i physicsp i llinois george gollin, cornell lc 7/031 a fourier series kicker for the tesla damping...
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George Gollin, Cornell LC 7/031 IPhysicsPIllinois
A Fourier Series Kicker for the TESLA Damping Rings
George Gollin
Department of Physics
University of Illinois at Urbana-Champaign
LCRD 2.22
George Gollin, Cornell LC 7/032 IPhysicsPIllinois
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 function.
•Various issues such as finite bunch size, cavity geometry, and tune-related effects are under investigation.
George Gollin, Cornell LC 7/033 IPhysicsPIllinois
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
4 IPhysicsPIllinois
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.
George Gollin, Cornell LC 7/035 IPhysicsPIllinois
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.
George Gollin, Cornell LC 7/036 IPhysicsPIllinois
Overview: TESLA TDR fast kickerFast 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.
George Gollin, Cornell LC 7/037 IPhysicsPIllinois
Something new: a “Fourier series kicker”
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.
injection path extraction path
kicker rf cavities
injection/extraction deflecting magnet
injection/extraction deflecting magnet
pT
George Gollin, Cornell LC 7/038 IPhysicsPIllinois
Fourier series kicker
Kicker would be a series of N “rf cavities” oscillating at harmonics of the linac bunch frequency 1/(337 nsec) = 2.97 MHz:
1
0
2cos ;
337 ns
cavitiesj N
T j high low lowj
p A A j t
injection path extraction path
kicker rf cavities
fhigh fhigh + 3 MHz
fhigh + 6 MHz
fhigh + (N-1)3 MHz
...
George Gollin, Cornell LC 7/039 IPhysicsPIllinois
Fourier series kicker
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?
fhigh fhigh + 3 MHz
fhigh + 6 MHz
fhigh + (N-1)3 MHz
...
George Gollin, Cornell LC 7/0310 IPhysicsPIllinois
Kicker pT
A ten-cavity system might look like this (fhigh = 300 MHz):
0 50 100 150 200 250 300 350
10
5
0
5
10
Kick vs. time, 10cavity system, 300MHz lowest frequency, f 3MHz
(actually, one would want to use more than ten cavities)
1
0
~ coscavitiesj N
T high lowj
p j t
IPhysicsPIllinois
Bunch timing
0 50 100 150 200 250 300 350
10
5
0
5
10
Kick vs. time, 10cavity system, 300MHz lowest frequency, f 3MHz
Kicked bunches are here…
…undisturbed bunches are here (call these “major zeroes”)
1 2 3 4 5 6 7 8 9 10
Interval between kick and adjacent “major zeroes” is uniform.
2 1 0 1 210
5
0
5
10Kicking pulse, 10cavity system, 300MHz lowest frequency, f 3MHz
32 33 34 35
0.4
0.2
0
0.2
0.4
Kick vs. time, 10cavity system, around first major zero
George Gollin, Cornell LC 7/0312 IPhysicsPIllinois
Extraction cycle timing
Assume bunch train contains a gap between last and first bunch while orbiting inside the damping ring.
first bunch
last bunch
1. First deflecting magnet is energized.
George Gollin, Cornell LC 7/0313 IPhysicsPIllinois
Extraction cycle timing
bunches 1, N+1, 2N+1,...
2. Second deflecting magnet is energized; bunches 1, N+1, 2N+1,… are extracted during first orbit through the bypass.
George Gollin, Cornell LC 7/0314 IPhysicsPIllinois
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)
George Gollin, Cornell LC 7/0315 IPhysicsPIllinois
Injection cycle timingJust run the movie backwards…
With a second set of cavities, it should work to extract and inject simultaneously.
George Gollin, Cornell LC 7/0316 IPhysicsPIllinois
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 2 300MHz; 2 3MHz; high low high lowK
1
0
coscavitiesj N
T high lowj
p j t
1 12 2
12
sin sin
2sincavities low low
low
K N t K t
t
17 IPhysicsPIllinois
Lots of algebra. Visualizing this…
1
0
~ coscavitiesj N
T high lowj
p j t
Represent each cavity’s kick as a “phasor” (vector) whose x component is the kick, and whose y component is not...
cos high lowj t
j
sin high lowj t j high lowj t
Each cavity’s phasor spins around counterclockwise…
George Gollin, Cornell LC 7/0318 IPhysicsPIllinois
pT
Phasors: visualizing the pT kick
The horizontal component of the phasor (vector) sum indicates pT.
