Measuring%20and%20Analyzing%20Transverse%20Emittances%20of%20Charged%20Particle%20Beams

1
Measuring and Analyzing Transverse Emittances of
Charged Particle Beams
Martin P. Stockli and many collogues at SNS and
other Accelerator Labs
BIW06 Fermi National Accelerator
Laboratory Batavia, IL, May 1, 2006
2
CD-4 achieved 4-28-06 1530
3
Outline

• Concepts and Definitions
• Applications
• The Emittance Ellipse
• Dilemmas
• Measuring Emittance Distributions (Destructive)
• Nondestructive Measurements of the Emittance
  Ellipse
• Analysis of emittance Ellipse
• Analysis of Emittance Distributions
• Conclusions

4
The Emittance
p
The emittance is the 6-dimensional hypervolume in
the phase space x,y,z,px,py,pz that is occupied
by a number of beam particles. The coordinates
are normally referenced with respect to
the center, by zeroing the first moments
y
(x0,y0,z0)
x
z
If the axial motion does not couple to the
transverse motions, the hypervolume can be
separated into the 2-dimensional longitudinal
emittance, which describes the beam current
profile as a function of time, and the transverse
emittance which describes the beam current as a
function of transverse position. The transverse
emittance is the 4-dimensional, occupied
hypervolume in the phase space x,y,px,py
If transverse motions are not coupled, the
emittance can be separated into its components,
which form 2-dimensional areas in x,px and
y,py
with form-factor ??2
5
Emittance in Trace-Space
For pz invariant along the beam axis, p can be
factored out, yielding the transverse emittance
in the trace space x,y, x?dx/dz, and y?dy/dz.
If transverse motions are not coupled, the
emittance can be separated into its components,
which form the 2-dimensional areas x,x? and
y,y?
All these terms are normally called Emittance.
However, rigorous authors call them either
Volume Emittance or Area Emittance. Most
then go on to introduce the Emittance as the
semi-axis-product of an hyper-ellipsoid with the
same area or volume
Confusion can be avoided by stating whether the
quoted emittance value is a volume, an area, or a
semi-axis-product!
6
Units of Emittances in the Trace-Space
Emittances have the dimension of
(length?angle)n. Common are mmmrad, cmmrad,
and mrad However, the radian angle is a
dimensionless ratio, and therefore some people
use m, mm, and ?m ( mmmrad).
For semi-axis-products it is common to write
??mmmrad, ??cmmrad, or ??mrad The ? is
supposed to assure the reader that the has the ?
has been factored out of the phase space area
(Sanders, 1990). However, if the ? was factored
out, it was factored out in the definition. The ?
in the unit has no clear meaning. It is neither a
real unit, nor a true multiplier. It is a
one-of-a-kind object that has no precedent in the
physics literature! It has created as much
confusion as it intended to eliminate. A trend
has started to omit the ? in the unit.
Confusion can be avoided by stating whether the
quoted emittance value is a volume, an area, or a
semi-axis-product! Unless otherwise stated,
semi-axis-products will be quoted throughout this
presentation!
7
Normalized Emittances
x2?
x1?
vT
vT
As the particles are accelerated from vz1 to vz2,
the trace angles narrow, causing the emittance to
shrink.
vz1
vz2
The emittance can be normalized by multiplying
the emittance with the dimensionless
particle-velocity to speed-of-light ratio
with
and
with
or
The normalized emittance stays roughly the same
throughout most parts of most accelerators!
8
The RMS Emittance
Emittance volumes or areas that contain all
particles are of limited merit because they are
very large and dominated by a very few particles
of questionable character. The volume of an
entire Gaussian distribution is infinite. This
problem can be reduced by quoting the emittance
volume of a certain fraction of the beam, e.g.
90, yielding E90 or A 90 .
The problem is resolved with the rms emittance
that averages over all particles with a weight
given by the particles distance from the center
,
, with
e.g.
, and
,
,
This is the semi-axis-product of an ellipse. For
a Gaussian distribution, the ellipse contains 39
of the beam. (E90 4.6?Erms) For a finite
current , the rms-emittance is
finite. There is no absolute need to threshold
the data, but tresholded rms-emittances are
common, e.g. E rms,90. Unfortunately many
authors fail to be specific!
9
What is it all good for?

