fnal-pxie hwr: electromagnetic design · fnal-pxie hwr: electromagnetic design b. mustapha physics...

FNAL-PXIE HWR: Electromagnetic Design

B. Mustapha

Physics Division, ANL

Review of FNAL-PXIE 162.5 MHz HWR Cryomodule

Argonne, March 5, 2012

B. Mustapha FNAL-PXIE HWR: EM Design Review of FNAL-PXIE HWR Cryomodule, March, 5, 2012

2

Content

The EM Design Optimization Procedure – Fully parameterized geometry

– Optimization goals

– Semi-automatic optimization using CST parameter sweeps

The Original Race-Track Geometry – Problems, Solutions & Limitations

– Final Race-Track Design

The Ring-Shaped Center Conductor Geometry – Comparison to the race-track geometry

– Significant increase in shunt impedance !?

Final HWR Design – Re-Optimization Using Tetrahedral Mesh in CST-2011

– Effect of Coupling and Processing Ports


3

EM Design Optimization: Fully Parameterized Geometry

The table shows the list of geometry parameters as seen in MW-Studio The geometry parameters are NOT independent


4

EM Design Optimization: RF Parameters to Optimize

E-peak: Minimize peak surface electric field to limit field emission

B-peak: Minimize peak magnetic field to maintain superconductivity

R/Q = V^2/ωU: Maximize R/Q to produce more accelerating voltage (V) with less stored energy in the cavity (U)

G = Rs*Q: Maximize the geometry factor to increase the cavity effectiveness of providing accelerating voltage due to its shape alone


5

EM Design Optimization: Parameter Sweeps in MWS

Dri

ft T

ub

e O

ute

r R

adiu

s

DT

Inn

er

Ble

nd

Rad

ius

Gap

Wid

th

DT

Ou

ter

Ble

nd

Rad

ius


6

Race-Track HWR Design: Geometry


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Race-Track HWR Design: Problems, Solutions & Limitations

The race-track center conductor produces a quadrupole electric field component leading to a transverse beam asymmetry Elliptical aperture.

The loft from the race-track to the round cavity top results in a non uniform magnetic field around the center conductor with the highest fields in the welding areas Intermediate round loft.

The race-track geometry may be optimum for the E-peak but it is NOT optimum for the shunt impedance.

All of these problems are solved in the ring-shaped center conductor geometry.


8

HWR Quadrupole Asymmetry Correction: Elliptical Aperture

Asymmetry

Round Aperture

Asymmetry

Gone

Elliptical Aperture

The required elliptical aperture is 33-36 mm.


9

Race-Track versus Round Loft in the Center Conductor

Race-Track Loft

Round Loft


10

Race-Track HWR Design: Final Geometry


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Race-Track HWR Design: Final RF Parameters

Cavity Mesh

Cells

Freq

MHz

β_opt Leff

(cm)

Ep/Ea

-

Bp/Ea

Gs/.

R/Q

Ω

G

Ω

Round Aperture

1.08M 162.50 0.110 20.3 4.60 66.77 218.55 48.17

Elliptical Aperture

1.18 M 162.50 0.110 20.3 4.67 69.78 215.48 48.60

Round Loft

1.02M 162.49 0.110 20.3 4.69 59.43 194.96 47.77

The elliptical aperture almost preserves the RF parameters

Using an intermediate Round Loft, lowers the B-peak by making it more uniformly distributed around the stem, it also reduces R/Q.

The final cavity is capable of delivering 1.7 MV at 40 MV/m and 51 mT

or 2.4 MV at 55 MV/m and 70 mT


12

Ring-Shaped Center Conductor HWR: Geometry


13

Ring-Shaped vs. Race-Track Design: RF Parameters

Cavity Mesh

Cells

Freq

MHz

β_opt Leff

(cm)

Ep/Ea

-

Bp/Ea

Gs/.

R/Q

Ω

G

Ω

Race-Track

1.02M 162.49 0.110 20.3 4.69 59.43 194.96 47.77

Ring-Shaped

1.14M 162.50 0.112 20.7 4.87 51.00 271.28 47.27

The ring-shaped geometry has slightly higher E-peak but a lower B-peak

The shunt impedance (R/Q) is significantly increased: by ~ 39 %.

The ring-shaped cavity is capable of delivering 1.7 MV at 40 MV/m and 42 mT

or 2.8 MV at 67 MV/m and 70 mT


14

Ring-Shaped vs. Race-Track Design: Shunt Impedance

R/Q = V^2/ωU, ωU is the same in MW-Studio R/Q α V^2


15

Ring-Shaped vs. Race-Track Design: Field Patterns


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Re-Optimization Using Tetrahedral Mesh in CST 2011

Mesh

Type

Mesh

Cells

Freq

MHz

β_opt Leff

(cm)

Ep/Ea

-

Bp/Ea

Gs/.

R/Q

Ω

G

Ω

Hexahedral 1.14M 162.50 0.112 20.7 4.87 51.00 271.28 47.27

Tetrahedral 236k 162.50 0.112 20.7 4.67 50.23 271.51 48.19

The tetrahedral mesh is a 2nd order curved mesh that better describes the curvature of the geometry and should lead to more accurate peak surface fields

Peak surface fields from tetrahedral mesh are typically lower by 2-5 % than those obtained using the hexahedral mesh.

We will use the tetrahedral mesh for future studies.


17

Field Distributions


18

Field Distributions


19

Cavity Geometry: Adding the Coupling Ports

Symmetric case: For simulation only

Non symmetric case: Real cavity geometry


20

RF parameters: Effect of Coupling & Processing Ports

Ports

Mesh

Cells

Freq

MHz

β_opt Leff

(cm)

Ep/Ea

-

Bp/Ea

Gs/.

R/Q

Ω

G

Ω

No Ports 236k 162.50 0.112 20.7 4.67 50.23 271.51 48.19

Ports, Full Sym.

200k 162.39 0.112 20.7 4.64 50.22 271.33 48.03

Ports, No Sym.

186k 162.40 0.112 20.7 4.65 50.37 270.21 48.59

The realistic case is with ports and no symmetry (last line) but the full symmetric case offer eight times the total number of mesh cells (tetrahedrons).

The peak surface fields and other RF parameters are practically the same for the symmetric and non symmetric cases.

Adding the ports should not affect the RF parameters

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