Here’s a four-phasor sum as an example:
19 IPhysicsPIllinois
Phasors: visualizing the pT kickHere’s a 10-cavity phasor diagram for equal-amplitude cavities…
start here
end here
pT
…and 30-cavity animations (30, A, B, C).
IPhysicsPIllinois
Phasors: visualizing the pT kick
Both the x and y components of the phasor sum…
1
0
1 12 2
12
: cos
sin sin
2sin
cavitiesj N
high lowj
cavities low low
low
x j t
K N t K t
t
1
0
1 12 2
12
: sin
cos cos
2sin
cavitiesj N
high lowj
cavities low low
low
y j t
K N t K t
t
…are zero when (m is integral)2cavities lowN t m
George Gollin, Cornell LC 7/0321 IPhysicsPIllinois
Phasors: visualizing the pT kick
One kicker cycle comprises a kick followed by (Ncavities - 1) major zeroes.
Kicks occur when the denominator is zero:2 4
0, , ,low low
t
“Major zeroes” between two kicks are evenly spaced and occur at
1 22 4, , cavities
cavities low cavities low cavities low
Nt
N N N
22 IPhysicsPIllinois
Phasors when pT = 0 (30 cavities)
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 11.1111
scaled kick 7.21645 1017
Zero crossing 1
x,y 6.37275 1015, 1.43387 1014vx,vy 1.1002, 2.471091.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 22.2222
scaled kick 4.69994 1016
Zero crossing 2
x,y 1.06798 1014, 1.17477 1014vx,vy 0.909964, 1.01062
Phasor diagrams for major zeroes of one specific example:
• 30 cavity system
• 300 MHz lowest frequency, 3 MHz spacing
zero #1 zero #2
green dot:
tip of first phasor
larger red dot:
tip of last phasor
George Gollin, Cornell LC 7/0323 IPhysicsPIllinois
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 33.3333
scaled kick 1.31006 1015
Zero crossing 3
x,y 1.16765 1015, 3.59276 1016vx,vy 0.870195, 0.2827431.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 44.4444
scaled kick 7.17944 1016
Zero crossing 4
x,y 1.77423 1015, 1.61728 1014vx,vy 0.0726631, 0.691343
Phasors when pT = 0 (30 cavities)
zero #3 zero #4
George Gollin, Cornell LC 7/0324 IPhysicsPIllinois
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 55.5556
scaled kick 6.51331 1016
Zero crossing 5
x,y 5.10703 1015, 2.88658 1015vx,vy 0.489726, 0.2827431.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 66.6667
scaled kick 1.66904 1015
Zero crossing 6
x,y 1.03885 1015, 7.5553 1016vx,vy 0.389163, 0.282743
Phasors when pT = 0 (30 cavities)
zero #5 zero #6
George Gollin, Cornell LC 7/0325 IPhysicsPIllinois
Phasors when pT = 0 (30 cavities)
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 77.7778
scaled kick 8.69675 1016
Zero crossing 7
x,y 1.32736 1015, 6.45015 1015vx,vy 0.0878538, 0.4133191.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 88.8889
scaled kick 1.07692 1015
Zero crossing 8
x,y 1.74232 1014, 3.66018 1015vx,vy 0.372155, 0.0791039
zero #7 zero #8
George Gollin, Cornell LC 7/0326 IPhysicsPIllinois
Phasors when pT = 0 (30 cavities)
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 100.
scaled kick 1.46179 1016
Zero crossing 9
x,y 1.784 1015, 2.47016 1015vx,vy 0.205425, 0.2827431.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 111.111
scaled kick 5.03671 1015
Zero crossing 10
x,y 3.39723 1015, 5.89709 1015vx,vy 0.163242, 0.282743
zero #9 zero #10
George Gollin, Cornell LC 7/0327 IPhysicsPIllinois
Phasors when pT = 0 (30 cavities)
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 122.222
scaled kick 5.16994 1015
Zero crossing 11
x,y 1.01401 1014, 1.09376 1015vx,vy 0.307806, 0.03235171.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 133.333
scaled kick 7.84558 1016
Zero crossing 12
x,y 5.25311 1016, 1.48838 1015vx,vy 0.0918689, 0.282743
zero #11 zero #12
George Gollin, Cornell LC 7/0328 IPhysicsPIllinois
Phasors when pT = 0 (30 cavities)
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 144.444
scaled kick 8.9669 1015
Zero crossing 13
x,y 1.47553 1015, 1.36203 1015vx,vy 0.214813, 0.1934191.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 155.556
scaled kick 1.56912 1015
Zero crossing 14
x,y 8.12136 1015, 3.6281 1015vx,vy 0.259722, 0.115636
zero #13 zero #14
George Gollin, Cornell LC 7/0329 IPhysicsPIllinois
Phasors when pT = 0 (30 cavities)
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 166.667
scaled kick 0.
