forces: ε increases in gases; electron, stochastic, laser cooling σ = ⎛σ 11 σ 21 ⎫ ⎝σ 21 σ 22 ⎭ σ −1 = 1/ε 2 ⎛σ 22 −σ 21 ⎫ ⎝−σ 21 σ 11 ⎭ Exercise 1: Show that: 2 dimensional cut x-Θ is shown Real, pos. definite symmetric σ Matrix σσ −1 = ⎛1 0 ⎫ ⎝ 0 1⎭ Inverse Matrix = I (Unity Matrix) 2-dim. Coord. vectors (point in phase space) X = ⎛x ⎫ X T = (x Θ) ⎝Θ⎭ Ellipse in Matrix notation: X T σ −1 X = 1 (6) Exercise 2: Show that Matrix notation is equivalent to known Ellipse equation: σ 22 x 2 −2σ 21 x Θ + σ 11 Θ 2 = ε 2
Page 1 and 2: An Introduction to the Ion-Optics o
Page 3 and 4: 1st Lecture 1 st Lecture: 2/27/06,
Page 5 and 6: Who needs ion-optics optics ? • A
Page 7 and 8: Basic tools of the trade • Geomet
Page 9 and 10: Ions in static or quasi-static stat
Page 11 and 12: Code TRANSPORT: (x, Θ, y, Φ, 1, d
Page 13 and 14: 6x6 Matrix representing optic eleme
Page 15 and 16: 6x6 Matrix representing first optic
Page 17: Defining a BEAM Ellipse Area = π(d
Page 21 and 22: Transport of 6-dim 6 σ Matrix Cons
Page 23 and 24: Increase of Emittance ε due to deg
Page 25 and 26: Emittance ε measurement by tuning
Page 27 and 28: Kinematic affect in K600 spectrum w
Page 29 and 30: Effect of 2 nd order aberrations Sa
Page 31 and 32: (15) Solving the equations of Motio
Page 33 and 34: Schematic Layout of an Achromatic M
Page 35 and 36: Achromatic magnet separator with We
Page 37 and 38: Design of a Fragment Separator 1 st
Page 39 and 40: TRIμP ion-optics optics This study
Page 41 and 42: Intermediate, dispersive Focal Plan
Page 43 and 44: The First Users at the TRIμP Separ

An Introduction to the Ion-Optics of Magnet Spectrometers

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