• According to Liouvilles theorem, emittances are
  conserved if the particles are subjected only to
  conservative forces, such as time-invariant
  electric and magnetic fields. Therefore the
  emittance allows for predicting the downstream
  beam transport, the beams focusability, the
  losses in downstream restricted beam line
  apertures, etc. It is invaluable for designing
  accelerators and beam lines!
• Some non-conservative forces, such as collisions,
  scattering, and fluctuations of electric or
  magnetic fields, increase the emittance.
• Other non-conservative forces, such as E-M
  radiation, decrease the emittance.
• The emittance is conserved under space charge as
  long as the forces are caused by the charged
  particle cloud, rather than by individual
  particles.

Due to the nature of the beam formation in ion
sources and/or the collimation in the extractor-
and other apertures, emittances are normally of
elliptical shape. Beams collimated by rectangular
wave guides (in dipole magnets) or by straight
slits can exhibit rectangular shapes. In this
presentation we will focus on elliptical
emittances.
10
The Emittance ellipse
While the area is constant, the emittance ellipse
shape and orientation changes. It is described
by
beam waist
beam envelope
z
x?
x?
x?
x?
x?
x
x
x
11
The Ellipse and the Twiss parameter
x?
diverging beam ?lt0 waist or lens
?0 converging beam ?gt0
?gt0 by definition mm/mrad 0lt? constant
mm?mrad
?
a
x
mrad/mm
b
Divergence Beam radius
Orientation Aspect ratio
12
The Transformation of Ellipses
The transfer matrix is normally used to calculate
individual particle rays
e.g.
with
or
Similarly, the ellipse equation can be written as
with
Which allows to calculate the beam envelope as
13
Real emittances
SNS LEBT (65 keV)
SNS MEBT (2.5 MeV)
70 mrad
15 mrad

• Angular spread shrinks as as beam is accelerated.
• Non linear forces, such as lens aberrations and
  space charge, often cause low-energy emittances
  to be S-shaped.
• Particles far from the central ellipse are
  preferentially lost in the RFQ. Ellipses are good
  approximations for high energy beams.

14
Emittance Dilemmas
Focused by linear forces
Focused by non-linear forces
Initial beam

• Liouvilles theorem applies to the area that is
  conserved.
• Elliptical approximations do not work very well
  at low beam energies. To calculate losses and
  acceptances one has to fit the smallest ellipse
  that encloses the desired beam fraction. These
  ellipses are not conserved.
• RMS emittances are only conserved for systems
  with linear forces (elliptical emittances).
  Despite, they are normally a useful figure of
  merit!

15
A Pedestrian Emittance Measurement
x?
d2
x?

• The x emittance can be approximately determined
  with 2 pairs of slits separated by distance L in
  a drift space
• Open fully one of the pair of slits while
  narrowing the other pair.
• Maximize beam transmission through the narrow set
  of slits.
• Set both collimating slits to cut (1-x)/4 of the
  beam. Repeat 2 3 as needed.
• Set the corresponding slits of the other set to
  each remove another (1-x)/4 of the beam.
• Read the (1x)/2 beam waist diameter dW and the
  (1x)/2 downstream beam diameter d2.
  Ex?dW?(d2-dW)/(4?L).

x
x
dW
16
Measuring Emittances

• Measuring the 4-dimensional emittance requires 4
  pairs of slits
• First 2 pairs define the geometrical position x,
  ?x, y, ?y
• Distance L downstream a 2nd set defines the
  tangent of the traces x, ?x, y, ?y
• The Faraday cup measures only the current passing
  through all slits!

This is the only method to measure with
infinite resolution all detailed ion beam
information, including coupling between x and y
motions.
17
Measuring Emittances
The measured current signal

• Problems
• The measured current signal c(x,y,x,y) is very
  small c ? Itot/104
• Requires NxNyNxNy measurements, e.g. 108 for
  100 positions per scan
• Takes forever or longer!

18
Pepper Pot Emittance Probe

• Uses a pepper-pot plate to form many small
  beamlets from the beam. Holes 0.05mm, 2-3 mm
  apart.
• A truly 4 dimensional, single shot measurement,
  but with limited resolution. Samples only 0.1
  of the beam, yielding tiny signals.
• Traditionally used screens and/or photographic
  paper. Electronic readout possible with CCD
  camera or high density wire screens.

