BINP geometry (= cavity inner dimensions which define the boundary)

BINP geometry (= cavity inner dimensions which define the boundary) is based on CERN geometry (as of August 4, 2008)with some adjustments made in order to adapt (= to keep the frequency) design modifications suggested by BINP and VNIITF

Ri

g

Rci F =

Fd

c

Ro

Rco

D /

2FEq

LT

g / 2Ld

Rc

f=fo=fi

Rdo

Rdi

FdeqHdHd

Rb

Rcb

d / 2

INNER_NOSE_radius Ri

INNER_CORNer_radius Rci

FLAT_length F

DIAMeter D

EQUATOR_flat FEq

CONE_angle c

OUTER_NOSE_radius Ro

GAP_Length gOUTER_CORNer_radius Rco

DT_INNER_NOSE_radius Rdi

DT_INNER_FACE_angle fi

DT_FLAT_length Fd

DT_DIAMeter dDT_CORNer_radius Rc

DT_OUTER_FACE_angle fo

DT_OUTER_NOSE_radius Rdo

cav_length LT

nose_base_radius Rcb

dt_length Ld

dt_equator_flat Fdeq

dt_nose_length dnose_length

BORE_radius Rb

c

f

Beam axis

Ver

tical

sym

met

ry p

lane

Constant definition(Superfish style)

Tan

k

Cav

ity le

ngth

EQ

UA

TO

R_f

lat

OU

TE

R_C

OR

Ner

_rad

ius

DIA

Met

er

INN

ER

_CO

RN

er_r

adiu

s

OU

TE

R_N

OS

E_r

adiu

s

INN

ER

_NO

SE

_rad

ius

FLA

T_l

engt

h

CO

NE

_ang

le

Nos

e le

ngth

Nos

e ba

se r

adiu

s

dt le

ngth

dt e

quat

or f

lat

DT

_DIA

Met

er

DT

_CO

RN

er_r

adiu

s

DT

_OU

TE

R_N

OS

E_r

adiu

s

DT

_IN

NE

R_N

OS

E_r

adiu

s

DT

_FLA

T_l

engt

h

DT

_OU

TE

R_F

AC

E_a

ngle

DT

_IN

NE

R_F

AC

E_a

ngle

dt n

ose

leng

th

BO

RE

_rad

ius

GA

P_L

engt

h

# LT Feq

Rco D Rci

Ro Ri F

alph

ac

H Rcb Ld F

deq

d Rc

Rdo Rdi Fd

alph

afo

alph

afi

Hd

Rb g

1 695.3 615.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 41.4 53.1 197.9 83.1 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 72.22 715.2 635.2 40.0 520.0 15.0 12.0 2.0 7.0 20.0 44.1 54.0 200.1 85.3 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 75.63 734.6 654.6 40.0 520.0 15.0 12.0 2.0 7.0 20.0 46.5 54.9 202.3 87.5 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 79.04 754.0 674.0 40.0 520.0 15.0 12.0 2.0 7.0 20.0 48.9 55.8 204.3 89.5 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 82.55 772.9 692.9 40.0 520.0 15.0 12.0 2.0 7.0 20.0 51.2 56.6 206.3 91.5 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 86.06 792.1 712.1 40.0 520.0 15.0 12.0 2.0 7.0 20.0 53.7 57.5 208.2 93.4 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 89.57 810.3 730.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 55.7 58.3 210.0 95.2 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 93.08 828.2 748.2 40.0 520.0 15.0 12.0 2.0 7.0 20.0 57.8 59.1 211.7 96.9 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 96.49 846.3 766.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 60.0 59.9 213.3 98.5 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 14.0 99.9

