Transverse Matching

1. J-PARC Transverse Matching Using Transverse Profiles and Longitudinal Beam arrival Times

2. USPAS 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 (e) is a measure of the phase space size (position/angle) • Beta (b) is characteristic of amount of beam with large displacement • Alpha (a) 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

3. Twiss Parameters Each plane (Horizontal and Vertical) have independent Twiss sets Each Twiss set contains 3 un-knowns (a, b, e) and needs at least 3 independent measurements to solve for these

4. Beam Size vs. Focusing Transverse position s • 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)

5. 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

6. 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

7. 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

8. 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

9. Harp Profile mn

10. 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

11. XAL Twiss Solution Example (CCL) With design Twiss at CCL start After solving for Twiss at the start of the CCL to best fit measured beam size Beam size vs longitudinal position Red – horizontal, blue = vertical Dots = measurements, lines = model

12. 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

13. Example of Averaging the Measured Twiss Parameters Use the measurement cluster average for calculations and modeling

14. 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.

15. 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 Twiss orientations Focusing Quadrupole Transverse position Beam profile measurement s Beam Size Quad strength

16. Example of Single Profile Measurement Twiss Calculation

17. 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 a and b 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)

18. 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 Increase vertical beam (blue) size at Harp Initial beam conditions Wires harp Decrease horizontal beam (red) size at harp

19. 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)