For axial-symmetric beams the full
emittance to be calculated as

• (R?D/2?z)?(Dz/d Sz/S)?(1-(S/R)2)-1/2 (J.G.
  Wang et al.)
• With D, Dz hole and image diameter
• S, Sz distance from beam center
• Z distance between pepper pot and screen
• R full beam radius at pepper pot

19
The GSI Pepper Pot, State of the Art
15x15 0.1 mm ? holes, 2.5 mm apart Pepper-pot
plate continues to improve Alumina (Al2O3)
screen Separation adjustable 15-25 cm Chamber
interior totally blackened Fast Shutter CCD
camera Reference coordinates laser calibrated
Laser calibration
Emittance data
20
The assembled GSI Pepper Pot

• Pepper Pot Advantages
• Single shot measurements
• Limits thermal stress
• Allows for high energy measurements
• Detects shot-shot variation
• Detects coupling between x and y

• Potential Peeper Pot Problems
• Linearity of screen and camera response
• Measuring near beam waist

21
The GSI Visualization State of the Art
22
Measuring Two-Dimensional Emittance Distributions

• Two slit method
• Assuming independence of the two transverse
  emittances, we can integrate over one transverse
  direction while scanning over the other.

A slit corresponds to the integration over two
variables, e.g. y and y?
This is again a Gaussian x, x distribution
The two slits need to be parallel! Non-parallel
slits cause an overestimation of the emittance!
23
Electrical sweep scanners

• Electrical sweep scanners have no moving parts
  and therefore are very reliable and can be very
  fast.
• The position is scanned by dog-legging (parallel
  shifting) the beam in front of the first aperture
  using two deflectors with reversed polarity.
• A deflector behind the first aperture scans the
  beams transverse velocity.
• Oscilloscope can display instantaneous emittance
  distribution!
• Great for tuning!

• Potential drawbacks ? Alignment of the slits
• Aperture restriction from the deflector plates
• Sometimes installed in a separate beam line

24
Two slits and collector
ISDR _at_ ISIS

• Measuring emittances in the main beam transport
  line requires the insertion and the fine stepping
  of the first slit to probe the position
  distribution.
• The second slit also needs to be inserted and
  stepped through the distribution to probe the
  trace angle distribution. The Faraday cup can be
  attached to the second slit.

• Potential drawbacks
• Alignment of the slits
• Tilted background if the Faraday cup is not well
  shielded
• Wavy background if the Faraday cup is not well
  shielded

25
Allison scanners

• P. Allison developed in the early 1980s a hybrid
  emittance scanner at LANL, known today as Allison
  scanner.
• A stepper motor scans the entire unit through the
  beam to sample position x with the entrance slit.
  
• Saw-tooth voltages of opposite polarity are
  applied to the deflector plates located between
  the two set of slits to sample angle x.
• A suppressed Faraday cup measures the beam
  passing through both slits.
• Allison scanners are gaining popularity!
• Shown are the Allison scanners designed at LBNL
  by M. Leitner.

26
Fundamentals of Allison Emittance Scanners

• Ions with charge q, mass m, and energy Ekin
  m?vz2/2 q?U, with axial velocity vz
  (2?q?U/m)1/2 z/t , traveling in an electrical
  field E 2?V/g, change their transverse velocity
  vx vx vx0 ?ax?dt

Suppressor
Ground Shield
Ion Beam Position Scan
Faraday Cup
V
x
g
x
Ion Beam Trajectory
Leff
z
-V
Entrance Slit
Exit Slit

• vx0 ?(q?E/m)?dt vx0 q?E?t/m vx0
  q?E?z/(m?vz)
• Particles that pass the first slit (xx00 for
  t0z)
• x ?vx?dt vx0?t q?E?t2/(2?m)
  z?vx0/vzq?E?z2/(2?m?vz2)
• x?z E?z2/(4?U) x?z -V?z2/(2?g?U)

• For particles that pass the second slit (x0) at
  zLeff x V?Leff/(2?g?U) or V 2?U?x?(g/Leff)

