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 =
4π
3R
e
2
4ππ 0
E
mc 2
4
(9.14)
Linear Accelerator
Total length
L =
1
2 f
2 eV
m
1 / 2
Σ
√
n
(9.15)
where n is the number of drift tubes.
Colliders
Luminosity
L =
n N 1 N 2 f
A
(9.16)
The number of interactions per second
N = Lσ
(9.17)
where σ is the interaction cross-section of a given type
N 1 or N 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)
where N is number of ion pairs released.
487
ω
ω 0
=
m 0
m
=
1
γ
(9.13)
Synchrotron
The synchrotron radiation loss per turn
ΔE =
4π
3R
e
2
4ππ 0
E
mc 2
4
(9.14)
Linear Accelerator
Total length
L =
1
2 f
2 eV
m
1 / 2
Σ
√
n
(9.15)
where n is the number of drift tubes.
Colliders
Luminosity
L =
n N 1 N 2 f
A
(9.16)
The number of interactions per second
N = Lσ
(9.17)
where σ is the interaction cross-section of a given type
N 1 or N 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)
where N is number of ion pairs released.