Transcript Slides - Indico

Two Beam Accelerator Studies
Lee Carver
Group Meeting
Monday 2nd June 2014
Lee Carver
OUTLINE OF TALK:
I.
Cavity detuning for collinear acceleration
II.
Multi-harmonic cavities
III.
Multi-harmonic collinear accelerator structure
IV.
Conclusions
Lee Carver
2
I.I Cavity detuning for collinear
acceleration
Monopole Mode Detuning
• Detuned cavities allow for collinear beams
• Phase shift, ϕ=ArcTan(-2Qδ) causes high current
drive bunch to see low decelerating field.
• Low current test bunch phased to arrive π/2 later,
sees high accelerating field.
• Transformer Ratio, T is the ratio of test bunch field to
drive bunch field, T>>1
• Can be shown that T = -2Qδ for unloaded case, Q is
the cavity quality factor, δ is the magnitude of
detuning.
Lee Carver
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I.II - Beam Excitation: Detuned-Cavity Two-Beam
Accelerator
Fixed Detuning
+∆F +∆F +∆F +∆F
+∆F +∆F
Cavity period Λ
Alternative Detuning
+∆F
-∆F
+∆F -∆F +∆F
-∆F
Every other cavity, detuning flips sign
Details in “High-gradient two-beam accelerator structure”, S. Yu Kazakov, S.V. Kuzikov, Y. Jiang, and J. L. Hirshfield, PRSTAB 13, 071303 (2010)
Slide courtesy of Y.Jiang
Lee Carver
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I.III - Single Mode TBA Experimental Plan
Detuning angle Δθ=φ
Oscilloscope
I/Q Demodulator
Phase Shifter
I/Q
Attenuator
Field Probe
Beam Position
Monitor
T3P
Drive Bunch
π-mode SW Structure
final energy spread of
accelerated unbunched beam
(1) To measure the transformer ratio by
measuring the phase relationship
between the drive bunch and the
excited wakefield in the detuned
accelerator structure.
(2) To measure the acceleration gradient by
measuring the final energy distribution
of DC test beam.
Slide courtesy of Y.Jiang
Lee Carver
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II. Multi Harmonic Cavities
Dual mode excitation
• TM010 + TM020 could reduce onset of rf breakdown
due to anode cathode effect.
• TM010 + TM011 / TM021 could reduce effects from
pulsed surface heating.
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II.I - Motivation: Why excite multiple harmonics?
Superimposing harmonically-related modes
• Anode – Cathode effect: Electric fields that point into metallic cavity surfaces (cathodelike) can be smaller than fields that point away from the surfaces (anode-like), thereby
inhibiting field emission and potentially preventing onset of rf breakdown.
Potential energy u of an electron near the surface of a metal
with x the distance of electron from surface.
• may lower the pulsed surface heating. By
superimposing two modes
(Ideal pillbox η=H2max/H1max=2)
Slide courtesy of Y.Jiang
Lee Carver
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II.II - Field profiles in dual-harmonic cavities
b
TM010 + TM020
Peak Electric Field (A.U.)
Cathode-like Peak Surface Field
Contributed to Breakdown
a
b
Anode
a S
c de
TM010 + TM011
c
ed
Z
Cathode
Cathode
Anode-like Peak
Surface Field
axis
Anode
Peak Accelerating Field
Magnetic Field H2 (A.U.)
periphery distance s (mm)
a
bc
d
b c
aS
Single mode multi-mode
d
periphery distance s (mm)
Lee Carver
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II.III - Pulsed Surface Heating Reduction
Single mode and two mode superposition
normalized at the same acceleration gradient 100 MV/m
The preliminary design shows it can lower the
pulse heating by about 20% at the cost of
increasing maximum electric field by 20%, and
satisfy the constraint:
(1) surface electric field Max(Esurf)<260 MV/m
(2) pulsed surface heating ΔTmax<56oC
Optimisation Goals:
[1]
(1) minimize the ratio of peak magnetic fields and the ratio of
peak electric fields
(2) maximize the ratio of shunt impedances
between the second mode to the first one
and balanced with design goal for both harmonics
(3) minimize peak magnetic field and peak electric field
(4) maximize the shunt impedance
[1] Details in “RF Pulsed Surface Heating”, David Pritzkau - Thesis, ARDB271 (2001)
Lee Carver
Slide courtesy of Y.Jiang
9
III. Multi Harmonic Accelerator
Structure
Beam driven accelerating cavity
• Longitudinal Beam Dynamics
• Mode configuration
• Cavity parameters
Lee Carver
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III.I – Longitudinal Dynamics – Single Mode
•
For a linac with SW, π-mode cavities, the
coupled differential equations for βsγs is
constant are given by:
•
Hamiltonian can be calculated as
φs=-π/3, red is separatrix, blue is
Hamiltonian, black is single particle
tracker.