For 65 kV ions in the LBNL scanner (Leff
4.77g 0.275) xmrad VV/7.5 VV
7.5?xmrad xmax 115 mrad

• Deflection plates are vignetting the angular
  range x when x(L/2) g/2
• xmax xmax?L/2 -V?L2/(8?g?U) xmax?L/4 g/2
  
• or xmax 2?g/L ltlt1

27
Designing an Allison Emittance Scanner
Acceptance limit x?max  2?g/Leff
Voltage limit x?max  V0?Leff/(2?g?U0)
Ideal V0 ? x?max2?U0 Only feasible for low
energies Elt1 MeV
For energies lt 1 MeV, the range is lt10 ?, less
than the 25 ? rough edge observed on
Beam
machined slits. As long as the shim angle exceeds
the maximum divergence of the beam (or
acceptance), no slit scattering is observed.
x?max
25 ?
28
Ghost Signals in Allison Emittance Scanner

• At SNS, the emittance of strongly focused beams,
  as injected into the RFQ, is normally measured.

• In 2004 D.Moehs (FNAL) tuned an almost parallel
  beam while testing the source for the new
  Fermilab driver. We found many small inverted
  signals!

• Checking old data, we found the same ghost
  signals present but hard to detect because they
  are overlapping with the real signals!

29
Is Ghost Busting Trickery?
The symmetry with
respect to the beamlet passing through the
entrance slit, and the 30 mrad ghost-free gaps
suggested protons backscattered from the
deflector plates.

• Using deflector plates with a staircase shaped
  surface changes the impact angles to close to
  normal, stopping the forward momentum.

Original Plates
70?/20?staircase plates
But are the ghost signals completely
gone?
30
No, Ghost Busting is Science!
x  x?s?z ?V?z2/(2?g?U)
For x(z  Leff)  0 x?s  V?Leff/(2?g?U)
And for xmax  g/2 x?max   2?g/Leff
x  x?b?z x?s?z2/Leff
Exit slit zie Leff for
?x?s ?x?b?? g/(2?Leff) Upper plate
ziu  (x?b ?(x?b2 ?2?x?s?g/Leff)1/2)?Leff/(2?x?s)
Lower plate ziL  (x?b (x?b2 2?x?s?g/Leff)1/2)
?Leff/(2?x?s)
x?ie(z  Leff)  x?b ?2?x?s x?iU  (x?b2 ?2?x?s?g
/Leff)1/2 x?iL  ?(x?b2 2?x?s?g/Leff)1/2
31
The Ghostbusters did it again!

• The largest reasonable trajectory angle at impact
  is (8)1/2?g/Leff.
• It occurs when beamlets with x?b ?
  2g/Leff (the geometrical acceptance limit) are
  scanned with x?s -x?b, the opposite
  geometrical acceptance limit.

• For our scanner this is 10?, less than the
  20? staircase angle of our new deflection plates.
  
• ? All particles impact on the faces of the
  stairs!

• An optical comparator suggest rough edges with a
  width of 1 mil.
• The steps are 1 mm high, 115 mils apart.

• gt99 of ghosts eliminated!
• A 10? staircase angle could reduce the ghosts by
  another factor of 2!

32
Neutral Beam Detection with Allison Scanners
Switching off the suppressor reveals the neutral
beam and possible alignment problems!
33
Allison Scanners

• Advantages
• Properly designed Allison Scanners with
  stair-cased deflector plates yield highly
  reliable emittance data because the shielded and
  suppressed Faraday cup measures directly the
  current carried by the beamlet.
• The shielded and suppressed Faraday cup measures
  only particles that are passing through both
  slits, because all other charged particles are
  intercepted by the surrounding light-tight
  shield.
• Low-energy charged particles, such as convoy
  electrons, are swept away by the electric field.
  (lacking quantification!)
• A properly designed mounting block supporting
  both set of slits allows for their alignment
  within tight tolerances. Fully adjustable
  resolution.

