Exchange of Transverse and Longitudinal Emittance at the A0 Photoinjector

Exchange of Transverse and
Longitudinal
Emittance

at the

A0
Photoinjector

Tim
Koeth

(this talk was initially prepared for TK’s
committee meeting of March 11, 2008)

Updated March 14
th
, 2008

Outline

•
Brief Photoinjector introduction

•
Motivation & Theory of Emittance Exchange

•
Exchange Apparatus at the A0 Photoinjector

•
Results to date…

•
Next Steps

•
Acknowledgements

The A0 Photoinjector

•
Laser energy 16
m
J/pulse @ 263nm

•
<5nC/bunch (have had >12 nC in the past)

•
Typically 10 bunches/RF pulse. 1 Hz rep rate

•
4 MeV gun output energy

•
16 MeV total energy

•
D
p/p ≈ 0.3%@ 16MeV (1nC)

•
Bunch length ≈ 2 mm (1nC)

•
ge
z

≈ 120 mm
-
mrad (RMS @ 1nC)

•
ge
x
,
ge
y
≈4 mm
-
mrad (RMS @ 1nC)


Next, Artur will talk about the low level
RF systems that keep the laser, two 1.3
GHz and one 3.9 GHz systems in sync.

The Idea:
Emittance

Exchange (EEX)

•
In 2002 M.
Cornacchia

and P. Emma proposed using a TM
110

deflecting
mode cavity in the center of a chicane to exchange a
smaller longitudinal
emittance

with a
larger transverse
emittance

for a FEL.

•
Kim &
Sessler

in 2005 proposed using a flat beam (
e
x
<<
e
y
) combined with a
deflecting mode cavity between 2 doglegs to produce a beam with very
small transverse
emittances

and large longitudinal
emittance

to drive an
FEL.

•
We are doing a proof of principle
emittance

exchange at A0 using the
double dogleg approach with a round beam (
e
x
=
e
y
) .

–
We’ll be exchanging a larger longitudinal
emittance

with a smaller transverse
emittance
.

–
Keep in mind that
emittance

is the area beam phase space,

•
Why ?

•
Basic and unique beam dynamics manipulation
–

proof of principle

•
FEL’s
-

low transverse
emittance
, large brightness

•
This phase space manipulation could have application in a linear
collider



2
2
2
'
'
xx
x
x


e
TM110 (Deflecting) Mode Cavity

•
No longitudinal electric field on axis.

•
Electric field imparts an energy kick
proportional to distance off axis.

–
Plan to use this to change the
momentum deviation in presence of
dispersion!

•
Electro
-
magnetic field provides
deflection as a function of arrival time.

•
This is the type of cavity used as a crab
cavity or for bunch length
measurement.

kx



(from Figure 1 of C&E)

Electric field at synchronous phase.

Magnetic field a quarter period later.

kz
x

'
aE
eV
k
0

k

is the integrated

longitudinal energy gain

at a reference offset
a

normalized to the beam

energy
E
.

a

Concept of Emittance Exchange

in
out
z
x
x
D
D
D
D
A
A
A
A
z
x
x













































'
0
0
0
0
0
0
0
0
'
22
21
12
11
22
21
12
11
in
out
z
x
x
C
C
C
C
B
B
B
B
z
x
x













































'
0
0
0
0
0
0
0
0
'
22
21
12
11
22
21
12
11
A typical non
-
dispersive transport matrix:

What we want to develop is a matrix like:

EEX: Linear Optics Model

final e
-

bunch

Initial e
-

bunch

D1

e
x

>
e
z

D2

D3

D4

3.9 GHz TM
110

First, break the EEX
-
line into three sections:


Magnetic dogleg before cavity: M
bc


TM
110

cavity (thin lens): M
cav


Magnetic dogleg after cavity: M
ac

















1
0
0
0
1
0
0
0
1
0
0
1
D
D
D
L
M
M
ac
bc
















1
0
0
0
1
0
0
0
1
0
0
0
0
1
k
k
M
cav












































1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
D
D
D
L
k
k
D
D
D
L
M
M
M
R
bc
cav
ac


and

To get:

EEX: Linear Optics Model
































Dk
kL
k
Dk
ad
k
D
D
Dk
aDkL
Dk
D
D
Dk
Dk
k
Dk
DkL
Dk
D
D
kL
L
Dk
Dk
L
Dk
R
1
0
)
1
(
1
)
1
(
1
0
)
1
(
)
1
(
1
2





However, if we take the special case of k =
-
1/D = k
o

we get:


























0
0
1
0
0
1
0
0
0
0
D
L
D
aL
D
D
L
D
D
L
R



All of the X
-
X and Z
-
Z coupling elements are zero !

