Beryllium Windows Lorentz Force Detuning and Field Enhancement F. - - PowerPoint PPT Presentation

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Beryllium Windows Lorentz Force Detuning and Field Enhancement F. - - PowerPoint PPT Presentation

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Beryllium Windows Lorentz Force Detuning and Field Enhancement F. Marhauser, MuPlus, Inc. 2014-01 Be Windows Beryllium windows (transparent for muons) close cavities such that neighboring cavities (closely packed) can be

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SLIDE 1

Beryllium Windows Lorentz Force Detuning and Field Enhancement

  • F. Marhauser,

MuPlus, Inc. 2014-01

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SLIDE 2
  • F. Marhauser, 01/2014, p.2

Be Windows

  • Beryllium windows (‘transparent’ for muons) close cavities such that neighboring cavities (closely

packed) can be independently powered and adjusted in phase

  • Window R&D steered already in early 2000s by LBNL within the frame of the MICE project
  • First tests of thin (flat) windows with 805 MHz high power pillbox-like cavity
  • Space outside cavity was evacuated to prevent differential pressure on windows
  • Thinnest Be RF windows ever built and tested were flat with the following dimensions:

thickness = 157 um, Radius = 8 cm, brazed between annular Be frames

Be foil (99% purity, IF-1) brazed between two annular Be frames (98.5% purity, PS-200)

2001 window still wavy

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SLIDE 3
  • F. Marhauser, 01/2014, p.3

Be Windows

  • Pre-stress was required to keep the foils flat
  • Pre-stress was induced ‘naturally’ during the brazing process, but exact pre-stress unknown as difficult

to measure and simulate

  • Pre-stress effected by CTE difference of ring and Be foil and braze temperature
  • Pre-stress can vary considerably with small changes in braze temperature

2002

11.5 ppm/K for 99% pure Be and noted deviations for ring with 98.5% Be purity

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SLIDE 4
  • F. Marhauser, 01/2014, p.4

MICE Windows

First successful Beryllium window manufactured for a prototype cavity, Be window is brazed between two annular copper frames

  • Progress for MICE cavity design required mechanically more robust RF windows

 pre-curved, pre-stressed Be windows conceived (designed by Oxford University)  designed to remain rigid during thermal cycling

  • Dimensions for MICE: thickness = 380 um, Radius = 21 cm, brazed between annular copper frames
  • Be windows are TiN coated to mitigate multipacting
  • Brazing process still delicate (only one specific company in California has expertise so far to do it right)

2005

Prototype 201.25 MHz (MICE) cavity

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SLIDE 5
  • F. Marhauser, 01/2014, p.5

805 MHz High Power Test Observations

  • Be has larger breakdown limit than copper, i.e. copper limits performance (LINAC04 paper)
  • Flat Windows:
  • Flat Be windows caused unpredictable pulse-to-pulse instabilities at high field levels
  • ∆f = ± 30 kHz (no field level cited)
  • Instabilities are due to RF detuning and instantaneous RF heating and subsequent oscillation of

the window

  • Curved Windows:
  • Flat RF windows were replaced by pre-curved (380 um thick), pre-stressed windows
  • Both RF windows were installed with curvature in same direction
  • RF heating relaxes window and detuning was predictable (no pulse-to-pulse oscillations)
  • The PAC07 paper states that the 380 thick pre-curved windows were thinner than the flat windows

(but no thickness cited). Yet, the latter caused pulse-to-pulse instabilities

  • Eddy current braking (when external magnet is switched on) has been mentioned to eliminate pulse-

to-pulse instabilities, not really explained in this of other papers, very questionable if this can help us

  • Even is so, would yet not allow to operate cavity without magnets and very thin windows conceived for

HCC cavities (slides to come)

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SLIDE 6
  • F. Marhauser, 01/2014, p.6

201 MHz High Power Test Observations

  • Flat Windows:
  • 11 mm thick windows (not 11 cm as stated in PAC07 paper) were employed first to avoid

potential deflections

  • not sure, why this thick
  • Curved Windows:
  • Flat RF windows were replaced by pre-curved (380 um thick), pre-stressed windows

(frequency shift observed by geometry change was -379 kHz)

  • Cavity reached up to 18 MV/m without issues
  • No visible arc pits or damage in the interior
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SLIDE 7
  • F. Marhauser, 01/2014, p.7