10 862.9 782.9 40.0 520.0 15.0 7.0 2.0 3.0 20.0 66.1 58.0 223.6 79.0 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 94.411 881.5 801.5 40.0 520.0 15.0 7.0 2.0 3.0 20.0 68.7 58.9 225.2 80.5 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 97.912 897.3 817.3 40.0 520.0 15.0 7.0 2.0 3.0 20.0 70.0 59.4 226.7 82.1 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 101.213 915.7 835.7 40.0 520.0 15.0 7.0 2.0 3.0 20.0 72.7 60.4 228.0 83.4 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 104.714 930.1 850.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 73.7 60.8 229.5 84.9 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 107.915 948.1 868.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 76.3 61.7 230.7 86.0 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 111.316 962.2 882.2 40.0 520.0 15.0 7.0 2.0 3.0 20.0 77.3 62.1 232.1 87.4 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 114.517 978.7 898.7 40.0 520.0 15.0 7.0 2.0 3.0 20.0 79.6 62.9 233.1 88.5 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 117.818 992.5 912.5 40.0 520.0 15.0 7.0 2.0 3.0 20.0 80.7 63.3 234.3 89.7 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 120.819 1 008.4 928.4 40.0 520.0 15.0 7.0 2.0 3.0 20.0 82.8 64.1 235.3 90.6 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 124.120 1 021.4 941.4 40.0 520.0 15.0 7.0 2.0 3.0 20.0 83.7 64.4 236.4 91.7 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 127.021 1 037.1 957.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 85.9 65.2 237.3 92.6 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 14.0 130.2

CERN geometry (as of August 4, 2008)

Constant for all tanks Constant for tanks 1-9 and 10-21 Variable Dependent variable

Ri

g

Rci F =

Fd

c

Ro

Rco

D /

2FEq

LT

g / 2Ld

Rc

f=fo=fi

Rdo

Rdi

FdeqHdHd

Rb

Rcb

d / 2



FLAT_length F

DIAMeter D

CONE_angle c


OUTER_CORNer_radius Rco



DT_FLAT_length Fd




cav_length LT


dt_length Ld



BORE_radius Rb

c

f

Beam axis

Ver

tical

sym

met

ry p

lane

GAP_Length gEQUATOR_flat FEq


Constant for all tanks

Constant for tanks 1-9 and 10-21

Variable

Dependent variable

695

795

895

995

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Cavity length

40

60

80

100

120

140

160

180

200

220

240

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Drift tube length

Gap length

Nose length

50

55

60

65

70

75

80

85

90

95

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Drift tube equator flat

Drift tube nose

50

52

54

56

58

60

62

64

66

68

70

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Nose base radius

CERN geometry

CERN geometry BINP geometry

Design modifications:1. Drift tube to stem connection2. Gridded port for an ion pump3. Waveguide input coupler

BINP geometry (= cavity inner dimensions which define the boundary) is based on CERN geometry (as of August 4, 2008)with some adjustments made in order to adapt (= to keep the frequency) design modifications suggested by BINP and VNIITF

BINP prototype design

CERN prototype design

Conjoint cylinders

Cylinder machined from a sphere

Design modifications / Drift tube to stem connection

Drift tube to stem connection requires forming mating cylinder on the drift tube

ISTC prototype

CERN hot model

Cu-plating

Cu-plating

100

100

10.5

DN100CF(STDVFUHV0052)

DN100CF

Design modifications / Gridded port for an ion pump

290 x 40 114 cm2

290 x 40 114 cm2

303 x 50 146 cm2

13

58

0.9

5

80

.9

19

19

~5

5~

34

15

ISTC prototype

Very difficult access to the nuts

M6 thread, studs

Easier access to the nuts

M8 thread, tapped holes, studs or bolts

Easy access to the nuts

M8 thread, studs or bolts

Same HELICOFLEX dimensions as for DTL and PIMS structures

Design modifications / Waveguide input coupler port

Tank # 3m2 Tank # 3m1 Tank # 3m

(-28kHz for tank #1)303 x 50, R25

Each accelerating cavity is calculated with detuned coupling cavity (-ies)

Sphere on a drift tube is accounted.Vacuum gridded port is accounted (1st and 3rd tanks in each module).Waveguide coupler port is accounted (2nd tank in each module)