• Drawbacks and Issues
• Can only be used for low energy beams (lt1 MV).
• Slit heating for high power-beams (A problem of
  high power beams!)
• Changes of the emittance due to the space charge
  from the secondary electrons created by the
  intercepted beam. (A low-energy beam problem).
• Time-consuming 10,000 position- and voltage
  combinations required. This can be cut by a
  factor of 2-3 with position dependent voltage
  ranges!
• Meaningful data require very stable beams!
• Electric fields do not separate different ions
  with the same energy/charge. In a purely electric
  LEBT all ions from the ion source contribute to
  the emittance distribution.

34
The Emittance-Mass Scanner
D. Yuan, K. Jayamanna, T. Kuo, M. McDonald, and
P. Schmor, Rev. Sci. Instrum. 67 (1996) 1275.
By combining an Allison scanner with a
perpendicular magnetic field, TRIUMF has
introduced a Wien filter for emittance analysis.
The magnetic field separates momentum, and
therefore different ions. It does, however, it
also disperses the ions energy distribution.
35
Slit and Collector method

• A multi electrode collector can measure the
  trajectory angle distribution in a single shot,
  using one amplifier and one ADCs for each
  collector segment. This reduces the measuring
  time by 100.

• A positive bias can cause cross talk between
  neighboring segments.

• A negative bias increases the current of a
  positive beam but decreases the current of a
  negative beam. It also shows a current for
  neutral beams. After some time and beam exposure,
  the gain can start to vary from plate to plate,
  as the secondary electron coefficient ? changes
  with changing surface condition.

• Drawbacks and Issues
• Positive biases can also attract the numerous
  electrons generated on the entrance slit.
  Barriers are highly desirable!

36
Slit and Harp methodSlit scans the position
distribution. The wire harp measures the
trajectory angle distribution.
SNS MEBT (2.5 MeV)
Macro and micro stepping make angular resolution
flexiblea) increase angular resolutionb)
increase angular rangec) increase angular range
while doubling resolution in the center

• C-C slits lt50?s pulses16 x 100 ?m W wires,
  spaced by 0.5 mmMoves in macro and micro steps
  (0.1mm)Harp moves with slit following ellipse 5
  Hz, 4 min/scan Has back plane

• Drawbacks and Issues
• Optimize biases for best signals
• Fields depend on wire and nearby electrodes.
  Fields can be improved with nearby electrodes.
  But beam dumping generates more electrons.
• Limited to 10 MeV due to difficulty of stopping
  99 of beam on slits.

37
SNS emittance scanner control
W. Blokland and C. Long, ICALEPCS05
SNS diagnostics platform is PC-based running
Windows XP Embedded and LabVIEW. Uses
rack-mounted PCs running LabVIEW to acquire and
process the data, and EPICS IOC to communicate
with the SNS control system.
Moves the slit Moves the harp Moves the harp
with the slit
38
SNS emittance scanner control
W. Blokland and C. Long, ICALEPCS05
The current is measured as a function of time.
The current is averaged over a interval before
calculating the emittance and Twiss parameters
39
SNS rms emittance visualization and analysis
W. Blokland and C. Long, ICALEPCS05
The background (or bias) current is measured
before the beam pulse and subtracted. Residual
bias 0.01 affect rms-emittances by 1.
40
Data file 670
A tiny bias or halo allows for showing the
scanned range in yellow. The harp following the
center significantly reduces measuring time.
However, contour plots can be deceiving. An
overlapping double scans would have been
desirable.
41
Initial Noise problems with the raw emittance
data
E.M. Plus Stepper Motors Noise
Stepper Noise removed by support from Controls
(Ernest Williams, et. al.)
All noise issues were removed. Diagnostic group
(Jim Pogge Richard Witkover)
Problem Solved!
42
Data file SN1
Even if noise is very bad, meaningful Twiss
values can still be extracted. Noise is just
noise, it preserves the average, but it makes it
less certain.
43
Nondestructive 3 Beam Profiles yield Emittance
Ellipse
The SNS 1 GeV Wire Harp Beam Profile Monitor C
wires 30 ?m ? 3 harps X, Y, and diagonal
(Z) Intermediate harps for secondary electron
suppression
Harp Assembly
Harp
Harp Vessel
44
Wire Harp Controls and Analysis
Diagonal profiles allow for detecting couplings
between x and y.
45



The Laser Profile Monitor
H-
H0 e
hn

• Many negative ions can be photo-neutralized.
• This is a new way of diagnosing the transverse
  profile of our H- beam

