Transcript Speculations About a Fourier Series Kicker for the TESLA

A Fourier Series Kicker for the
TESLA Damping Rings
George Gollin
Department of Physics
University of Illinois at Urbana-Champaign
LCRD 2.22
1
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Introduction
•The TESLA damping ring fast kicker must inject/eject every nth
bunch, leaving adjacent bunches undisturbed.
•The minimum bunch separation inside the damping rings (which
determines the size of the damping rings) is limited by the kicker
design.
•We are investigating a novel extraction technique which might
permit smaller bunch spacing: a “Fourier series kicker” in which a
series of rf kicking cavities is used to build up the Fourier
representation of a periodic d function.
•Various issues such as finite bunch size, cavity geometry, and tunerelated effects are under investigation.
2
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Outline
Overview
• TESLA damping rings and kickers
• how a “Fourier series kicker” might work
Phasor representation of pT and dpT/dt
Flattening the kicker’s dpT/dt
Some of the other points:
• finite separation of the kicker elements
• timing errors at injection/extraction
Conclusions
3
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Illinois participants in LCRD 2.22
Guy Bresler (REU student, from Princeton)
Keri Dixon (senior thesis student, from UIUC)
George Gollin (professor)
Mike Haney (engineer, runs HEP electronics group)
Tom Junk (professor)
We benefit from good advice from people at Fermilab and
Cornell. In particular: Dave Finley, Vladimir Shiltsev, Gerry
Dugan, and Joe Rogers.
4
I
Physics
P
llinois
Overview: linac and damping ring beams
Linac beam (TESLA TDR):
•One pulse: 2820 bunches, 337 nsec spacing (five pulses/second)
•length of one pulse in linac ~300 kilometers
•Cool an entire pulse in the damping rings before linac injection
Damping ring beam (TESLA TDR):
•One pulse: 2820 bunches, ~20 nsec spacing
•length of one pulse in damping ring ~17 kilometers
•Eject every nth bunch into linac (leave adjacent bunches undisturbed)
17 km damping ring circumference is set by the minimum bunch
spacing in the damping ring: Kicker speed is the limiting factor.
5
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Overview: TESLA TDR fast kicker
Fast kicker specs (à la TDR):
•  B dl = 100 Gauss-meter = 3 MeV/c
• stability/ripple/precision ~.07 Gauss-meter = 0.07%
• ability to generate, then quench a magnetic field rapidly determines
the minimum achievable bunch spacing in the damping ring
TDR design: bunch “collides” with electromagnetic pulses traveling
in the opposite direction inside a series of traveling wave structures.
TDR Kicker element length ~50 cm; impulse ~ 3 Gauss-meter. (Need
20-40 elements.)
Structures dump each electromagnetic pulse into a load.
6
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Something new: a “Fourier series kicker”
kicker rf cavities
injection/extraction
deflecting magnet
injection/extraction
deflecting magnet
pT
injection path
extraction path
Fourier series kicker would be located in a bypass section.
While damping, beam follows the dog bone-shaped path (solid line).
During injection/extraction, deflectors route beam through bypass
(straight) section. Bunches are kicked onto/off orbit by kicker.
7
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Fourier series kicker
injection path
extraction path
kicker rf cavities
fhigh
fhigh +
3 MHz
fhigh +
6 MHz
...
fhigh +
(N-1)3 MHz
Kicker would be a series of N “rf cavities” oscillating at harmonics of
the linac bunch frequency 1/(337 nsec) = 2.97 MHz:
 j  N cavities 1

2
pT  A   Aj cos  high  jlow  t   ; low 
337 ns
 j 0

8
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Fourier series kicker
fhigh
fhigh +
3 MHz
fhigh +
6 MHz
...
fhigh +
(N-1)3 MHz
Run them at 3 MHz, 6 MHz, 9 MHz,… (original idea) or
perhaps at higher frequencies, with 3 MHz separation: fhigh,
fhigh+3 MHz, fhigh+6MHz,... (Shiltsev’s suggestion)
Cavities oscillate in phase, possibly with equal amplitudes.
They are always on so fast filling/draining is not an issue.
Kick could be transverse, or longitudinal, followed by a
dispersive (bend) section (Dugan’s idea).
High-Q: perhaps amplitude and phase stability aren’t too hard to
manage?
9
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Kicker pT
A ten-cavity system might look like this (fhigh = 300 MHz):
Kick vs. time, 10 cavity system, 300MHz lowest frequency,
f
3MHz
10
j  N cavities 1
pT ~
5

