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)

(15)

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

(16)

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

- Static and Kinetic Friction
- Friction
- Newton's Laws
- Simulation at NASA for the Space Radiation Effort
- Practical Applications of Solar Energy
- Solar Thermal Energy
- Sensory and Motor Mechanisms

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