Page

**2**

Linear Algebra (Matrix calculations), first order ion-optics (e.g. TRANSPORT)

Higher order ion-optics code to solve equation of motion, (e.g. COSY Infinity,

GIOS, RAYTRACE (historic)

Electro-magnetic field program (solution of Maxwell’s Equations),

(e.g. finite element (FE) codes, 2d & 3d: POISSON, TOSCA, MagNet)

Properties of incoming charged particles and design function of electro-magnetic

facility, beam, reaction products (e.g. kinematic codes, charge distributions of

heavy ions, energy losses in targets)

Many other specialized programs, e.g for accelerator design (e.g. synchrotrons,

cyclotrons) not covered in this lecure series.

Slide 7

Optics of Charged Particles, Hermann Wollnik, Academic Press, Orlando, 1987

The Optics of Charged Particle Beams, David.C Carey, Harwood Academic

Publishers, New York 1987

Accelerator Physics, S.Y. Lee, World Scientific Publishing, Singapore, 1999

TRANSPORT, A Computer Program for Designing Charged Particle Beam

Transport Systems, K.L. Brown, D.C. Carey, Ch. Iselin, F. Rotacker,

Report CERN 80-04, Geneva, 1980

Computer-Aided Design in Magnetics, D.A. Lowther, P. Silvester, Springer 1985

Slide 8

Ions in static or quasi-static electro-magnetic fields

Lorentz Force

q = electric charge

B = magn. induction

E = electric field

v = velocity

For momentum analysis the magnetic force is preferred because the force is always perpendicular to B. Therefore v, p and E are constant.

Force in magnetic dipole B = const: p = q B r

p = mv = momentum

= bending radius

Br = magn. rigidity

For ion acceleration electric forces are used.

Dipole field B

perpendicular

to paper plane

Radius r

Object (size x0)

General rule:

Scaling of magnetic system

in the linear region results

in the same ion-optics

Note: Dispersion dx/dp

used in magnetic analysis,

e.g. Spectrometers, magn.

Separators,

x

p

p+dp

(1)

Slide 9

Definition of BEAM for mathematical formulation of ion-optics

What is a beam, what shapes it,

how do we know its properties ?

Beam parameters, the long list

Beam rays and distributions

Beam line elements, paraxial lin. approx.

higher orders in spectrometers

System of diagnostic instruments

Not to forget: Atomic charge Q

Number of particles n

Slide 10

Ion-optical

element

Code TRANSPORT:

(x, Q, y, F, 1, dp/p)

(1, 2, 3, 4, 5, 6 )

Convenient “easy to use” program

- 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

- Magnetic field uses sound waves to ignite sun's ring of fire
- Heat-Energy on the Move
- Resource Acquisition and Transport in Vascular Plants
- Simulation at NASA for the Space Radiation Effort
- Friction
- Newton's laws of motion
- Understanding Heat Transfer, Conduction, Convection and Radiation

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