j 0
cos  high  jlow  t 
0
5
(actually, one would want to
use more than ten cavities)
10
10
0
50
George Gollin,
7/03
100
150Cornell LC
200
250
I
300
Physics
P 350
llinois
Bunch timing
Kicked bunches are here…
Kick vs. time, 10 cavity system, 300MHz lowest frequency,
f
3MHz
10
5
1
2
3
4
5
6
7
8
9
10
0
5
…undisturbed bunches are here
(call these “major zeroes”)
10 cavity system, 300MHz
Kick vs.
lowest
time,frequency
10 cavity
, system,
f
3MHz
around first major zero
10
0.4
10
5
0.20
50
100
150
200
250
300
350
0
0
0.2
5
0.4
10
2
1
0
1
2
32
33
34
35
Interval between kick and adjacent “major zeroes” is uniform.
I
Physics
P
llinois
Extraction cycle timing
Assume bunch train contains a gap between last and first bunch
while orbiting inside the damping ring.
1. First deflecting magnet is energized.
last
bunch
first
bunch
12
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Extraction cycle timing
2. Second deflecting magnet is energized; bunches 1, N+1,
2N+1,… are extracted during first orbit through the bypass.
bunches
1, N+1, 2N+1,...
13
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Extraction cycle timing
3. Bunches 2, N+2, 2N+2,… are extracted during second orbit
through the bypass.
4. Bunches 3, N+3, 2N+3,… are extracted during third orbit
through the bypass.
5. Etc. (entire beam is extracted in N orbits)
14
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Injection cycle timing
Just run the movie backwards…
With a second set of cavities, it should work to extract
and inject simultaneously.
15
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Sometimes pT can be summed analytically…
Here are some plots for a kicker system using frequencies 300
MHz, 303 MHz, 306 MHz,… and equal amplitudes Aj :
Define  high  2  300MHz; low  2  3MHz; K   high  low
pT 
j  N cavities 1

j 0
cos  high  j low  t 
sin  K  12  N cavities  lowt   sin  K  12  lowt 

2sin  12 lowt 
16
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Lots of algebra. Visualizing this…
Represent each cavity’s kick as a “phasor” (vector) whose x
component is the kick, and whose y component is not...
j  N cavities 1
pT ~

j 0
cos  high  jlow  t 
Each cavity’s phasor spins around counterclockwise…
 j   high  j low  t
17
j
cos  high  j low  t
sin  high  jlow  t
I
Physics
P
llinois
Phasors: visualizing the pT kick
The horizontal component of the phasor
(vector) sum indicates pT.

pT
Here’s a four-phasor sum as an example:



18






George Gollin, Cornell LC 7/03


I
Physics
P
llinois
Phasors: visualizing the pT kick
Here’s a 10-cavity phasor diagram for equal-amplitude cavities…
pT
start here
end here
19
…and 30-cavity animations (30, A, B, C).
I
Physics
P
llinois
Phasors: visualizing the pT kick
Both the x and y components of the phasor sum…
j  N cavities 1
x:

j 0
cos  high  jlow  t 
sin  K  12  N cavities  lowt   sin  K  12  lowt 

2sin  12 lowt 
j  N cavities 1
y:

j 0
sin  high  j low  t 
 cos  K  12  N cavities  lowt   cos  K  12  lowt 

2sin  12 lowt 
…are zero when N cavitieslowt  m  2 (m is integral)
I
Physics
P
llinois
Phasors: visualizing the pT kick
Kicks occur when the denominator is zero: t  0,
2
low
,
4
low
,
“Major zeroes” between two kicks are evenly spaced and occur at
t
2
N cavitieslow
,
4
N cavitieslow
,
 N cavities  1  2
N cavitieslow
One kicker cycle comprises a kick followed by (Ncavities - 1)
major zeroes.
21
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor diagrams for major zeroes of one specific example:
• 30 cavity system
• 300 MHz lowest frequency, 3 MHz spacing
Phasor plot
Phasor plot
2
2
t
nsec
scaled kick
t
11.1111
7.21645 10
Zero crossing 1
1.5
22.2222
1
1
0.5
0.5
0
0
0.5
0.5
1
1
larger red dot:
tip of last phasor
4.69994 10
16
Zero crossing 2
1.5
green dot:
tip of first phasor
1.5
1.5
6.37275 10
x,y
1.5
1
0.5
15
, 1.43387 10
14
x,y
0
0.5
zero #1
1
1.06798 10
vx,vy
1.1002, 2.47109
vx,vy
22
nsec
scaled kick
17
1.5
2
1.5
1
0.5
14
,
1.17477 10
14
0.909964, 1.01062
0
0.5
zero #2
I
1
1.5
2
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor plot
Phasor plot
2
2
t
nsec
33.3333
scaled kick
t
1.31006 10
15
Zero crossing 3
1.5
44.4444
1
1
0.5
0.5
0
0
0.5
0.5
1
1
7.17944 10
16
Zero crossing 4
1.5
1.5
1.5
x,y
1.16765 10
vx,vy
1.5
1
0.5
0.870195,
0
0.5
15
, 3.59276 10
16
x,y
0.282743
1
1.77423 10
vx,vy
1.5
2
1.5
zero #3
23
nsec
scaled kick
1
0.5
15
, 1.61728 10
14
0.0726631, 0.691343
0
0.5
1
1.5
2
zero #4
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor plot
Phasor plot
2
2
t
nsec
scaled kick
55.5556
t
6.51331 10
16
Zero crossing 5
1.5
66.6667
1.66904 10
15
, 7.5553 10
16
Zero crossing 6
1.5
1
1
0.5
0.5
0
0
0.5
0.5
1
1
1.5
1.5
x,y
5.10703 10
vx,vy
1.5
1
0.5
15
,
2.88658 10
15
x,y
0.489726, 0.282743
0
0.5
1
1.03885 10
vx,vy
1.5
2
1.5
zero #5
24
nsec
scaled kick
1
0.5
0.389163,
0
0.5
15
0.282743
1
1.5
2
zero #6
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor plot
Phasor plot
2
2
t
nsec
t
77.7778
scaled kick
8.69675 10
16
Zero crossing 7
1.5
88.8889
1
1
0.5
0.5
0
0
0.5
0.5
1
1
1.07692 10
15
Zero crossing 8
1.5
1.5
1.5
x,y
1.32736 10
vx,vy
1.5
1
0.5
15
,
6.45015 10
15
x,y
0
0.5
1
1.74232 10
vx,vy
0.0878538, 0.413319
1.5
2
1.5
zero #7
25
nsec
scaled kick
1
0.5
14
,
3.66018 10
15
0.372155, 0.0791039
0
0.5
1
1.5
2
zero #8
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor plot
Phasor plot
2
2
t
nsec
100.
scaled kick
t
1.46179 10
16
Zero crossing 9
1.5
111.111
1
1
0.5
0.5
0
0
0.5
0.5
1
1
5.03671 10
15
Zero crossing 10
1.5
1.5
1.5
1.5
1
0.5
x,y
1.784 10
vx,vy
0.205425,
0
0.5
15
,
2.47016 10
15
x,y
0.282743
1
3.39723 10
vx,vy
1.5
2
1.5
zero #9
26
nsec
scaled kick
1
0.5
15
, 5.89709 10
15
0.163242, 0.282743
0
0.5
1
1.5
2
zero #10
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor plot
Phasor plot
2
2
t
nsec
scaled kick
122.222
t
5.16994 10
15
Zero crossing 11
1.5
133.333
1
1
0.5
0.5
0
0
0.5
0.5
1
1
7.84558 10
16
Zero crossing 12
1.5
1.5
1.5
x,y
1.01401 10
vx,vy
1.5
1
0.5
14
, 1.09376 10
15
x,y
0.307806, 0.0323517
0
0.5
1
5.25311 10
vx,vy
1.5
2
1.5
zero #11
27
nsec
scaled kick
1
0.5
16
, 1.48838 10
15
0.0918689, 0.282743
0
0.5
1
1.5
2
zero #12
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor plot
Phasor plot
2
2
t
nsec
t
144.444
scaled kick
8.9669 10
15
Zero crossing 13
1.5
155.556
1
1
0.5
0.5
0
0
0.5
0.5
1
1
1.56912 10
15
Zero crossing 14
1.5
1.5
1.5
x,y
1.47553 10
vx,vy
1.5
1
0.5
15
, 1.36203 10
15
x,y
0
0.5
1
8.12136 10
vx,vy
0.214813, 0.193419
1.5
2
1.5
zero #13
28
nsec
scaled kick
1
0.5
15
,
3.6281 10
15
0.259722, 0.115636
0
0.5
1
1.5
2
zero #14
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor plot
Phasor plot
2
2
t
nsec
166.667
scaled kick
t
0.
Zero crossing 15
1.5
177.778
1
1
0.5
0.5
0
0
0.5
0.5
1
1
1.84482 10
15
Zero crossing 16
1.5
1.5
1.5
x,y
0.,
vx,vy
1.5
1
0.5
8.82123 10
7.54029 10
0
0.5
15
15
x,y
,
0.282743
1
1.5
2.43083 10
vx,vy
2
1.5
zero #15
29
nsec
scaled kick
1
0.5
14
, 1.07727 10
14
0.259722, 0.115636
0
0.5
1
1.5
2
zero #16
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors when pT = 0 (30 cavities)
Phasor plot
Phasor plot
2
2
t
nsec
188.889
scaled kick
t
1.34337 10
15
Zero crossing 17
1.5
200.
1
1
0.5
0.5
0
0
0.5
0.5
1
1
2.15383 10
15
Zero crossing 18
1.5
1.5
1.5
x,y
9.70447 10
vx,vy
1.5
1
0.5
15
,
8.68295 10
15
x,y
0.214813, 0.193419
0
0.5
1
1.57593 10
vx,vy
1.5
2
1.5
zero #17
1
0.5
0.0918689,
0
0.5
15
,
4.9029 10
15
0.282743
1
1.5
2
zero #18
…and so forth. (There are 29 major zeroes in all.)
30
nsec
scaled kick
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
dpT/dt considerations
We’d like the slopes of the pT
curves when not-to-be-kicked
bunches pass through the kicker to
be as small as possible so that the
head, center, and tail of a (20 ps
rms) bunch will experience about
the same field integral.
Kick vs. time, 10 cavity system, 300MHz lowest frequency,
0
5
10
0
50
0.05
0.1
100
150
200
250
33.4
33.6
300
350
Kick vs. time, 10 cavity system, around second major zero
0.1
1% of kick
33.2
3MHz
5
Kick vs. time, 10 cavity system, around first major zero
0.1
0.05
f
10
33.8
0.05
66.2
66.4
66.6
66.8
1 nsec
0.05
pT in the vicinity of two zeroes
I
Physics
P
llinois
0.1
Sometimes dpT/dt at zeroes can be calculated…
jN
1