3D simulations

m = 1…7 – module number

Ri

g

Rci F =

Fd

c

Ro

Rco

D /

2FEq

LT

g / 2Ld

Rc

f=fo=fi

Rdo

Rdi

FdeqHdHd

Rb

Rcb

d / 2



FLAT_length F

DIAMeter D

EQUATOR_flat FEq

CONE_angle c


GAP_Length gOUTER_CORNer_radius Rco



DT_FLAT_length Fd




cav_length LT


dt_length Ld



BORE_radius Rb

dt_sphere_radius Rs

Rs

c

f

Beam axis

Ver

tical

sym

met

ry p

lane


Dependent variableBINP geometry

Tan

k

Cav

ity le

ngth

EQ

UA

TO

R_f

lat

OU

TE

R_C

OR

Ner

_rad

ius

DIA

Met

er

INN

ER

_CO

RN

er_r

adiu

s

OU

TE

R_N

OS

E_r

adiu

s

INN

ER

_NO

SE

_rad

ius

FLA

T_l

engt

h

CO

NE

_ang

le

Nos

e le

ngth

Nos

e ba

se r

adiu

s

dt le

ngth

dt e

quat

or f

lat

DT

_DIA

Met

er

DT

_CO

RN

er_r

adiu

s

DT

_OU

TE

R_N

OS

E_r

adiu

s

DT

_IN

NE

R_N

OS

E_r

adiu

s

DT

_FLA

T_l

engt

h

DT

_OU

TE

R_F

AC

E_a

ngle

DT

_IN

NE

R_F

AC

E_a

ngle

dt n

ose

leng

th

dt s

pher

e ra

dius

BO

RE

_rad

ius

GA

P_L

engt

h

# LT Feq

Rco D Rci

Ro Ri F

alph

ac

H Rcb Ld F

deq

d Rc

Rdo Rdi Fd

alph

afo

alph

afi

Hd

Rs

Rb g

1 695.3 615.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 41.8 53.2 198.6 83.8 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 71.52 715.2 635.2 40.0 520.0 15.0 12.0 2.0 7.0 20.0 43.9 54.0 199.8 85.0 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 76.03 734.6 654.6 40.0 520.0 15.0 12.0 2.0 7.0 20.0 46.9 55.1 203.0 88.2 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 78.34 754.0 674.0 40.0 520.0 15.0 12.0 2.0 7.0 20.0 49.4 56.0 205.1 90.3 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 81.75 772.9 692.9 40.0 520.0 15.0 12.0 2.0 7.0 20.0 51.0 56.6 206.1 91.3 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 86.26 792.1 712.1 40.0 520.0 15.0 12.0 2.0 7.0 20.0 54.1 57.7 209.0 94.2 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 88.77 810.3 730.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 56.2 58.5 210.8 96.0 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 92.18 828.2 748.2 40.0 520.0 15.0 12.0 2.0 7.0 20.0 57.7 59.0 211.4 96.6 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 96.69 846.3 766.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 60.5 60.0 214.1 99.3 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 99.0

10 862.9 782.9 40.0 520.0 15.0 7.0 2.0 3.0 20.0 66.6 58.2 224.6 79.9 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 93.511 881.5 801.5 40.0 520.0 15.0 7.0 2.0 3.0 20.0 68.6 58.9 225.2 80.5 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 97.912 897.3 817.3 40.0 520.0 15.0 7.0 2.0 3.0 20.0 70.5 59.6 227.7 83.0 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 100.313 915.7 835.7 40.0 520.0 15.0 7.0 2.0 3.0 20.0 73.2 60.6 229.0 84.3 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 103.814 930.1 850.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 73.7 60.8 229.5 84.8 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 107.915 948.1 868.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 76.8 61.9 231.6 86.9 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 110.416 962.2 882.2 40.0 520.0 15.0 7.0 2.0 3.0 20.0 77.8 62.2 233.0 88.3 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 113.517 978.7 898.7 40.0 520.0 15.0 7.0 2.0 3.0 20.0 79.7 63.0 233.3 88.6 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 117.618 992.5 912.5 40.0 520.0 15.0 7.0 2.0 3.0 20.0 81.1 63.5 235.3 90.6 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 119.919 1 008.4 928.4 40.0 520.0 15.0 7.0 2.0 3.0 20.0 83.3 64.3 236.2 91.5 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 123.120 1 021.4 941.4 40.0 520.0 15.0 7.0 2.0 3.0 20.0 83.9 64.5 236.7 92.0 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 126.821 1 037.1 957.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 86.4 65.4 238.2 93.5 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 129.3