• A 10 ns long laser pulse photo neutralizes a
  fraction of H- ions in a narrow slice of the
  beam.
• A magnetic field sweeps the freed electrons to
  the side.
• A MCP amplifies the electron current.
• The electron current is measured as a function of
  the laser beam position

Electron Deflector
Ion beam
MCP
46


SCL Laser Profile Monitor Control and Analysis is
PC based
47
Residual Gas Fluorescence Monitor

• D.P. Sandoval et al, 5th BIW 1993
• G. Burtin et al, 6th EPAC (2000)
• A. Peters et al, DIPAC01

• Beam ions collide with residual gas atoms and
  molecules, which become excited.
• When de-exiting after 50 ns, the residual gas
  gives of light, mostly in the range between 350
  and 470 nm.
• A photo cathode converts the light into electrons.

• MCP multiply the electron current for single
  photon counting.
• The photo-cathode to MCP voltage can be used for
  gating the camera.
• Gas pressure of 10-5 Torr needed for sufficient
  light.

• Advantages
• Nondestructive
• No movable parts

48
Three Position Beam Width Method
Beam Width based Emittance Analysis
This analysis is based on the normal beam
model
, where
is the jk element of matrix R for transfer
between point I and F
Measure 3 beam half-widths WA, WB, and WC in 3
different locations. Solve the equations
With
Often this method can done without interfering
with normal operations. It is an attractive
diagnostic at all beam energies.
49
Three Gradient Beam Width Method
Measure 3 beam half-widths WA, WB, and WC for 3
different focal strength. With
being is the ij element of matrix R for transfer
between lens and beam width monitor when focusing
with strength X, and the
Normal Beam Model
One finds
With
This method requires a significant change in
focal strength and therefore interferes with
regular operations!
50
Multi Gradient Beam Width Method
V. Danilov
Based on the normal beam model
Measure the beam half-widths Wk for more 3
different focal strengths. If
is the ij element of matrix R for transfer
between lens and beam width monitor when focusing
with strength k, then
and
51
Determining Emittance Areas from Distributions
To determine the x emittance area, one often
counts the number of measurements that exceed
(1-x) of the measured peak current. For Gaussian
beams this corresponds to x of the beam. For
non-Gaussian beams this differs significantly. A
problem, especially for low beam energies! To
determine the emittance area for x of the beam
one needs to determine the sum of all real
current signals. However, this sum is very
sensitive to bias, especially if most of the data
are background data. A self-consistent bias
subtraction is advised. Once a reliable sum of
all real current signals has been established,
the relation between beam and peak current
can be mapped. This allows to determine the area
for a fraction of the beam current! But most
important, whenever you publish emittance area
results, PLEASE state whether the refers to the
peak current (intensity) or the total beam
current (beam). To determine which fraction of
the beam passes through a circular aperture, the
acceptance ellipse needs to be fitted to maximize
the enclosed current. However, this ellipse is
not conserved!
52
Determining RMS Emittances from Distributions
For rms emittances the Twiss parameters can be
calculated from the transverse emittance data.
For example for x and x?
, and
,
,
,
with
,
,
, and
However, when calculated from all data points,
one gets very erratic numbers, especially if the
data are dominated by background data.
What can we do?
Threshold to exclude the background!
53
Emittance Analysis
O. Sanders, BIW89
54
Ghost Signals affect RMS Emittances
High-noise with ghosts
Gaussian
Medium-noise with ghosts
Ghost-free
Low-noise with ghosts

• Thresholding non-Gaussian distributions excludes
  normally a much larger fraction of the beam
  current than the percentage of the quoted of the
  peak current!

