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Transverse Matching. Using Transverse Profiles and Longitudinal Beam arrival Times. Transverse Matching. The Challenge : get the beam Twiss parameters set to desired values (usually design) The beam Twiss parameters characterize the beam size and divergence - PowerPoint PPT Presentation
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04/22/23 J-PARC 1
Transverse Matching
Using Transverse Profiles and Longitudinal Beam arrival Times
June 16-27, 2008 USPAS 2
Transverse Matching The Challenge : get the beam Twiss parameters set to
desired values (usually design) The beam Twiss parameters characterize the beam size
and divergence Emittance () is a measure of the phase space size
(position/angle) Beta () is characteristic of amount of beam with large
displacement Alpha () is indicative of whether the beam is converging or
diverging If you know the beam Twiss parameters at some point,
and the downstream optics, you can predict the downstream beam size with an envelope model
Twiss Parameters
Each plane (Horizontal and Vertical) have independent Twiss sets Each Twiss set contains 3 un-knowns () and needs at least
3 independent measurements to solve for these
Beam Size vs. Focusing
•The three measurements to solve for the Twiss parameters can be three separate profile measurements
•Need to know the optics affecting the beam between the measurements (magnet strengths and locations)
s
Transverse position
Profile Measurement
Running wires through the beam gives the integrated intensity vs. position
Can get an RMS beam size from this
Need multiple beam pulses to aquire a profile
Profile Measurement
Often beam profiles are fit with a Gaussian shape to get an RMS beam size Easy But it misses halo
More precise method is a statistical RMS calculation Choosing the noise-floor cut-off is
tricky
Other Profile Measurement Techniques
Harp : grid of wires - Single shot gives a full profile Laser profiles For H- beams – laser strips outer electron and a weak
magnet sweeps the electron to a detector Phosphor view screens – works for low inensity Gas ionization
View Screen Profile
Gives full X-Y distribution (easily see tilt / coupling effects) Detector saturation is an issue Extremely invasive – usually used at low intensity
Harp Profile
mn
Calculating the Twiss Parameters
If you measure the beam size at least three points in a beamline, you can use the online model to calculate the Twiss Parameters at some point upstream of the first profile
Configure the model based on the machine settings Use a solver to find the initial Twiss parameters to best match the
measured beam sizes Variables are the initial Twiss values Figure –of – merit is to minimize the difference between model
predicted and measured beam sizes If only three profiles are available, the solution is exact and can be
done using linear algebra XAL uses a more general method to accommodate an arbitrary
number of profile measurements
XAL Twiss Solution Example (CCL)
Beam size vs longitudinal position
Red – horizontal, blue = vertical
Dots = measurements, lines = model
With design Twiss at CCL start
After solving for Twiss at the start of the CCL to best fit measured beam size
Uncertainties in Twiss Calculations
Beam size measurements have uncertainties Few % shot-to-shot repeatability is good
Knowledge of the magnetic field 1% error is good without beam-based techniques to refine
How to minimize the uncertainty You can repeat the entire procedure to verify the calculation You can vary magnets between the point at which you
calculating the Twiss parameters and at least one of the beam size measurement locations
Example of Averaging the Measured Twiss Parameters
Use the measurement cluster average for calculations and modeling
MEBT Twiss Input (10/03/04)
-2
-1
0
1
2
3
4
0 0.1 0.2 0.3 0.4 0.5
beta (m)
alph
a
HorizontalVertical<H><V><H-old><V>-old
Alternate method for Twiss Calculation
If only a single profile measurement is available Vary a quadrupole upstream of the profile
measurement Measure at least three beam sizes (preferably find a waist) Solve for the initial Twiss parameters that match the measured
beam sizes under the different quadrupole settings.
Single Profile Measurement Method for Twiss Calculation
Be sure to find a waist
Solve for the initial Twiss parameters that give the right beam size for all the measured conditions
s
Tran
sver
se p
ositi
on
Focusing Quadrupole
Twiss orientations
Beam profile measurement
Quad strength
Bea
m S
ize
Example of Single Profile Measurement Twiss Calculation
Finding quadrupole values
Once the Twiss parameters are known at some point it is possible to “match”
Usually the goal is to recover the design Twiss values along a beamline.
Emittance cannot be affected (directly) by magnet settings but the alpha and beta can.
You need at least 2 independent magnets to correct and in each plane (4 magnets to get horizontal and vertical bth corrected)
Sometimes magnet power supply limits are a problem – easier to match if you have more “knobs”
Usually at lattice transitions there are independently adjustable quadrupoles for this purpose (matching quads)
Control the beam size at a point Stripper foil, interaction point, spallation target
Example: determine the beam size near the end of the beamline approaching the SNS Target Measure the beam size at a 4 wires + 1 harp Determine the initial Twiss parameters Use the model to choose intervening quad values to predictably
modify the beam size at the harp
Other “Matching” Options
Initial beam conditions
Wires harpDecrease horizontal beam (red) size at harp
Increase vertical beam (blue) size at Harp
Summary
Transverse beam size control is an essential part of beam studies
First step is to characterize the Twiss parameters Need 3 independent beam size measurements + an
envelope model Model can predict quadrupole changes to controllably
change beam size / divergence (beta and alpha - not emittance)