Changes are highlighted

Constant for all tanks Constant for tanks 1-9 and 10-21

Variable

Variable Dependent variable

CERN - BINP geometry

Tan

k#

CERN BINP delta CERN BINP delta CERN BINP delta CERN BINP delta CERN BINP delta1 41.4 41.8 -0.4 53.1 53.2 -0.2 197.9 198.6 -0.7 83.1 83.8 -0.7 72.2 71.5 0.82 44.1 43.9 0.2 54.0 54.0 0.1 200.1 199.8 0.3 85.3 85.0 0.3 75.6 76.0 -0.33 46.5 46.9 -0.4 54.9 55.1 -0.2 202.3 203.0 -0.7 87.5 88.2 -0.7 79.0 78.3 0.84 48.9 49.4 -0.4 55.8 56.0 -0.2 204.3 205.1 -0.8 89.5 90.3 -0.8 82.5 81.7 0.85 51.2 51.1 0.1 56.6 56.6 0.1 206.3 206.1 0.2 91.5 91.3 0.2 86.0 86.2 -0.26 53.7 54.1 -0.4 57.5 57.7 -0.1 208.2 209.0 -0.8 93.4 94.2 -0.8 89.5 88.7 0.87 55.7 56.2 -0.4 58.3 58.5 -0.2 210.0 210.8 -0.8 95.2 96.0 -0.8 93.0 92.1 0.88 57.8 57.7 0.1 59.1 59.0 0.0 211.7 211.4 0.3 96.9 96.6 0.3 96.4 96.6 -0.39 60.0 60.5 -0.4 59.9 60.0 -0.2 213.3 214.1 -0.8 98.5 99.3 -0.8 99.9 99.0 0.8

10 66.1 66.6 -0.5 58.0 58.2 -0.2 223.6 224.6 -1.0 79.0 79.9 -1.0 94.4 93.5 0.911 68.7 68.7 0.0 58.9 58.9 0.0 225.2 225.2 0.0 80.5 80.5 0.0 97.9 97.9 0.012 70.0 70.6 -0.5 59.4 59.6 -0.2 226.7 227.7 -1.0 82.1 83.0 -1.0 101.2 100.3 0.913 72.7 73.2 -0.5 60.4 60.6 -0.2 228.0 229.0 -1.0 83.4 84.3 -1.0 104.7 103.8 0.914 73.7 73.7 0.0 60.8 60.8 0.0 229.5 229.5 0.0 84.9 84.8 0.0 107.9 107.9 0.015 76.3 76.8 -0.5 61.7 61.9 -0.2 230.7 231.6 -0.9 86.0 86.9 -0.9 111.3 110.4 0.916 77.3 77.8 -0.5 62.1 62.2 -0.2 232.1 233.0 -0.9 87.4 88.3 -0.9 114.5 113.5 1.017 79.6 79.7 -0.1 62.9 63.0 -0.1 233.1 233.3 -0.2 88.5 88.6 -0.2 117.8 117.6 0.218 80.7 81.2 -0.5 63.3 63.5 -0.2 234.3 235.3 -1.0 89.7 90.6 -1.0 120.8 119.9 0.919 82.8 83.3 -0.5 64.1 64.3 -0.2 235.3 236.2 -0.9 90.6 91.5 -0.9 124.1 123.1 1.020 83.7 83.9 -0.1 64.4 64.5 0.0 236.4 236.7 -0.3 91.7 92.0 -0.3 127.0 126.8 0.321 85.9 86.4 -0.5 65.2 65.4 -0.2 237.3 238.2 -0.9 92.6 93.5 -0.9 130.2 129.3 0.9

Nos

e le

ngth

dt le

ngth

GA

P_L

engt

h

H Ld g

Nos

e ba

se r

adiu

s

Rcb

dt e

quat

or f

lat

Fdeq

Differences are within 1 mm

2 2 3 0T dL H L g gapcenter-to-gapcenter 0

Tank R / Q Q0 MWS R Qext TTFOhm MOhm

1 494 54 166 0.852 505 52 429 6 070 0.843 520 54 477 0.844 533 55 068 0.835 541 53 167 6 508 0.826 558 55 286 0.827 569 55 700 0.818 579 53 962 6 758 0.809 592 55 804 0.8010 616 55 914 0.8211 627 54 787 7 028 0.8112 638 56 263 0.8013 650 56 175 0.7914 658 54 895 7 321 0.7915 670 56 519 0.7816 678 56 606 0.7817 687 54 865 7 640 0.7618 697 56 454 0.7619 707 56 756 0.7620 712 55 019 8 000 0.7521 724 56 783 0.74