Now if we take the trivial case of k =0 we get:
















1
0
0
0
2
1
2
0
0
0
1
0
2
0
2
1
D
D
D
L
R

EEX: Linear Optics Model

With our k=k
o



































D
C
B
A
D
L
D
aL
D
D
L
D
D
L
R
0
0
1
0
0
1
0
0
0
0































z
z
z
z
z
z
z
z
x
x
x
x
x
x
x
x
z
x
o
g
e

e

e

e
g
e

e

e

e



0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
We can transports the initial uncoupled beam (sigma) matrix through the EEX line

via

T
o
R
R



a complete swap of the emittances is seen.

z
x
e
e



2
det
x
x
e


And remember

:

Then take the determinate of
σ
x
,
σ
z

and we get:



2
det
z
x
e




2
det
x
z
e















T
z
T
x
T
z
T
x
T
z
T
x
T
z
T
x
D
D
C
C
B
D
A
C
D
B
C
A
B
B
A
A
o
o
o
o
o
o
o
o









We know from above that A = D = 0, so this reduced to:










T
x
T
z
C
C
B
B
o
o



0
0
EEX Beam Line at the
Photoinjector

= Beam Position Monitor (BPM)

-

Transverse beam position

= Diagnostic cross: viewing screen(s) & digital camera

-

Measuring transverse beam size

= Slit/Screen pair for transverse emittances.

Not shown: Streak camera & Interferometer
–

e
-

bunch length, Phase Mon
–

e
-

TOF

= MagneticSpectrometer
–

P & ∆P

Diagnostics:

Vertical bend
avoids residual
dispersion of X
-
plane

EEX Beam Line at the Photoinjector

Beam
direction

Dipoles

Vertical

Spectrometer

TM
110

Cavity

Beamline Layout

Deflecting Mode Cavity

0
5
10
15
20
25
5
6
7
8
9
10
11
12
s(m)
beta (m)
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
eta (m)
betax
betay
etax
etay
EEX Beam Line at the
Photoinjector

(
Cav

off)

TM110 Cavity Details

Construction:


5 cells (of CKM design)


Punched OFHC Copper


Vacuum brazed

Radio Frequency:


3.9 GHz (3x 1.3GHz)


Q
300K
=14,900


Q
80K
=35,600


Coupling (
β
) = 0.7


Req’d RF power @ full gradient: 50kW

Cavity
Polarizaton

and Field Flatness

Red: theory
Black: fit cell 2
Blue: fit cell 3
Green: fit cell 4
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200
205
210
215
220
225
230
235
240
245
250
255
260
265
270
275
280
285
290
295
300
305
310
315
320
325
330
335
340
345
350
355
•
Longitudinal electric field vs angle in
cells 2
-
4 determined by bead pull.

•
Cavity polarization is set by input
coupler

•
Bead pull results of cavity field
flatness tuning.

Vertical

-10
-8
-6
-4
-2
0
2
4
6
0
50
100
150
200
250
300
350
400
450
TM
110

Cavity: 1
st

Deflection


The induced kick is about 70% of what was expected for the input power, however, sufficient
contingency was built into the cavity to accommodate this.




Operating phase

for exchange

BPM26

•
Preliminary investigations showed
encouraging results. For instance, as
we increased the TM
110

cavity
strength we saw a reduction in
momentum spread…

Early Vertical Spectrometer Images

Cavity: OFF

Cavity 10%

Cavity 20%

Cavity 30%

Cavity 40%

Cavity 50%

Cavity 60%

Cavity 70%

Cavity 80%

Cavity 100%

Spectrometer Screen

~ 550keV

Measuring the EEX Line Matrix

There is exciting evidence that the cavity was indeed modifying the momentum
spread, so we have begun to systematically measure the EEX beam line matrix.

in
out
z
y
y
x
x
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
z
y
y
x
x































































'
'
'
'
66
65
64
63
62
61
56
55
54
53
52
51
46
45
44
43
42
41
36
35
34
33
32
31
26
25
24
23
22
21
16
15
14
13
12
11
Again, describing the beam line with linear optics we have:

Adjusting one input parameter at a time and measuring all output parameters we can
map out the transport matrix. For example, introducing a momentum offset yields
the 6
th

column:

Do this with the TM110 cavity off, partially on, 100% on, and greater

in
out
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
z
y
y
x
x




















D









































D
D
D
D
D
D


0
0
0
0
0
'
'
66
65
64
63
62
61
56
55
54
53
52
51
46
45
44
43
42
41
36
35
34
33
32
31
26
25
24
23
22
21
16
15
14
13
12
11
EEX Beamline: Vertical Spectrometer BPM

For a given TM
110

strength, k, changed beam central momentum by
±

2.15 % in
0.70% increments by varying 9
-
Cell cavity gradient. Repeated for several TM
110

k:

TM
110

cavity
strength, k
o

Intro

p from 9
-
Cell

Vary k

record vertical BPM reading

in
out
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
z
y
y
x
x




















D









































D
D
D
D
D
D


0
0
0
0
0
'
'
66
65
64
63
62
61
56
55
54
53
52
51
46
45
44
43
42
41
36
35
34
33
32
31
26
25
24
23
22
21
16
15
14
13
12
11
Intro

p from 9
-
Cell

OFF

73%

90%

100%

105%

EEX: Beam Line Horizontal Dispersion

measurement with TM
11O

cavity off

Lines: ideal

Dots : Horizontal
BPM measured
difference data

δ
P =
±

1.05 %

in 0.35 % increments

D1

D2

D3

D4

TM
110

SPECT.