dpT
d  cavities
   cos  high  jlow  t  
dt
dt  j 0

At the mth “major zero” the expression evaluates to
K  12  


N cavitieslow cos  m  2

N
dpT
cavities 


dt
 m 
2sin 

N
 K  high low 
 cavities 
Note that magnitude of the slope does not depend strongly
on high. (It does for the other zeroes, however.)
I
Physics
P
llinois
Flattening out d pT/d t
pT = 0
Endpoint is moving this
way at the zero in pT
(80 psec intervals)
33
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Flattening out d pT/d t
In terms of phasor sums: we want the endpoint of the phasor sum
to have as small an x component of “velocity” as possible.
Endpoint velocity components (m ranges from 1 to Ncavities – 1):
K  12  


N cavitieslow
vx 
cos  m  2

N
 m 
cavities 

2sin 

N
 cavities 
34
K  12  


N cavitieslow
vy 
sin  m  2

N
 m 
cavities 

2sin 

N
 cavities 
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Flattening out d pT/d t
How large a value for vx is acceptable?
• Size of kick: Ncavities
• rms bunch length: 20 psec (6 mm)
• maximum allowable kick error: ~.07%
 .020 nsec  v x  0.07  102  N cavities
Work in units of nsec and GHz… for 30 cavities: vx < 1.05 nsec-1.
35
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasor plots for d pT/d t
Phasor magnitude for mth zero’s dpT/dt:
v 
N cavitieslow
 m 
2sin 

