Ana səhifə

Y. Chao 10/26/01 Betatron Matching

Yüklə 32.05 Kb.
ölçüsü32.05 Kb.

Y. Chao


Betatron Matching

  • Basic Concept

  • What’s Special about CEBAF?

  • What is Currently Done

  • What is in the Plan

Basic Concept

  • Containment of beam trajectory (and thus spot size) is highly desirable  Betatron Matching

  • Good (nominal) Betatron Matching means

  • Reality

 Really a combination of good design, good construction, and good operation.

Beam Transport

  • Every practical beam transport line is a delicately balanced system.  Natural tendency of beam transport elements is to compound coupling between orbit coordinates. This must be periodically undone through careful balancing.

Propagation of orbit ensemble in a random beam line

same phase space area

in (X,X’)

    • Standardized transport systems & modules with well-known properties have been developed to ensure this.

    • For special cases, this balancing must be demonstrated explicitly by design. This is verified through the “Twiss” parameters at all locations.

Spreader-Arc-Recombiner 1 & Linac 2

  • The designer has taken care of this.

Beam Transport - continued

  • But the Twiss parameters address only a specific set of initial conditions.

    • The main beam distribution should conform to the design initial distribution as much as possible. Profile Matching

    • An adequate region in the phase space around the center should be transportable by the system. Acceptance

    • These properties should be relatively immune to minor defects in the machine. Sensitivity Analysis

  • These are taken for granted given sound betatron design.


Good Match

Bad Match

unaway X-X’ coupling due to poor betatron matching

also implies

Skewed acceptance + High sensitivity to initial coordinates

  • If betatron matching is correctly executed at all levels,

    • Properly matched initial beam will be transported at reasonable amplitudes everywhere.

    • All orbits in a reasonably shaped region in the initial phase space will be transported without excessive sensitivity.

    • Sensitivity to machine defects will decrease too.

  • Initial phase space distribution is important to eliminate the need of excessive matching effort later.

What’s Special about CEBAF?

  • Long Recirculating Linac

    • Need many special sections to bridge periodic structures

    • Need large Twiss parameters at certain places

    • Long drifts for higher passes (X-X’ coupling)

  • Complicated Orbit Manipulation

  • Measuring Betatron Mismatch (difference orbit)

    • X-X’ coupling makes long range measurement very difficult

    • M
      An Example of Mismatch (Oct 13, 2001)

      odel for Linacs

      • Amplitude should damp to ~72% from Arc1 to Arc 2

      • Damping of phase space measured for this data set is actually 66%  Strong Y-Y’ coupling has developed.

What is Currently Done

Matching betatron transport through the machine

  • Segmented compensation via Courant Snyder parameters

Does not “restore” the transfer matrix to design, but ensures good matching around the neighborhood of “design beam”.

    • Real time (30 hz signal)

    • Immune to slow drifts and quad steering effects

    • Intuitive measure of match


    • 30 hz signal can be noisy

    • Only works in Arcs (so far)

    • Procedure can be cumbersome and convergence difficult

    • Loss of signal orthogonality over long range

    • Cannot fine-tune

What is Currently Done - continued

Matching beam profiles at both ends

  • Injector beam profile measurement (multiple harp)

  • Hall beam profile measurement (multiple harp or quad scan)

  • Deterministic matching algorithm

This is indirectly important to ensuring orbit damping as explained earlier.

X & Y Phase space: Measured vs Design

Hall B profile measurement & match (July 2001)



What is in the Plan

New algorithm for matching betatron transport ready for testing

  • Use DC difference orbits to measure transfer matrix

    • Higher resolution, possibility of fine-tuning

    • More localized compensation independent of 30 hz

    • Less vulnerable to loss of signal orthogonality

  • Deterministic matching algorithm

    • Well-defined, unambiguous procedure

    • Efficient

    • Can reveal configuration problems

  • Preliminary Test (03/28/00, matching from Arc 6 to Arc 7)


After 1st Iteration

Peak Twiss Deviation

RMS Twiss Deviation

Peak Twiss Deviation

RMS Twiss Deviation











What is in the Plan - continued

    • Better understanding of exceptions

    • Improved matching configuration

    • Improved data taking scheme

    • Availability of special model parameters

    • 2001 testing

  • Ready for 2001 testing

    • Related tools debugged or being debugged

    • Start with standard Arc-to-Arc matching

    • Arc-to-Linac & Linac-to-Arc (reduced range)

    • Low energy sections (most to gain?)

Need time for dedicated tests!

  • O

    DC Signal Courant Snyder Plot:
    ther important factors:

    • Orbit

    • X-Y coupling

    • Better modeling (Linac etc.)


  • Good betatron matching must be ensured on a short-range level to prevent degradation of beam transport quality

    • Beam distribution (size & divergence)

    • Containment of orbits

    • Sensitivity to defects

  • Some special challenges at CEBAF

    • Multi-pass recirculating linac

    • Dynamic range

    • Orbit

    • Difficulty in measuring mismatch

  • Existing transport matching method (30 hz Courant Snyder) is a useful online tool for coarse matching.

    • Operationally more efficient and unambiguous

    • More accurate matching

    • Possibility for shorter range

Need time for dedicated tests!

Verilənlər bazası müəlliflik hüququ ilə müdafiə olunur © 2016
rəhbərliyinə müraciət