ANSYS Eigenmode Results of Full 4m RFQ with Vacuum Ports and 43.8mm Quadrant Radius
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Transcript of ANSYS Eigenmode Results of Full 4m RFQ with Vacuum Ports and 43.8mm Quadrant Radius
ANSYS Eigenmode Results of Full 4m RFQ with Vacuum
Ports and 43.8mm Quadrant Radius
Study Performed
• Use Pete’s latest 4m RFQ internal models• Vacuum ports only on major top vane• Vacuum ports on top and bottom
• Find all eigenmodes and Q between 300 to 400 MHz (quadrupole and both dipoles)
• Use symmetry planes where possible
Symmetry Planes• Different vacuum port configurations imply
vertical asymmetry∴ Use two quadrants of half (2m) of RFQ
• Once it’s confirmed how vacuum ports affect fields, need to confirm longitudinal modes∴ Use just one quadrant but full 4m length
With One or Two Vac Ports
Vacuum ports top & bottom Vacuum ports top only
Removing the bottom vacuum port increases frequencies by 25 kHz
Open squares indicate theoretical modes, missing due to symmetry
Confirming Missing Odd Modes
Full 4m-long RFQ model confirms missing modes, but slightly poorer mesh quality shifts whole spectra up ~0.5MHz
Two quadrants, longitudinal symmetry One quadrant, full 4m long
Mesh Quality
Results converge for vanetip mesh size < 2mm and quadrant mesh size < 15mm.
Results in previous slides for one quadrant of full 4m RFQ are on limit of memory, using 2mm vanetip and 12mm bulk quadrant mesh sizes, but are sufficiently accurate.
Electric Field in Vane Gap for Different Longitudinal
Modes
TE210: 324.5MHz
Electric Field in Vane Gap for Different Longitudinal
Modes
TE211: 327.7MHz
Electric Field in Vane Gap for Different Longitudinal
Modes
TE212: 334.6MHz
Electric Field in Vane Gap for Different Longitudinal
Modes
TE213: 345.3MHz
Electric Field in Vane Gap for Different Longitudinal
Modes
TE214: 359.9MHz
Electric Field in Vane Gap for Different Longitudinal
Modes
TE215: 378.0MHz
Electric Field in Vane Gap for Different Longitudinal
Modes
TE216: 397.2MHz
Absolute Electric Field of First Four Longitudinal Modes
Conclusions• Mesh density sufficient to solve 4m RFQ
• Longitudinal modes well resolved
• …however the fundamental is not flat!
• Fundamental TE210 mode is ~0.5MHz too high so adjust quadrant radius to 44mm
• Next nearest modes ~3MHz away. All have high Q so should not cross-talk
• Vacuum port asymmetry 25kHz shift
New stuff hot off the press!
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Example of a frequency error at a single point x0
Suppose the local error is a delta function at some point x0. Local error magnitude is defined as
02 (x) (x x0 )
1 (x x0 )dx
0
V
(1)02 0
2 2V
(x x0 )dx0
V
02 2V
This is the new resonant frequencyof the cavity in terms of local frequency error
0
V0
This relates the cavity frequency change to .
(1)V 0(x) 2
V12V
(x x0 )cos(kmx)dx0
V
02 m
2 cos(kmx)m1
is the new wavefunction
(Talk I’ve found possibly explaining non-flat field)
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Fractional vane-voltage error
V0 (x)V0
800
V
2 cos(mx0 / V )m2
cos(mx / V )m1
V0 (x)V 0
4 200
V
213
xV
12
xV
2
12x0V
2
, x x0
1
3 x0
V 12
x
V
2
12
x0V
2
, x0 x
An analytic solution exists for this summation. It is.
Each of the higher modes m contributes a term proportional to the voltage value of each mode at the point of the perturbing error, divided by the mode index m squared so nearest modes in frequency contribute most.
(Talk I’ve found possibly explaining non-flat field)
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Dependence of the fractional voltage error at each point x on the
parameters.
The fractional voltage error at each point increases with the fractional cavity frequency error and as the square of the vane length to wavelength ratio.
This next graph shows that if the local error at some point x0 causes the local resonant frequency to increase, the local voltage decreases, and vice versa.
V0 (x)V0
4 200
V
213
xV
12
xV
2
12x0V
2
, x x0
1
3 x0
V 12
x
V
2
12
x0V
2
, x0 x
(Talk I’ve found possibly explaining non-flat field)
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x/Vx/lV
V0(x)
m=0
m=0 and 1
m=1 to 20
Perturbed voltage distribution for problem with a -function error at the vane end, where
x0/lV = 0, lV/ = 2 and 0/0 = 0.01.
(Talk I’ve found possibly explaining non-flat field)
As-Designed End RegionNo Radial Matcher
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As-Designed End RegionWith Radial Matcher
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On-Tune End RegionNo Radial Matcher
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On-Tune End RegionWith Radial Matcher
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