HCC Cavity Be Window Design

  • Katsuya (December, 6th, 2013):
  • 325 MHz (maybe re-entrant) cavities (segments 1-3), maybe 120 μm thick Be windows
  • 650 MHz dielectric loaded cavities (segments 4-6), maybe 30 μm thick Be windows
  • Cooling performance: simulation done with 0, 15, 30, 60 µm thin windows (both sides
  • f cavities)
  • RF window thickness influences equilibrium emittance:

1) reference (0 thickness)  equilibrium transverse emittance: 0.35 mm 2) 30 µm thick windows  equilibrium transverse emittance: 0.60 mm, i.e. almost factor 2 larger

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SLIDE 8
  • F. Marhauser, 01/2014, p.8

Lorentz Force Detuning

  • Very questionable whether such thin windows are practicable and reasonable to use
  • Studied Lorentz Force Detuning (LFD) for a typical re-entrant cavity (here 650 MHz)
  • Did simulations studies with ACE3P/Tem3P on NERSC calculating LFD deflection/detuning

as function of window thickness

  • Extremely dense mesh used for window to provide proper mechanical solution, i.e.

several mesh cells per thickness (down to 500 µm window thickness was feasible)

  • Cavity has 27.4 mm gap, no dielectric to ease calculations
  • Note: Tem3P requires single CPU run to export deformed result files

(e.g.: ~4 days CPU time required for 500 µm case)

cavity vacuum and mesh cavity wall and mesh

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SLIDE 9
  • F. Marhauser, 01/2014, p.9

Material Properties (at r.t.)

Units Copper (OFHC) Beryllium I Beryllium II Source NIST Wikipedia Brush Wellman IF1 Alloys, > 99.8% Be Mechanical Calculations Young’s modulus GPa 128.8 287 303 Poisson ratio 0.344 0.032 0.070 CTE 1/K 1.66e-5 1.13e-5 1.15e-5 Thermal calculations (usually non-linear function with temperature used) Thermal Conductivity W/(m·K) 390 200 216 RF Calculations Electrical Conductivity 1/(Ω·m) 5.81e7 2.78e7 2.33e7

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SLIDE 10
  • F. Marhauser, 01/2014, p.10

Window Deflection due to LFD (static)

  • Objective: Extrapolate to very thin windows as conceived for HCC cavities
  • RF windows (both sides) are flat and have a radius of 6 cm
  • Deflections/detuning is for field level within range conceived, here: Eeff(β = 1) = 20 MV/m

Note: TEM3P does not consider β < 1

  • Equates to ~24 MV/m on axis in this cavity

Be II, note: No detuning due to RF heating considered yet

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SLIDE 11
  • F. Marhauser, 01/2014, p.11

LFD Coefficient (static)

  • Same case, LFD normalized to peak field on axis
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SLIDE 12
  • F. Marhauser, 01/2014, p.12

LFD Coefficient (static)

  • Be II (larger Poisson ratio) lowers LFD coefficient, i.e. improvement, but not dramatic
  • Expect similar ‘ballpark’ numbers
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SLIDE 13
  • F. Marhauser, 01/2014, p.13

Results for Flat Windows (Be I)

Window thickness (µm)

  • Max. long.

Deflection @ 24.1 MV/m (mm) Frequency Detuning at 10/20/30 MV/m (MHz) Comments on Feasibility 30 355 277/1107/2490 impossible 60 46 36/144/324 impossible 120 6 5/19/42 very unlikely to work 380 (like MICE) 0.2 0.2/0.6/1.4 maybe possible at lower field levels (but expect significant emittance increase) 1000 0.012 0.01/0.04/0.09 likely to work (but expect significant emittance increase)

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SLIDE 14
  • F. Marhauser, 01/2014, p.14

Results for Flat Windows (Be I)

Window thickness (µm)

  • Max. long.

