6 Design and Principles of Synchrotrons and Circular Colliders
241
The luminosity is increased by the enhancement factor H D which takes into
account the reduction of the nominal beam size by the disruptive field (pinch
effects).
This enhancement foctor is related to the beam disruption parameter
D x,y =
2r e Nσ z
γ σ x,y
σ x + σ y
(6.43)
For weak disruption (D 1) and round beams the enhancement factor can be
written as:
H D = 1 +
2
3
√
π
D + O
D
2
(6.44)
When the disruption is strong or for flat beams, computer simulations are
necessary.
6.4.8.2 Beamstrahlung
The strong synchrotron radiation (beamstrahlung) has two main effects:
– Spread of the centre of mass energy.
– Pair creation and background in the detectors.
It is parametrized by the parameter Y which can be written as the mean field
strength in the rest frame, normalized to the critical field B c :
Y =
< E + B >
B c
≈
5
6
r 2
e γ N
ασ z
σ x + σ y
(6.45)
B c =
m 2 c 3
e
≈ 4.4 × 10
13 G
(6.46)
6.5 Synchrotron Radiation and Damping
L. Rivkin
6.5.1 Basic Properties of Synchrotron Radiation
Charged particles radiate when they are deflected in the magnetic field [47]
(transverse acceleration) [see also Sect. 11.1 for a more detailed treatment]. In the