LHeC RR interactive parameter list
, version 0.04, 26/02/2010 A simple LHC luminosity calculator is
here
.
Proton and electron
Number of bunches
k
b
=
revolution frequency
f
rev
=
Hz
Proton beam
Bunch population
N
p
=
protons
Beam momentum
p
p
=
GeV
energy
E
p
=
GeV
E
p
= √
p
p
2
+m
p
2
Lorentz gamma
γ
=
beta
β
=
γ = E
p
/ m
p
, β = √
1-γ
-2
Transverse emittance
ε
=
m
normalized
ε
N
=
m
ε
N
= ε β γ
Bunch length
σ
zp
=
m
Electron beam
bunch population
N
e
=
total current
I
e
=
A
I
e
= k
b
N
e
e f
rev
Beam momentum
p
e
=
GeV
Emittance horizontal
ε
xe
=
m
vertical
ε
ye
=
m
Bending radius
ρ
=
m
Synchr. loss per electron and turn
U
0
=
GeV
Synchr. loss total power
P
tot
=
MW
P
tot
= V
0
I
e
Bunch length
σ
ze
=
m
IP parameters
β
xp
=
m
β
yp
=
m
σ
xp
=
μm
σ
yp
=
μm
β
xe
=
m
β
ye
=
m
σ
xe
=
μm
σ
ye
=
μm
crossing angle Φ
x
=
rad
Performance
Lumi scalefactor
L
fac
=
cm
-2
s
-1
N
p
50mA / ( 4 π e ε)
Luminosity
L
0
=
cm
-2
s
-1
Crossing angle factor
F
c
=
Beam beam tune shift parameters, Φ
x
= 0
ξ
px
=
ξ
py
=
ξ
ex
=
ξ
ey
=