N
 cavities 
m  1, 2,
, N cavities  1
Phasor sum endpoint velocity magnitude vs. which major zero
2.5
~maximum allowable value
2
1.5
1
0.5
5
Phasor angle:
10
15
K  12 

 m  m  2
N cavities
20
25
vx  v cosm
I
Physics
P
llinois
Phasor plots for d pT/d t
kicker phasor endpoint velocity at the various major zeroes
Phasor plot for dpT/dt,
including the phasor
angles…
K  12 

 m  m  2
1
29
2
1
N cavities
K   high low
4
0
3
Ncavities = 30
1
K=100 (300MHz, 3 MHz)
There are lots of
parameters to play with.
28
2
Between the
blue lines is
good.
2
2
1
0
1
I
Physics
P
llinois
2
Changing parameters
kicker phasor endpoint velocity at the various major zeroes
kicker phasor endpoint velocity at the various major zeroes
kicker phasor endpoint velocity at the various major zeroes
2
2
2
1
1
1
0
0
0
1
1
1
Ncavities = 30, K=99
2
2
2
2
1
0
1
Ncavities = 30, K=100
2
2
1
0
1
kicker phasor endpoint velocity at the various major zeroes
Ncavities = 30, K=101
2
2
1
0
1
2
kicker phasor endpoint velocity at the various major zeroes
3
2
2
1
1
0
0
1
1
2
2
Ncavities = 29, K=100
2
1
0
1
2
I
Ncavities = 31, K=100
3
3
2
1
0
1
2
3
Physics
P
llinois
More dramatic d pT/d t reduction…
…is possible with different amplitudes Aj in each of the cavities.
We (in particular Guy Bresler) are investigating this right now. It
looks very promising!
Guy has constructed an algorithm to find sets of amplitudes
which have dpT/dt = 0 at evenly-spaced “major zeroes” in pT.
There are lots of different possible sets of amplitudes which will
work.
39
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
More dramatic d pT/d t reduction…
Here’s one set for a 29-cavity system (which makes 28 zeroes in
pT and dpT/dt in between kicks), with 300 MHz, 303 MHz,…:
Cavity amplitudes
0.04
0.03
0.02
0.01
0
40
5
10
15
George Gollin, Cornell LC 7/03
20
25
I
Physics
P
llinois
Kick corresponding to those amplitudes
Kick vs. time, 10 cavity system, 300MHz lowest frequency,
f
3MHz
1
0.5
0
0.5
0
50
100
150
200
250
300
350
The “major zeroes” aren’t quite at the obvious symmetry points.
41
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Kick corresponding to those phasors
Kick
vs . time , Guy 's amplitudes
, 300 MHz
lowest
frequency
,
f
3MHz
0.1
0.05
0
-0.05
100
120
140
160
Here’s where some of them are.
42
George Gollin, Cornell LC 7/03
180
200
I
Physics
P
llinois
Phasors with amplitudes chosen to give
dpT/dt = 0 and pT = 0 (29 cavities)
Phasor plot
Phasor plot
0.2
0.2
t
nsec
11.4943
scaled kick
4.63388 10
t
16
Zero crossing 1
0.1
0
0
0.1
0.1
x,y
2.44179,
0.1
18.0926,
0
8.79454
x,y
3.96832
0.1
1.27271,
vx,vy
0.2
zero #1
0.1
5.63785 10
17
0.765766
2.0668, 2.26901
0
0.1
0.2
zero #2
The phasor sums show less geometrical symmetry.
43
22.9885
Zero crossing 2
0.1
vx,vy
nsec
scaled kick
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Phasors with amplitudes chosen to give
dpT/dt = 0 and pT = 0 (29 cavities)
Phasor plot
Phasor plot
0.2
0.2
t
nsec
t
34.4828
scaled kick
4.2498 10
0.1
0.1
0
0
0.1
0.1
x,y
2.00884,
0.1
4.07264,
0
x,y
1.90287
0.1
0.2
zero #3
7.12755 10
16
1.27338
2.70045, 1.14132
0
0.1
0.2
zero #4
etc.
44
0.675104,
vx,vy
3.86521
0.1
45.977
Zero crossing 4
Zero crossing 3
vx,vy
nsec
scaled kick
16
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
How well do we do with these amplitudes?
Old, equal-amplitudes scheme:
Phasor sum endpoint velocity magnitude vs. which major zero
2.5
~maximum allowable value
2
1.5
1
0.5
5
10
15
20
25
bunch number
New, intelligently-selected-amplitudes scheme:
Head
of
bunch kick
when
center is
zero
0.001
0.0008
0.0006
Wow!
0.0004
~maximum allowable value
0.0002
0
5
10
15
bunch number
20
25
I
Physics
P
llinois
Multiple passes through the kicker
Previous plots were for a single pass through the kicker.
Most bunches make multiple passes through the kicker.
Modeling of effects associated with multiple passes must take
into account damping ring’s
• synchrotron tune (0.10 in TESLA TDR)
• horizontal tune (72.28 in TESLA TDR)
