1000 Solved Problems in Modern Physics

9.1 Basic Concepts and Formulae 487

ω

ω 0

=

m 0

m

=

1

γ

(9.13)

Synchrotron

The synchrotron radiation loss per turn

ΔE=

4 π

3 R

e^2

4 π 0

(

E

mc^2

) 4

(9.14)

Linear Accelerator

Total length

L=

1

2 f

(

2eV

m

)^1 / 2

Σ

√

n (9.15)

wherenis the number of drift tubes.

Colliders

Luminosity

L=

nN 1 N 2 f

A

(9.16)

The number of interactions per second

N=Lσ (9.17)

whereσis the interaction cross-section of a given type

N 1 orN 2 =the number of particles/bunch in each beam

A=area of cross-section of intersecting beams

n=number of bunches/beam

f=frequency of revolution

Detectors

Proportional counter

Gas multiplication factor

M=

CV

Ne

(9.18)

whereNis number of ion pairs released.