Page

**6**

magnets and paraxial beams

TRANSPORT code calculates 2nd order

by including Tmno elements explicitly

TRANSPORT formalism is not suitable

to calculate higher order ( >2 ).

TRANSPORT RAYTRACE

Notation

Rnm = (n|m)

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Slide 26

Methods of solving the equation of motion:

1) Determine the TRANSPORT matrix.

2) Code RAYTRACE slices the system in small sections along the z-axis and integrates numerically the particle ray through the system.

3) Code COSY Infinity uses Differential Algebraic techniques to arbitrary orders using matrix representation for fast calculations

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Slide 27

Some problems:

Range < 1 to > 1012 particles/s

Interference with beam, notably at low energies

Cost can be very high

Signal may not represent beam properties (e.g. blind viewer spot)

Some solutions:

Viewers, scintillators, quartz with CCD readout

Slits (movable) Faraday cups (current readout)

Harps, electronic readout, semi- transparent

Film (permanent record, dosimetry, e.g. in Proton Therapy)

Wire chambers (Spectrometer)

Faint beam 1012 ® 103 (Cyclotrons: MSU, RCNP, iThemba)

Slide 28

Typical in focal plane of

Modern Spectrometers:

Two position sensitive

Detectors:

Horizontal: X1, X2

Vertical: Y1, Y2

Fast plastic scintillators:

Particle identification

Time-of-Flight

Measurement with IUCF K600

Spectrometer illustrates from top

to bottom: focus near, down-

stream and upstream of

X1 detector, respectively

IUCF, K600 Spectrometer

Slide 29

Detector X1 X2

3 rays in focal plane

1.

2.

1.

2.

3.

Example Octupole

(S-shape in x-Q plane

Other Example:

Sextupole T122

C-shape in x-Q plot

3.

T1222

T126

- The Lecture Series
- 1st Lecture
- Motivation
- Who needs ion-optics anyway?
- Introductory remarks
- Basic tools of the trade
- Literature
- Defining a RAY
- Transport of a ray
- The 2-dimensional case ( x, Q )
- Courant-Snyder Notation
- Transport of 6-dim s Matrix
- Taylor expansion
- Solving the equations of Motion
- Discussion of Diagnostic Elements
- Diagnostics in focal plane of spectrometer
- Higher order beam aberrations

- Mechanical, Electromagnetic, Electrical, Chemical and Thermal
- Newton's laws of motion
- Direct heat utilization of geothermal energy
- Newton’s Laws of Motion
- Motion
- Newton’s law of universal gravitation
- Geophysical Concepts, Applications and Limitations

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