Deflection @ 24.1 MV/m (mm) Frequency Detuning at 10/20/30 MV/m (MHz) Comments on Feasibility 30 355 277/1107/2490 impossible 60 46 36/144/324 impossible 120 6 5/19/42 very unlikely to work 380 (like MICE) 0.2 0.2/0.6/1.4 maybe possible at lower field levels (but expect significant emittance increase) 1000 0.012 0.01/0.04/0.09 likely to work (but expect significant emittance increase)

  • Won’t bet on Eddy current braking, also not when theoretically two neighboring cavities

would cancel pressure since any power trip in one cavity could disrupt window

  • Curved window design is more robust, but seems to be not practical for very thin foils
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SLIDE 15
  • F. Marhauser, 01/2014, p.15

Thermal Calculation

  • Example: Be windows with 500 µm thickness (thermal: BNL notebook)
  • Copper walls are RRR=300 (NIST)
  • Pavg ~ 260 Watt (Eeff(β = 1)= 20 MV/m)
  • Assumptions: GH2 at 160 atm, Tref = 298 K
  • Cooling everywhere outside: Forced flow past a circular cylinder (R = 140.1 mm)

 equivalent heat transfer coefficient = 72 W/(m2·K) based on Reynolds and Prandtl number, could be larger depending on average velocity of gas (which is an input parameter)

  • Cooling inside disregarded, but present, probably less than outside

temperature rise within windows seems to be small thanks to gas cooling

0.5 mm windows h = 72 W/(m2·K)

temperature (K)

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SLIDE 16
  • F. Marhauser, 01/2014, p.16

0.5 mm windows h = 72 W/(m2·K)

temperature (K)

Thermal Calculation

2002

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SLIDE 17
  • F. Marhauser, 01/2014, p.17

Past Ideas on Window Design (2001)

1) Use stepped window to improve thermal capability over uniform foil 2) Use ribbed window to decrease muon scattering, while providing mechanical integrity e.g. ‘waffle’ pattern with reinforced ribs)

e.g. twice the thickness at some radius

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SLIDE 18
  • F. Marhauser, 01/2014, p.18

Past Ideas on Window Design (2003)

3) Gridded windows with various concepts and arrays (touching, non-touching, merged)

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SLIDE 19
  • F. Marhauser, 01/2014, p.19

Past Ideas on Window Design (2004)

4) Gridded windows with various concepts and arrays (touching, merged) 2004 Thesis

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SLIDE 20
  • F. Marhauser, 01/2014, p.20

Thermal Calculation (2004)

  • Example: Be 4 x4 waffle window with 254 um thin tubes
  • Gas heat transfer assumption: 250 W/(m2·K)

Tref = 0 deg. C

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SLIDE 21
  • F. Marhauser, 01/2014, p.21

Past Ideas on Window Design (2004)

  • Surface field enhancement on gridded window designs studied
  • Field enhancement (FE) defined as ratio of maximum surface field to on-axis electric field

baseline diameter = 9.53 mm

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SLIDE 22
  • F. Marhauser, 01/2014, p.22

Past Ideas on Window Design (2004)

  • Surface field enhancement on gridded window designs studied in 3D using ANSYS
  • Field enhancement (FE) defined as ratio of maximum surface field to on-axis electric field
  • FE factors likely not fully resolved in 3D

(even though models employ rather large tube diameters)

  • Full resolution is important since FE factor limits performance, what to expect?

baseline diameter = 9.53 mm

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SLIDE 23
  • F. Marhauser, 01/2014, p.23

Field Enhancement on Tubes

  • Different model employed: Rings of (10) tubes in quasi uniform electrical field
  • Extremely dense mesh possible (100 mesh cells per tube diameter, whatever the size)
  • Up to ~20 Million triangular within boundaries used

(limit for workstation RAM with Poisson/Superfish)

  • 1st Objective: Calculate field enhancement as a function of tube radius and gap

axis of rotation

1 kV 0 kV free space

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SLIDE 24
  • F. Marhauser, 01/2014, p.24

Field Enhancement on Tubes

  • Consider: In pillbox cavity there were straight tubes in quasi cylinder-symmetric field
  • Now we have cylinder-symmetric tubes in quasi straight (uniform 2D) field
  • Field enhancement factors should be similar to those observed on waffle window tubes if

adjacent tubes do not perturb field too much (i.e. center between hor./vert. tubes)

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SLIDE 25
  • F. Marhauser, 01/2014, p.25
  • Uniform field can be distorted artificially if upper electrical boundary is too close to tubes
  • Problematic only for large gap/R ratios as number of mesh cells increase dramatically
  • Thus: distance of upper electrical boundary varied

 then calculate FE factor for each gap/R with hyperbolic fit, i.e. boundary limit in infinity