Lee Carver
For the case acceleration is present: βsγs is
not constant. Separatrix becomes ‘input
acceptance’
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III.I – Longitudinal Dynamics – Multi Mode
•
•
•
α is the percentage contribution from first
mode, h is the harmonic number
Φ=φs+φh, allows for phase of additional
mode to be shifted (Cos(x) or Sin(x))
Hamiltonian can be calculated as
•
•
φh=0, φs=-π/9, h=3, points mark phase
positions of separatrix
Lee Carver
Black is separatrix for α=1,
Red is for α=0
Acceptance of third
harmonic alone is approx.
3 times that of
fundamental alone.
However, for h=3
-π/6 < φs < 0
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III.II – Second vs Third Harmonic
•
Fundamental mode is π-mode SW which follows a Cos(x) distribution (x=0
denotes cavity center).
Additional modes need to be given field pattern that accurately portrays excited
field: h=2 follows Sin(2x), h=3 follows Cos(3x)
•
•
For a sync. phase that gives acceleration for fundamental mode, second
harmonic gives stable deceleration. Not ideal for an accelerator.
•
This is only the case for beam driven multi-harmonic cavities. For rf driven,
phase shift between input rf of each mode can be varied to make both modes
accelerating.
Lee Carver
13
5245
45
0240
40
III.I - Beam driven multi-harmonic structure
5135
•
•
•
•
TM010 π-mode
30
30
25
25
The drive frequency is 11.9942 GHz
Detuning angle is 85.58 degree, 2Qδ=12.9
The chokes at either end of the structure
Each mode normalised to 100MV/m
01
5
20
20
0
08
15
07
06
05
04
03
02
01
Transformer ratio
T/10
Beam-to-beam efficiency
0
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tteS
TM021 3π-mode
10
10
5
5
0
2Qδ=13
35
0
0
10
20
30
40
50
60
70
80
Fundamental TM010
12002.5
Third Harmonic TM021
35964.7
Unit
MHz
0.77
0.43
1.471
11.4813
9364
12956
71.9
29.8
MOhm/m
56.6
337.950
216.29
5.24
1132.679
358.6
Ohm
kA/m
MV/m
s and Settings\Administrator\My Documents\MHC_Design\Pulsed_Surface_Heating_MHC\Third_Harmonic\Full_Structure\THREECELL2.AM 5− 30− 2014 16:00:40
Frequency
Transit-time
factor
Power
dissipation
Q
Shunt
impedance
r/Q
Maximum H
Maximum E
MW
Single cell rf parameters.
•
•
14% reduction in Pulsed Surface heating for
η=1.53.
Agreement between eqns. on slide 7 and
simulation results.
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IV. Conclusions
•Dual-harmonic operation of acceleration cavities may allow suppression of RF
breakdown and possible increase in acceleration gradient.
(1) TM010+TM020, exhibits anode-cathode effect that could increase acceleration
gradient without raising the surface cathode field.
(2) TM011 unsuitable for beam driven cavities in terms of longitudinal stability.
(3) TM010+TM021, exhibits smaller surface pulsed heating than TM010 alone.
•Detuned single-mode collinear structure shows high transformer ratio, and high beamto-beam efficiency. Detuned bimodal cavity two-beam structure could have the same
virtues with the additional benefit of reduced surface pulsed heating.
•Time domain and wakefield studies are underway to determine effect of HOM’s and to
verify transformer ratio calculations.
•Optimisation software currently being created in order to design a structure with the
greatest benefit.
Lee Carver
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