The standard approach to measure beam
emittance in a transfer line
Massimo Giovannozzi - CERN
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling Studies, Imperial College
Summary
✦ Definitions/Properties
✦ Measurement in Rings
✦ Measurement in Transfer Lines
✦ Emittance reconstruction
✦ Error sources
✦ Conclusion
Acknowledgements: R. Cappi, M. Martini
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 1) Massimo Giovannozzi - CERN
Definitions
✦ the orbit in phase space of a particle in a lin-
ear (i.e. the Hamiltonian is quadratic in the
phase space co-ordinates) magnetic trans-
port channel is an ellipse:
γy2 + 2αyy′ + βy′2 = A2
✦ The surface (A2/π) of such an ellipse is an
invariant of motion.
✦ The parameters β, α, γ = (1 + α2)/β are
the so-called Twiss-parameters.
✦ Accelerator beams comprise some 1010 −
1013 particles. the beam distribution is
near-Gaussian, hence the beam emittance
is defined as
y =
σ2y
βy
From: P. J. Bryant and K. Johnsen “Circular Accelerators
and Storage Rings”
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 2) Massimo Giovannozzi - CERN
Properties - I
✦ The beam emittance is an invariant of motion for constant energy.
✦ It is possible to define an invariant quantity even in presence of acceleration:
∗y = β γ
σ2y
βy
= β γ y
✦ Remarks:
✧ The emittance is a property of the beam.
✧ The Twiss-parameters belong to the transport system.
✧ The beam envelope (σy) is the convolution of beam and transport system.
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 3) Massimo Giovannozzi - CERN
Properties - II
So far only particles with the same nominal momentum p0 are considered. when momentum
spread is present, the solution of the equation of motion can be written:
y(s) = yβ(s) + yD(s)
and
yD(s) = D(s)
∆p
p0
where
∆p
p0
=
p− p0
p0
Under the hypothesis of statistical independence, one obtains
σ2y = σ2β + σ2D = σ2β +
(
σp
p0
D
)2
hence
σ2β = σ2y −
(
σp
p0
D
)2
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 4) Massimo Giovannozzi - CERN
M e a s u r e m e n t s i n R i n g s - I
T h e o p t i c s i s u s u a l l y w e l l - k n o w n ( h e n c e β
y
) . t h e b e a m
e m i t t a n c e i s t h e n m e a s u r e b y d i r e c t a p p l i c a t i o n o f t h e v e r y
d e fi n i t i o n .
N o n d e s t r u c t i v e d e v i c e s a r e : R e s i d u a l G a s P r o fi l e M o n i t o r s ,
W i r e S c a n n e r s .
F e b r u a r y 2 3 - 2 4 , 2 0 0 1
W k h I
T h e s t a n d a r d a p p r o a c h t o m e a s u r e b e a m e m i t t a n c e i n a M a s s i m o G i o v a n n o z z i - C E R N
M e a s u r e m e n t s i n R i n g s - I I
D e s t r u c t i v e d e v i c e s a r e : B e a m s c o p e , F a s t S c r a p e r s .
F r o m : P . J . B r y a n t a n d K . J o h n s e n “ C i r c u l a r A c c e l e r a t o r s a n d S t o r a g e R i n g s ”
F e b r u a r y 2 3 - 2 4 , 2 0 0 1
W k h I
T h e s t a n d a r d a p p r o a c h t o m e a s u r e b e a m e m i t t a n c e i n a M a s s i m o G i o v a n n o z z i - C E R N
Measurements in Transfer Lines - I
✦ The beam profile should be measured at different locations along the transport channel
(usually three monitors are used).
✦ Some examples of beam profiles monitors used in transfer lines are:
✧ Secondary Emission Monitors (wires).
✧ Optical Transition Radiation Monitors.
✧ Secondary Emission monitors (grids).
✧ Multi Proportional Wire Chambers.
Increasing effect on beam:
Multiple Coulomb Scattering
Energy loss
✦ The transfer matrices between monitors are known.
✦ The dispersion function at monitors’ location is known (it should be measured
independently).
✦ The beam momentum spread σp/p0 should be also known.
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 7) Massimo Giovannozzi - CERN
Measurements in Transfer Lines - II
Some examples of beam profiles as measured by SEM-wires, SEM-grids and OTR.
