B e t t t a t t t r r r o n M a t t t c h i i i n g

Basic Concept
 What’s Special about CEBAF?

What is Currently Done

What is in the Plan
Y. Chao
10/26/01


Containment of beam trajectory (and thus spot size) is highly desirable

Betatron Matching

Good (nominal) Betatron Matching means

Carefully designed transport system

Good control of initial condition

Reality

Defects in machine geometry, field quality, etc.

Quality of set-up

Ability to compensate for defects
 Really a combination of good design, good construction, and good operation.


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.
Wed Oct 24 23:18:17 2001 OptiM - MAIN: - O:\optim\current\arc1.opt
0 BETA_X BETA_Y DISP_X DISP_Y
Spreader-Arc-Recombiner 1 & Linac 2

The designer has taken care of this.
657.403


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.
Runaway X-X’ coupling due to
Image B & Inverse Image R of Unit Circle by M
20
Image B & Inverse Image R of Unit Circle by M
20
15 15 poor betatron
10 10
5 matching 5
0 also implies
 Skewed
0
-5 -5
-10 -10 acceptance + High
-15
-15 sensitivity to initial
-15 -10 -5 0 5 10 15 20 coordinates
-15 -10 -5 0 5
Good Match
10 15 20
Bad Match

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.


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)

Dynamic Range of Magnets

Complicated Orbit Manipulation

Measuring Betatron Mismatch (difference orbit)

X-X’ coupling makes long range measurement very difficult

Model for Linacs
8
Wed Oct 24 21:43:44 2001 O:\diforb\01oct131836\ (D:\BPMViewer\default.cfg) dif fer en tia l or bit
[m m]
ARC 1 LIN 2 ARC 2
-8
1
I
0
1
S
2
0
5
222.266
1
S
1
0
0
1
E
2
1
A
0
1
1
0
A
5
1
0
A
7
S[m]
1
1
A
1
1
1
A
6
1
1
A
9
1
2
A
3
Legend:
1
A
2
6
1
A
2
9 x1
1
A
3
3
1
A
3
8
1
R
0
2 y1
1
R
0
8
2
L
0
2
2
L
0
5
2
L
0
7 x2
2
L
1
0
2
L
1
2
2
L
1
5 y2
2
L
1
7
2
L
2
0
2
L
2
3
2
L
2
5
2
S
0
1
2
S
0
7
2
E
0
1
2
E
0
3
2
A
0
3
2
A
0
6
2
A
0
9
2
A
1
3
2
A
1
8
2
A
2
3
An Example of Mismatch (Oct 13, 2001)
2
A
2
8
2
A
3
3
3
2
A
8
2
R
0
3
2
0
R
9
1328.58

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 .


Segmented compensation via Courant Snyder parameters
Does not “restore” the transfer matrix to design, but ensures good matching around the neighborhood of “design beam”.
PROS:

Real time (30 hz signal)

Immune to slow drifts and quad steering effects

Intuitive measure of match
CONS:

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


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.
0.1
0.04
Hall B profile
0.05
-0.05
0
0.02
-0.02
0 measurement & match (July 2001) -0.1
-0.4
-0.2
0 0.2
0.4
-0.04
-0.15
-0.1 -0.05
0 0.05
X & Y Phase space: Measured vs Design
Wed Jul 25 11:24:05 2001 OptiM - MAIN: - O:\optim\HallB_match_Chao\bsya_tob5734g8_allfit_0715_test6.opt
0.1
0.15
0 BETA_X BETA_Y DISP_X DISP_Y
BEFORE
Wed Jul 25 11:01:33 2001 OptiM - MAIN: - O:\optim\HallB_match_Chao\bsya_tob5734g8_allfit_0715_test6_fixed.opt
330.241
0 BETA_X BETA_Y DISP_X DISP_Y
AFTER
330.241


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 k n o w n u p s t r e a m f i t t i n g s e c t i o n
A m a t c h i n g s e c t i o n
B u n k n o w n s e c t i o n w i t h o p t i c a l e r r o r
C k n o w n d o w n s t r e a m f i t t i n g s e c t i o n x , x ' , y , y ' f i t t e d t o h i g h a c c u r a c y d e s i g n t w i s s
 x a
 x a
 y a
 y a
4 X 4 e m p i r i c a l m a t r i x M
A C m e a s u r e d x , x ' , y , y ' f i t t e d t o h i g h a c c u r a c y u n k n o w n m a t r i x
M
B C
= M
A C
M
A B
1 d e s i g n t w i s s
 x c
 x c
 y c
 y c t a r g e t t w i s s
 x b
 x b
 y b
 y b c a l c u l a t e d u s i n g
M
B C

Preliminary Test (03/28/00, matching from Arc 6 to Arc 7)
Peak Twiss
Initial
RMS Twiss
After 1 st Iteration
Peak Twiss RMS Twiss
Deviation Deviation Deviation Deviation
1 113%
2 31%
63%
20%
19%
10%
12%
7%


Upgraded program

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?)


Other important factors:

Orbit

X-Y coupling

Better modeling (Linac etc.)
DC Signal Courant Snyder Plot:


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.

Proposed deterministic matching scheme

Operationally more efficient and unambiguous

More accurate matching

Possibility for shorter range