2

0

2TE L

RP

/ 2

0

/ 2

1 T

T

L

mT L

E E z dzL

BINP geometry (hereinafter)

Cavity parameters from 3D simulations

Tank R / Q Q0 MWS 0.75 Q0 MWS R Qext TTFOhm MOhm

1 494 54 166 40 625 0.852 505 52 429 39 322 6 070 0.843 520 54 477 40 858 0.844 533 55 068 41 301 0.835 541 53 167 39 875 6 508 0.826 558 55 286 41 465 0.827 569 55 700 41 775 0.818 579 53 962 40 472 6 758 0.809 592 55 804 41 853 0.8010 616 55 914 41 936 0.8211 627 54 787 41 090 7 028 0.8112 638 56 263 42 197 0.8013 650 56 175 42 131 0.7914 658 54 895 41 171 7 321 0.7915 670 56 519 42 389 0.7816 678 56 606 42 455 0.7817 687 54 865 41 149 7 640 0.7618 697 56 454 42 341 0.7619 707 56 756 42 567 0.7620 712 55 019 41 264 8 000 0.7521 724 56 783 42 587 0.74

2

0

2TE L

RP

/ 2

0

/ 2

1 T

T

L

mT L

E E z dzL

More realistic, but we better scale the values measured

on the prototype …

Tank R / Q Q0 MWS 0.75 Q0 MWS 0.7 Q0 MWS R Qext TTFOhm MOhm

1 494 54 166 40 625 37 916 18.7 0.852 505 52 429 39 322 36 700 18.5 6 070 0.843 520 54 477 40 858 38 134 19.8 0.844 533 55 068 41 301 38 548 20.5 0.835 541 53 167 39 875 37 217 20.1 6 508 0.826 558 55 286 41 465 38 700 21.6 0.827 569 55 700 41 775 38 990 22.2 0.818 579 53 962 40 472 37 773 21.9 6 758 0.809 592 55 804 41 853 39 063 23.1 0.8010 616 55 914 41 936 39 140 24.1 0.8211 627 54 787 41 090 38 351 24.0 7 028 0.8112 638 56 263 42 197 39 384 25.1 0.8013 650 56 175 42 131 39 323 25.5 0.7914 658 54 895 41 171 38 427 25.3 7 321 0.7915 670 56 519 42 389 39 563 26.5 0.7816 678 56 606 42 455 39 624 26.9 0.7817 687 54 865 41 149 38 406 26.4 7 640 0.7618 697 56 454 42 341 39 518 27.5 0.7619 707 56 756 42 567 39 729 28.1 0.7620 712 55 019 41 264 38 513 27.4 8 000 0.7521 724 56 783 42 587 39 748 28.8 0.74