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 8) Massimo Giovannozzi - CERN
Emittance reconstruction
The deconvolution of beam and optical parameters is based on the following assumptions:
✦ No linear coupling is present in
the transfer line (i.e. no skew
quadrupoles or solenoids).
✦ The beam should fill completely
the phase space ellipse.
The following formulas are used
y = σ2β,0 Λ βy =
1
Λ
αy =
Γ
2Λ
Γ =
[(σβ,2/σβ,0)2 − C22 ]/S22 − [(σβ,1/σβ,0)2 − C21 ]/S21
(C1/S1)− (C2/S2)
Λ2 = (σβ,1/σβ,0)2/S21 − (C1/S1)2 + (C1/S1)Γ− Γ2/4
Remark: Under certain hypothesis, D,D′ can be measured using more than three monitors.
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 9) Massimo Giovannozzi - CERN
Error sources - I
Two main error sources affect the reconstructed beam and optical parameters:
✦ Transport matrices: Their computation is based on the knowledge of the geometry (very
accurate) of the transfer line and of the magnetic properties of its elements.
In general these errors are very small and they can be neglected. Exceptions are extreme
cases, i.e. low or high energy beams. Also a possibility exists of direct measuring the
transfer matrices.
✦ Beam profiles: Many different effects influence the accuracy of the measured beam
profiles.
In the case of SEM-wires (mostly used at CERN) noise on the wires and the number of
wires covering the beam width are two important sources of errors.
The fitting procedure (Gaussian or spline at CERN) can also introduce a bias in the value
of the reconstructed emittance.
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 10) Massimo Giovannozzi - CERN
E r r o r s o u r c e s - I I
T h e f o l l o w i n g p l o t s s h o w s t h e e r r o r o n t h e r e c o n s t r u c t e d
b e a m e m i t t a n c e v s n u m b e r o f w i r e s a n d r e l a t i v e e r r o r p e r w i r e
( s e e M . M a r t i n i , C E R N P S / P A N o t e 9 2 - 0 3 ) .
0
5
1 0
1 5
2 0
3 8 1 3 1 8 2 3
N u m b e r o f w i r e s o v e r 4 σ
∆
ε/
ε
(%
)
S e r i e s 1 S e r i e s 2
S e r i e s 3 S e r i e s 4
R e l . e r r . 0 . 5 % R e l . e r r . 1 %
R e l . e r r . 5 % R e l . e r r . 1 0 %
0
5
1 0
1 5
2 0
2 5
3 0
3 5
4 0
3 8 1 3 1 8 2 3
N u m b e r o f w i r e s o v e r 4 σ
∆
ε/
ε
(%
)
S e r i e s 1 S e r i e s 2
S e r i e s 3 S e r i e s 4
A b s . e r r . 0 . 5 % A b s . e r r . 1 %
A b s . e r r . 5 % A b s . e r r . 1 0 %
T h e a b s o l u t e e r r o r i s n o r m a l i s e d
w i t h r e s p e c t t o t h e c e n t r a l w i r e
s i g n a l
F e b r u a r y 2 3 - 2 4 , 2 0 0 1
W k h I
T h e s t a n d a r d a p p r o a c h t o m e a s u r e b e a m e m i t t a n c e i n a M a s s i m o G i o v a n n o z z i - C E R N
Conclusion
It seems interesting to conclude this overview by presenting a paragraph from the conclusions
of the 4th ICFA Beam dynamics Mini-Workshop on Transverse Emittance Preservation and
Measurement (CERN PS/DI Note 98-03, by H. Koziol and K. Wittenburg)
...The overall conclusion is that no emittance measurement
is yet proven to be precise to better than 10 %.
Certainly, a number of instruments are basically capable of
measuring the beam size quite precisely, but the details of
data treatment play an important roˆle for the final result.
Furthermore, when calculating emittance from beam size,
one relies on the knowledge of the beam optical parameters
at the place of the instrument and these are often fraught
with considerable uncertainties...
February 23-24, 2001
Workshop on Instrumentation for Muon Cooling
Studies, Imperial College
The standard approach to measure beam emittance in a transfer line (page 12) Massimo Giovannozzi - CERN