fine-tuning the rfq end region
DESCRIPTION
Fine-Tuning the RFQ End Region. “…The Devil is in the Detail”. RFQ bulk design very close to completion But before drafting need to check: Repeatability & agreement of codes/meshes Frequency of full 4m RFQ If asymmetry is caused if pumps only on top - PowerPoint PPT PresentationTRANSCRIPT
Fine-Tuning theRFQ End Region
“…The Devil is in the Detail”• RFQ bulk design very close to completion
• But before drafting need to check:• Repeatability & agreement of codes/meshes• Frequency of full 4m RFQ• If asymmetry is caused if pumps only on top• Tunability of cavity using slug tuners (Saad)• Field flatness• If small machining details have an effect
ANSYS Mesh Quality
• In ANSYS, results converge for vane-tip mesh < 2mm and quadrant mesh < 15mm.• Full 4m RFQ solution needs careful allocation of mesh due to size of problem!• Now Compare with other codes…
ANSYS Maximum Resolution: 324.131 MHz
Superfish Maximum Resolution:324.137 MHz
CST Maximum Resolution:324.129 MHz
Vacuum Port Placement
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, but confirmed real when solving one entire 4m long quadrant
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
50% Field drop at ends is unacceptable and cannot be tuned out!
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
[Ref: Thomas Wangler, Michigan State UniversityLinac Seminar Series – “RFQ Basics”]
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.
[Ref: Thomas Wangler, Michigan State UniversityLinac Seminar Series – “RFQ Basics”]
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
[Ref: Thomas Wangler, Michigan State UniversityLinac Seminar Series – “RFQ Basics”]
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.
[Ref: Thomas Wangler, Michigan State UniversityLinac Seminar Series – “RFQ Basics”]
Having matcher on/off does indeed drastically affect field flatness due to its local frequency error
Matcher On
Matcher Off
Matcher Off/On
Adding the matcher hugely affects the capacitance (inductance to a lesser extent)Want 324MHz (almost midway between these two) which suggests:1)Increase capacitance as much as possible by reducing material removed for matcher2)Increase inductance by reducing vacuum volume removed to ensure 7mm end gap
This region removed lowers inductance
Addition of matcher lowers capacitance
LC
1
Initial design of radial matcher was a circle, tangent to vane at two points.
Quadrupole frequency of this end region = 375.125 MHz
No radial matcher on cold model: vane had square ends.
Quadrupole frequency of this end region = 291.078 MHz
H-field
Modified Radial Matcher Design7mm
R 5
R 21.8
E-field
334.708 MHz
To fine-tune toward 324 MHz, modify cutback radius
H-field
Fine-tune Inductance by Varying Cut-back radius
Original cutback radius = 15mm
Rounding Off Corners
High magnetic field region, so will affect inductance & frequency
To reduce sparking and hot-spots, and to ease machining, the corners will be radiused
Fine-tune Inductance by Varying Cut-back radius
ANSYS Maximum Resolution: 324.131 MHz
Superfish Maximum Resolution:324.137 MHz
CST Maximum Resolution:324.129 MHz44.0mm Quadrant
radius is uncomfortably close to 324 MHz
∴ Relax it slightly by increasing to 44.1mm
44.0mm
Varying Quadrant Radius in CST
Fine-tune Inductance by Varying Cut-back radius
As a bonus, these changes also improve the Q by ~20%
Final Design
CST and ANSYS results for final geometry, 4m RFQ with flush tuners.
Taking into account meshing accuracy for these large models (see slides 3 & 4), both agree with the frequency being (323.5 ± 0.5) MHz
Original Matcher
No Matcher
Optimised Matcher
New matcher design achieves considerably flatter field and ensures (323.5 ± 0.5) MHz along the entire RFQ
Questions?