2

0

2TE L

RP

/ 2

0

/ 2

1 T

T

L

mT L

E E z dzL

ISTC prototype: Tank 1 Q0 = 38 080 Tank 2 Q0 = 37 600

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21400

500

600

700

800

Tank

R o

ver

Q, O

hm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 213.6 10

4

3.7 104

3.8 104

3.9 104

4 104

Tank

Q

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2115

20

25

30

Tank

R, M

Ohm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.7

0.75

0.8

0.85

Tank

TT

F

2

0

2TE L

RP

Tanks of a single module are highlighted

Cavity fields

0.5 0 0.50

0.5

1

z, m

E1

0.5 0 0.50

0.5

1

z, m

E2

0.5 0 0.50

0.5

1

z, m

E3

0.5 0 0.50

0.5

1

z, m

E4

0.5 0 0.50

0.5

1

z, mE

50.5 0 0.5

0

0.5

1

z, m

E6

0.5 0 0.50

0.5

1

z, m

E7

0.5 0 0.50

0.5

1

z, m

E8

0.5 0 0.50

0.5

1

z, m

E9

0.5 0 0.50

0.5

1

z, m

E10

0.5 0 0.50

0.5

1

z, m

E11

0.5 0 0.50

0.5

1

z, m

E12

0.5 0 0.50

0.5

1

z, m

E13

0.5 0 0.50

0.5

1

z, m

E14

0.5 0 0.50

0.5

1

z, m

E15

Ez field on tank axis (z) from MWS Normalization Emax = 1

0.5 0 0.50

0.5

1

z, m

E13

0.5 0 0.50

0.5

1

z, m

E14

0.5 0 0.50

0.5

1

z, m

E15

0.5 0 0.50

0.5

1

z, m

E16

0.5 0 0.50

0.5

1

z, mE

170.5 0 0.5

0

0.5

1

z, m

E18

0.5 0 0.50

0.5

1

z, m

E19

0.5 0 0.50

0.5

1

z, m

E20

0.5 0 0.50

0.5

1

z, m

E21

Normalization Emax = 1Ez field on tank axis (z) from MWS

0.5 0 0.50

0.5

1

z, m

E1

0.5 0 0.50

0.5

1

z, m

E21

L21 = 1 037.1 mm

L1 = 695.3 mm

Gap1 = 71.5 mm

Gap21 = 129.3 mm

Drift tube1 = 198.6 mm

Drift tube21 = 238.2 mm

Nose cone1 = 41.8 mm

Nose cone1 = 86.4 mm

Tank #1

Tank #21

Ez field on tank axis (z) from MWS

E0

E0LT

Normalization Emax = 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.15

0.2

0.25

0.3

0.35

Tank

T

/ 2

0

/ 2

1 T

T

L

mT L

E E z dzL

Tank Emax E0 E0/E02MV/m MV/m %

1 1.00 0.286 -1.722 1.00 0.291 0.003 1.00 0.292 0.34

4 1.00 0.294 -1.675 1.00 0.299 0.006 1.00 0.299 0.00

7 1.00 0.300 -1.328 1.00 0.304 0.009 1.00 0.303 -0.33

10 1.00 0.281 -1.7511 1.00 0.286 0.0012 1.00 0.282 -1.40

13 1.00 0.283 0.0014 1.00 0.283 0.0015 1.00 0.285 0.71

16 1.00 0.286 -0.3517 1.00 0.287 0.0018 1.00 0.285 -0.70

19 1.00 0.285 -0.7020 1.00 0.287 0.0021 1.00 0.285 -0.70Tanks of a single module are highlighted

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.26

0.28

0.3

0.32

0.34

0.36

Tank

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.4

0.5

0.6

0.7

Tank

Tank E0 W bout bavr l

MV/m MeV mm50.0 0.314

1 4.21 52.3 0.321 270.02 4.21 54.7 0.327 275.73 4.21 57.1 0.334 281.3

4 4.15 59.6 0.340 286.85 4.15 62.0 0.347 292.26 4.15 64.6 0.353 297.5

7 4.05 67.1 0.359 302.78 4.05 69.6 0.365 307.99 4.05 72.1 0.371 313.0

10 3.90 74.7 0.377 318.111 3.90 77.3 0.383 323.112 3.90 79.9 0.388 328.1

13 3.80 82.5 0.394 332.814 3.80 85.1 0.399 337.515 3.80 87.8 0.405 342.1

16 3.70 90.4 0.410 346.517 3.70 93.0 0.415 350.918 3.70 95.6 0.420 355.2

19 3.60 98.2 0.425 359.420 3.60 100.8 0.429 363.521 3.60 103.4 0.434 367.0

41 3 10avr

g

bb

bavrl

gap-to-gap center distance (within a single tank)

1.5boutl

gap-to-gap center distance (two adjacent tanks in a module)

Equal E0 in the tanks of a module

E0 has to satisfy bavrl = gap-to-gap center distance

(within a single tank)1.5boutl = gap-to-gap center distance

(two adjacent tanks in a module)

Tanks of a single module are highlighted

Tank E0 Emax E/E2 W bout bavr l

MV/m MV/m % MeV mm50.0 0.314

1 4.21 14.74 1.79 52.3 0.321 270.02 4.21 14.48 0.00 54.7 0.327 275.73 4.21 14.42 -0.38 57.1 0.334 281.3

4 4.15 14.10 1.59 59.6 0.340 286.85 4.15 13.88 0.00 62.0 0.347 292.26 4.15 13.89 0.08 64.6 0.353 297.5