Zero crossing 15
x,y 0., 8.82123 1015vx,vy 7.54029 1015, 0.2827431.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 177.778
scaled kick 1.84482 1015
Zero crossing 16
x,y 2.43083 1014, 1.07727 1014vx,vy 0.259722, 0.115636
zero #15 zero #16
George Gollin, Cornell LC 7/0330 IPhysicsPIllinois
Phasors when pT = 0 (30 cavities)
1.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 188.889
scaled kick 1.34337 1015
Zero crossing 17
x,y 9.70447 1015, 8.68295 1015vx,vy 0.214813, 0.1934191.5 1 0.5 0 0.5 1 1.5 2
1.5
1
0.5
0
0.5
1
1.5
2Phasor plot
tnsec 200.
scaled kick 2.15383 1015
Zero crossing 18
x,y 1.57593 1015, 4.9029 1015vx,vy 0.0918689, 0.282743
…and so forth. (There are 29 major zeroes in all.)
zero #17 zero #18
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dpT/dt considerationsWe’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.
33.2 33.4 33.6 33.8
0.1
0.05
0.05
0.1Kick vs. time, 10cavity system, around first major zero
66.2 66.4 66.6 66.8
0.1
0.05
0.05
0.1Kick vs. time, 10cavity system, around second major zero
0 50 100 150 200 250 300 350
10
5
0
5
10
Kick vs. time, 10cavity system, 300MHz lowest frequency, f 3MHz
1 nsec
1% of kick
pT in the vicinity of two zeroes
IPhysicsPIllinois
Sometimes dpT/dt at zeroes can be calculated…
1
0
coscavitiesj N
Thigh low
j
dp dj t
dt dt
12cos 2
2sin
cavities lowcavitiesT
cavities
KN m
Ndp
dt mN
At the mth “major zero” the expression evaluates to
Note that magnitude of the slope does not depend strongly on high. (It does for the other zeroes, however.)
high lowK
George Gollin, Cornell LC 7/0333 IPhysicsPIllinois
Flattening out d pT/d t
Endpoint is moving this way at the zero in pT
(80 psec intervals)
pT = 0
George Gollin, Cornell LC 7/0334 IPhysicsPIllinois
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):
12
sin 2
2sin
cavities lowy
cavities
cavities
KNv m
NmN
12
cos 2
2sin
cavities lowx
cavities
cavities
KNv m
NmN
George Gollin, Cornell LC 7/0335 IPhysicsPIllinois
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%
2.020 nsec 0.07 10x cavitiesv N
Work in units of nsec and GHz… for 30 cavities: vx < 1.05 nsec-1.
IPhysicsPIllinois
Phasor plots for d pT/d t
Phasor magnitude for mth zero’s dpT/dt:
2sin
cavities low
cavities
Nv
mN
1, 2, , 1cavitiesm N
122m
cavities
Km
N
Phasor angle:
5 10 15 20 25
0.5
1
1.5
2
2.5
Phasor sum endpoint velocity magnitude vs. which major zero
~maximum allowable value
cosx mv v
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Phasor plots for d pT/d t
Phasor plot for dpT/dt, including the phasor angles…
2 1 0 1 2
2
1
0
1
2
kicker phasor endpoint velocity at the various major zeroes
1
2
3
4
29
28
122m
cavities
Km
N
high lowK
Ncavities = 30
K=100 (300MHz, 3 MHz)
There are lots of parameters to play with.
Between the blue lines is
good.
