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)