55
RMS Emittance evaluation at JAERI
Courtesy of A. Ueno, KEK
56
There are many ways to evaluate RMS Emittances
Method lab estimate LBNL data mm?mrad JAERI data mm?mrad
Raw data (?0) 0.192 1.24
Threshold, histogram (8) 0.097 (6.7) 0.145
Threshold, change of slope (8) 0.097 (5) 0.194
Threshold, change of a (15) 0.079 (5) 0.194
Bias subtraction (0.16 ? 0.04 ) 0.182 ? 0.003 (0.164 ? 0.007 ) 0.28 ? 0.05
Bias subtraction, negative numbers suppressed (1.3) 0.152 (5.1) 0.13
57
Self Consistent Bias Estimation and Exclusion
Analysis
The size of the ellipses is characterized by HAP,
the product of their half-axes in mm-mrad.
100
300
10,000
3000
1000
58
Self Consistent UnBiased Elliptical Exclusion
Analysis
Average current outside ellipse
Top 90 ellipse
Emittance of outside current subtracted data
This is self-consistent!!
What ellipse ??
Top 90 ellipse
59
Robustness of SCUBEEx
Top 10 means all data with current signals
exceeding 90 of maximum signal For all
ellipses HAP 100
Top 10
Top 95
Top 80
60
Robustness of SCUBEEx
Average current outside ellipse
Top 10 ellipse
Emittance of outside current subtracted data
Estimate robust !!
61
Its about the same, says SCUBEEx
Method lab estimate LBNL data mm?mrad JAERI data mm?mrad
Raw data (?0) 0.192 1.24
Threshold, histogram (8) 0.097 (6.7) 0.145
Threshold, change of slope (8) 0.097 (5) 0.194
Threshold, change of a (15) 0.079 (5) 0.194
Bias subtraction (0.16 ? 0.04 ) 0.182 ? 0.003 (0.164 ? 0.007 ) 0.28 ? 0.05
Bias subtraction, negative numbers suppressed (1.3) 0.152 (5.1) 0.13
SCUBEEx 0.18 ? 0.01 0.20 ? 0.02
No, Scooby Doo, its not you, its SCUBEEx!!!
62
Testing Emittance Data for Ghost Signals

• Ghost signals cause the average outside current
  to under-shoot and interfere with the
  self-consistent bias estimation!

63
Conclusions

• Emittances are well defined and understood
• Always state whether your emittance is an area or
  an half-axis-product to avoid confusion on
  definitions.
• Emittances can be measured with many different
  sophisticated methods.
• The emittance ellipse can be determined from gt2
  beam diameters, which can be obtained without
  beam destruction
• Measuring the emittance distribution destroys the
  beam, but reveals the detailed distribution.
• High energy beams (beyond the RFQ) are rather
  elliptical, and therefore not a serious problem
• The non-elliptical, non-Gaussian nature of
  low-energy emittance pose a real challenge for
  comparing ion sources and LEBTs, or when
  designing them. Designs are typically based on
  elliptical Gaussian beams. Full emittances is
  likely to overestimate the losses, while 10
  thresholded values may underestimate the losses.
  More work is needed!

64
Bibliography

• C. Lejeune and J. Aubert, Emittance and
  Brightness Definitions and Mesurements, in
  Applied Charged Particle Optics, Part A, A.
  Septier, edt.,(Academic Press 1980) pp. 159-259.
• O. R. Sander, Transverse Emiitance Its
  Definition, Applications, and Measurements in
  Accelerator Instrumentation, E. R. Beadle and
  V. J. Castillo, edts., (AIP CP212, 1991) pp.
  127-155.
• M. P. Stockli, R. F. Welton, R. Keller, A. P.
  Letchford, R. W. Thomae, and J. W. G. Thomason,
  Accurate Estimation of the RMS Emittance from
  Single Current Amplifier Data, in Production
  and Neutralization of Negative Ions and Beams
  M. P. Stockli, edt., (AIP CP639, 2002) pp
  135-159.
• R. Becker and W. B. Herrmannsfeldt, Why ? and
  why mrad, Rev. Sci. Instrum. 77(2006).
• D. C. Carey, The Optics of Charged Particle
  Beams (Hardwood Academic Publishers, Chur, 1987)
  298 pp.
• H. Zhang, Ion Sources (Springer, New York,
  1999).
• T. Hoffmann, W. Barth, P. Forck, A. Peters, P
  Strehl, D.A. Liakin, (AIP CP546, 2000) pp
  432-439.
• T. Hoffmann, D.A. Liakin, (DIPAC 2001) pp
  126-128.
• P. W. Allison, J. D. Sherman, and D. B. Holtkamp,
  IEEE Trans. on Nucl. Sci. NS-30, 2204-2206
  (1983).