IPhysicsPIllinois
Changing parameters
2 1 0 1 2
2
1
0
1
2
kicker phasor endpoint velocity at the various major zeroes
Ncavities = 30, K=1002 1 0 1 2
2
1
0
1
2
kicker phasor endpoint velocity at the various major zeroes
Ncavities = 30, K=1012 1 0 1 2
2
1
0
1
2
kicker phasor endpoint velocity at the various major zeroes
Ncavities = 30, K=99
2 1 0 1 2
2
1
0
1
2
kicker phasor endpoint velocity at the various major zeroes
Ncavities = 29, K=1003 2 1 0 1 2 3
3
2
1
0
1
2
3
kicker phasor endpoint velocity at the various major zeroes
Ncavities = 31, K=100
George Gollin, Cornell LC 7/0339 IPhysicsPIllinois
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.
George Gollin, Cornell LC 7/0340 IPhysicsPIllinois
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,…:
0 5 10 15 20 25
0.01
0.02
0.03
0.04Cavity amplitudes
George Gollin, Cornell LC 7/0341 IPhysicsPIllinois
Kick corresponding to those amplitudes
The “major zeroes” aren’t quite at the obvious symmetry points.
0 50 100 150 200 250 300 350
0.5
0
0.5
1
Kick vs. time, 10cavity system, 300MHz lowest frequency, f 3MHz
George Gollin, Cornell LC 7/0342 IPhysicsPIllinois
Kick corresponding to those phasors
100 120 140 160 180 200
-0.05
0
0.05
0.1
Kick vs. time , Guy 's amplitudes , 300 MHz lowest frequency , f 3MHz
Here’s where some of them are.
George Gollin, Cornell LC 7/0343 IPhysicsPIllinois
Phasors with amplitudes chosen to give dpT/dt = 0 and pT = 0 (29 cavities)
zero #1 zero #2
0.1 0 0.1 0.2
0.1
0
0.1
0.2Phasor plot
tnsec 11.4943
scaled kick 4.63388 1016
Zero crossing 1
x,y 2.44179, 8.79454vx,vy 18.0926, 3.968320.1 0 0.1 0.2
0.1
0
0.1
0.2Phasor plot
tnsec 22.9885
scaled kick 5.63785 1017
Zero crossing 2
x,y 1.27271, 0.765766vx,vy 2.0668, 2.26901
The phasor sums show less geometrical symmetry.
George Gollin, Cornell LC 7/0344 IPhysicsPIllinois
Phasors with amplitudes chosen to give dpT/dt = 0 and pT = 0 (29 cavities)
zero #3 zero #4
0.1 0 0.1 0.2
0.1
0
0.1
0.2Phasor plot
tnsec 34.4828
scaled kick 4.2498 1016
Zero crossing 3
x,y 2.00884, 1.90287vx,vy 4.07264, 3.865210.1 0 0.1 0.2
0.1
0
0.1
0.2Phasor plot
tnsec 45.977
scaled kick 7.12755 1016
Zero crossing 4
x,y 0.675104, 1.27338vx,vy 2.70045, 1.14132
etc.
IPhysicsPIllinois
How well do we do with these amplitudes?
Old, equal-amplitudes scheme:
5 10 15 20 25
0.5
1
1.5
2
2.5
Phasor sum endpoint velocity magnitude vs. which major zero
~maximum allowable value
New, intelligently-selected-amplitudes scheme:
0 5 10 15 20 25
0.0002
0.0004
0.0006
0.0008
0.001Head of bunch kick when center is zero
~maximum allowable valueWow!
bunch number
bunch number
George Gollin, Cornell LC 7/0346 IPhysicsPIllinois
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…
47 IPhysicsPIllinois
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).
0 5 10 15 20 25
0.0002
0.0004
0.0006
0.0008
0.001Worstcase cumulative head of bunch kick when center is zero
maximum allowed value
bunch number
George Gollin, Cornell LC 7/0348 IPhysicsPIllinois
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)
George Gollin, Cornell LC 7/0349 IPhysicsPIllinois
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)
George Gollin, Cornell LC 7/0350 IPhysicsPIllinois
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)
George Gollin, Cornell LC 7/0351 IPhysicsPIllinois
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:
pT/pT~ 6 10-6
• 30-cavity system with 3.000GHz, 3.003GHz,… cavities:
pT/pT~ 9 10-4 so an extraction line corrector is probably necessary
George Gollin, Cornell LC 7/0352 IPhysicsPIllinois
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.
George Gollin, Cornell LC 7/0353 IPhysicsPIllinois
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.
George Gollin, Cornell LC 7/0354 IPhysicsPIllinois
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.