+1.05%

+0.70%

+0.35%

0

-
0.35%

-
0.70%

-
1.05%

EEX: Beam Line
with
TM
110

Cavity
On,

Ideal:


+1.05%

+0.70%

+0.35%

0

-
0.35%

-
0.70%

-
1.05%

Lines: ideal

δ
P =
±

1.05 %

in 0.35 %
increments

D1

D2

D3

D4

TM
110

SPECT.

OFF

20%

40%

60%

80%

100%

120%

EEX: Beam Line with TM
110

Cavity on

Measured:

+1.05%

+0.70%

+0.35%

0

-
0.35%

-
0.70%

-
1.05%

D1

D2

D3

D4

TM
110

SPECT.

Cavity
strength, k
o

OFF

44%

67%

85%

100%

in
out
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
z
y
y
x
x




















D









































D
D
D
D
D
D


0
0
0
0
0
'
'
66
65
64
63
62
61
56
55
54
53
52
51
46
45
44
43
42
41
36
35
34
33
32
31
26
25
24
23
22
21
16
15
14
13
12
11
Streak Camera TOF measurements

Introduce

p from 9
-
Cell

Streak camera ~
1pSec resolution

y = 8.0444x
-

115.04

R² = 1

y = 18.214x
-

260.38

R² = 0.9968

-1.00E+00
0.00E+00
1.00E+00
2.00E+00
3.00E+00
4.00E+00
5.00E+00
6.00E+00
14.25
14.3
14.35
14.4
14.45
14.5
14.55
14.6
delta
-
z [mm]

Beam energy [MeV]

TM110 k=75%ko
TM110 off
Similar for 2nd Column: vary ∆x
in
’

in
out
x
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
z
y
y
x
x




















D









































D
D
D
D
D
D
0
0
0
0
'
0
'
'
66
65
64
63
62
61
56
55
54
53
52
51
46
45
44
43
42
41
36
35
34
33
32
31
26
25
24
23
22
21
16
15
14
13
12
11

Impart
D
x
’ by adjusting a
horizontal corrector
magnet

… And
D
x,
D
y,
D
y’… The
D
z can be achieved by adjusting the TM
110

cavity phase

k=62%k
o

D
x’in data from today

Today’s BPM8/30 Dispersion Measurements

BPM8 & 30 Special 4
-
inch housing



Ray’s cald XS4 Vert Disp : 865mm

Tim’s measuremnt 855+/
-
5mm


Ray’s calc of XS3 Horz Disp: 225mm

Tim’s measurement 226mm


Finally nice agreement !


Note non
-
lin > 8 mm

Summary of Today & yesterday
data collection (March 13 thru 14)

TM110 5
-
Cell off

25%

ko

50%
ko

75%
ko

~90%

ko

∆x

X

X

X

X

X

∆x’

X

X

X

X

X

∆y

X

X

X

X

X

∆y’

X

X

X

X

X

∆z(
ф
)

-

X

X

X

X

δ

X

X

X

X

X

δ

energy incriments calibration against BPM8

Now, off to analyze…

in
out
z
y
y
x
x
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
z
y
y
x
x































































'
'
'
'
66
65
64
63
62
61
56
55
54
53
52
51
46
45
44
43
42
41
36
35
34
33
32
31
26
25
24
23
22
21
16
15
14
13
12
11
EEX: Next Steps

•
Continue to populate the matrix

•
Measure input and output emittances

•
Graduate !

Many thanks go to:

•
Helen Edwards
-

Advisor

•
Don Edwards
-

Voice of reason

•
Leo Bellantoni
–

[tor]Mentor & CKM

•
Ray Fliller
–

A0 Post Doc

•
Jinhao Ruan
–

Laser, All things optical

•
Jamie Santucci
–

fireman

•
Alex Lumpkin
–

streak camera

•
Uros Mavric
–

Ph.D. Student

•
Artur Paytan
–

Yerevan U. Ph.D. Student

•
Mike Davidsaver
–

UIUC staff, controls guru

•
Grigory Kazakevich
–

Guest Scientist, OTRI

•
Manfred Wendt & Co
–

Instrumentation, BPMs

•
Elvin Harms
–

kindly sharing a klystron

•
Randy Thurman
-
Keup
–

Instrumentation, Interferometer

•
Vic Scarpine
–

Instrumentation, OTR and cameras

•
Ron Rechenmacher
–

CD, controls

•
Lucciano Piccoli
–

CD, controls

•
Brian Chase, Julien Branlard, & Co
–

Low Level RF

•
Gustavo Cancelo
–

CD, Low Level RF

•
Wade Muranyi & Co
–

Mechanical Support

•
Bruce Popper
–

drafter & artist

•
Chris Olsen
-

assistant