Field Enhancement on Tubes

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SLIDE 26
  • F. Marhauser, 01/2014, p.26
  • Uniform field can be distorted artificially if upper electrical boundary is too close to tubes
  • Problematic only for large gap/R ratios as number of mesh cells increase dramatically
  • Thus: distance of upper electrical boundary varied

 then calculate FE factor for each gap/R with hyperbolic fit, i.e. boundary limit in infinity

  • Result: Field enhancement increases with gap between tubes (g) and

increases with smaller tube radius (R), i.e. thin tubes widely spaced are problematic

Field Enhancement on Tubes

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SLIDE 27
  • F. Marhauser, 01/2014, p.27

Comparison with Waffle Window

  • Compare FE factors with results for different waffle window design in 2004 thesis
  • Assumed total distance for each waffle design is same (not clearly stated in thesis), i.e. only

given for baseline, but seems to be right

  • New results look very reasonable, reveal larger FE factors, but no dramatic increase

3/8" diameter cases 9/16" diameter cases case 1 2 3 4 5 6 waffle design 4 x4 6 x 6 8 x 8 4 x 4 6 x 6 8 x 8 R (mm) 4.7625 4.7625 4.7625 7.14375 7.14375 7.14375 g (mm) 25.41 13.76 7.94 20.64 9.00 3.18 distance c-c 34.93 23.29 17.47 34.93 23.29 17.47 g/R 5.33 2.89 1.67 2.89 1.26 0.44 3D FEA ANSYS model (2004 thesis, M. Alsharo’a ) 1.90 1.65 1.42 1.75 1.52 1.31 Poisson 2D model (same g/R) 2.26 1.87 1.67 1.87 1.60 1.47

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SLIDE 28
  • F. Marhauser, 01/2014, p.28

Comparison with Waffle Window

  • Compare FE factors with results for different waffle window design in 2004 thesis
  • Assumed total distance for each waffle design is same (not clearly stated in thesis), i.e. only

given for baseline, but seems to be right

  • 2D results reveal larger FE factors, but not dramatic
  • Yet, these numbers show that field on surface (tubes) can be about factor 2 (or more)

larger than on axis

  • This is similar to conventional cavities with open beam tubes
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SLIDE 29
  • F. Marhauser, 01/2014, p.29

Comparison with Waffle Window

  • Compare FE factors with results for different waffle window design in 2004 thesis
  • Assumed total distance for each waffle design is same (not clearly stated in thesis), i.e. only

given for baseline, but seems to be right

  • 2D results reveal larger FE factors, but not dramatic
  • Yet, these numbers show that field on surface (tubes) can be about factor 2 (or more)

larger than on axis

  • This is similar to conventional cavities with open beam tubes
  • 2nd Objective: What tube radius grants similar field enhancement ?
  • Or can we get rid of Be windows ?
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SLIDE 30
  • F. Marhauser, 01/2014, p.30

Cavity with Dielectric (2D)

  • 650 MHz with dielectric studied (as conceived at this point for segments 1-3, cf. slide 7)
  • Reference is cavity without tubes, then tubes added
  • Several MHz-level frequency shift may be disregarded for now

R = 5mm (fixed)

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SLIDE 31
  • F. Marhauser, 01/2014, p.31

Field Enhancement (with/no Be windows)

waffle windows (2D model) DL cavity (2D model)

  • Note: For the dielectric loaded (DL) cavity with open beam tubes, the field enhancement

considers the max. electrical field on the metal surface (beam tube opening)

  • The overall max. field is actually on ceramic corners even when rounded quite generously
  • Same will be true for a DL cavity with typical waffle windows for small ratio of gap/R
  • Result: Small opening can yield lower FE factor on metal than some waffle window
  • designs. What beam tube hole size is large enough? From which segment on can such

cavities be employed? Beam dynamics must tell.

  • Further studies with offset holes (following helical path) planned
  • Is FE on ceramic rather the limit ? Then not limited by local field maximum on tube ?
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SLIDE 32
  • F. Marhauser, 01/2014, p.32

Field Enhancement (no Be windows)

electrical field contours

  • Personally favor re-entrant cavity design due to enormous conceptual advantages, but

beam dynamics may not allow small fill factor  should be further elaborated RF leakage could be kept small with small radius