We (in particular, Keri Dixon) are working on this now.
With equal-amplitude cavities some sort of compensating gizmo
on the injection/extraction line (or immediately after the kicker)
is probably necessary. However…
46
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Multiple passes through the kicker
…selecting amplitudes to zero out pT slopes fixes the problem! Here’s
a worst-case plot for 300 MHz,… (assumes tune effects always work
against us).
Worst case cumulative head of bunch kick when center is zero
0.001
0.0008
maximum allowed value
0.0006
0.0004
0.0002
0
47
5
10
15
bunch number
20
I
25
Physics
P
llinois
Some of our other concerns
1. Effect of finite separation of the kicker cavities along the
beam direction (George)
2. Arrival time error at the kicker for a bunch that is being
injected or extracted (Keri)
3. Inhomogeneities in field integrals for real cavities (Keri)
4. What is the optimal choice of cavity frequencies and
amplitudes? (Guy)
48
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Finite separation of the kicker cavities
...
Even though net pT is zero there can be a small displacement
away from the centerline by the end of an N-element kicker.
For N = 16; 50 cm cavity spacing; 6.5 Gauss-meter per cavity:
Non-kicked bunches only
(1, 2, 4, … 32)
49
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Finite separation of the kicker cavities
...
...
Compensating for this: insert a second set of cavities in phase
with the first set, but with the order of oscillation frequencies
reversed: 3 MHz, 6 MHz, 9MHz,… followed by …, 9 MHz,
6 MHz, 3 MHz.
Non-kicked bunches only
(N = 1, 2, 4, … 32)
50
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Arrival time error at the kicker for a bunch
that is being injected or extracted
What happens if a bunch about to be kicked passes through the kicker
cavities slightly out of time?
It depends on the details of the kicker system:
• 16-cavity system with 3MHz, 6MHz,… cavities:
dpT/pT~ 6  10-6
• 30-cavity system with 3.000GHz, 3.003GHz,… cavities:
dpT/pT~ 9  10-4 so an extraction line corrector is probably
necessary
51
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
What we’re working on now
• Lately we’ve been working with models using high-frequency
cavities, split in frequency by multiples of the linac bunch
frequency.
• We want to better understand how to select the best set of
cavity frequencies an geometries.
• We are in the process of incorporating tune effects into our
models.
• We will investigate the kinds of corrections necessary to
compensate for tune and cavity-related effects.
• We will look into the relative merits of horizontal and
longitudinal kicks.
52
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Comments on doing this at a university
• Participation by talented undergraduate students makes LCRD
2.22 work as well as it does. The project is well-suited to
undergraduate involvement.
• We get most of our work done during the summer: we’re all
free of academic constraints (teaching/taking courses). The
schedule for evaluating our progress must take this into
account.
• Support for students comes from (NSF-sponsored) REU
program. We have borrowed PC’s from the UIUC Physics
Department instructional resources pool for them this summer.
• LCRD 2.22 requested $2,362 in support from DOE (mostly for
travel). In spite of a favorable review by the Holtkamp
committee, DOE has rejected the proposal. (We don’t know
why.) We’re continuing with the work, in spite of this.
53
George Gollin, Cornell LC 7/03
I
Physics
P
llinois
Conclusions
• We haven’t found any obvious show-stoppers yet.
• It seems likely that intelligent selection of cavity amplitudes
will provide us with a useful way to null out some of the
problems present in a more naïve scheme.
• We haven’t studied issues relating to precision and stability
yet. later this summer…
• This is a lot of fun.
54
George Gollin, Cornell LC 7/03
I
Physics
P
llinois