7 4.05 13.48 1.14 67.1 0.359 302.78 4.05 13.33 0.00 69.6 0.365 307.99 4.05 13.39 0.42 72.1 0.371 313.0

10 3.90 13.89 1.91 74.7 0.377 318.111 3.90 13.63 0.00 77.3 0.383 323.112 3.90 13.82 1.39 79.9 0.388 328.1

13 3.80 13.43 -0.03 82.5 0.394 332.814 3.80 13.43 0.00 85.1 0.399 337.515 3.80 13.34 -0.65 87.8 0.405 342.1

16 3.70 12.96 0.40 90.4 0.410 346.517 3.70 12.91 0.00 93.0 0.415 350.918 3.70 12.97 0.50 95.6 0.420 355.2

19 3.60 12.65 0.95 98.2 0.425 359.420 3.60 12.53 0.00 100.8 0.429 363.521 3.60 12.62 0.77 103.4 0.434 367.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 212.5

3

3.5

4

4.5

E0, MV/MV, MV

Tank

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2112

13

14

15

Tank

Em

ax, M

V/M

/ 2

/ 2

VT

T

L

m

L

E z dz


E0 has to satisfy bavrl = gap-to-gap center distance



Ib=40 mATank E0 Pd W bout bavr l Pb Ptot

MV/m kW MeV mm kW kW50.0 0.314

1 4.21 229 52.3 0.321 270.02 4.21 245 54.7 0.327 275.73 4.21 241 715 57.1 0.334 281.3 285 1 000

4 4.15 238 59.6 0.340 286.85 4.15 255 62.0 0.347 292.26 4.15 250 744 64.6 0.353 297.5 297 1 042

7 4.05 243 67.1 0.359 302.78 4.05 257 69.6 0.365 307.99 4.05 254 754 72.1 0.371 313.0 303 1 057

10 3.90 235 74.7 0.377 318.111 3.90 246 77.3 0.383 323.112 3.90 244 725 79.9 0.388 328.1 312 1 037

13 3.80 237 82.5 0.394 332.814 3.80 247 85.1 0.399 337.515 3.80 245 729 87.8 0.405 342.1 314 1 043

16 3.70 236 90.4 0.410 346.517 3.70 249 93.0 0.415 350.918 3.70 245 729 95.6 0.420 355.2 313 1 042

19 3.60 235 98.2 0.425 359.420 3.60 247 100.8 0.429 363.521 3.60 242 723 103.4 0.434 367.0 310 1 033

Q0 = 0.7 Q0 MWS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21220

230

240

250

260

Tank

Pd,

kW

6


Eini 50.0 MeV Mass H+ 938.271998 MeVmass 939.293982 MeV/c^2 Mass H- 939.293982 MeVfrequency 352.2 MHzc 299792458 m/sl 0.851199483 mb ini 0.313891359 #b l 0.267184163 mcurrent 40.0 mA

b g*l GAPN. Cav E0 b g nose cone drift tube length b g SF b ini V1 TTFg1 fgap1 W1 E1 b end g1 V2

# [MV/m] # [mm] [mm] # # [MV] [#] [deg] [MeV] [MeV] # [MV]1 4.4 0.3173 41.4 197.9 0.3167 0.313891359 0.89685904 0.845082 -21.6 0.704695665 50.7 0.315928301 1.177733922 4.4 0.3239 44.0 200.1 0.3233 0.320610105 0.91670304 0.839212 -21.5 0.715777857 53.1 0.322621558 1.1999243 4.4 0.3305 46.5 202.3 0.3298 0.327229776 0.93614048 0.832938 -21.5 0.725490288 55.5 0.329213162 1.222247844 4.42 0.3370 48.9 204.4 0.3363 0.333750086 0.959759242 0.826888 -21.4 0.738898372 57.9 0.335716472 1.2503048485 4.42 0.3434 51.2 206.3 0.3427 0.340211265 0.978564574 0.820818 -21.4 0.747845833 60.3 0.342149499 1.272898126 4.42 0.3497 53.7 208.2 0.3490 0.346571207 0.997528142 0.814593 -21.3 0.757073138 62.8 0.348483245 1.2943258387 4.35 0.3559 55.7 210.0 0.3552 0.352840224 0.9993603 0.807432 -21.2 0.752306513 65.3 0.354692799 1.2957566858 4.35 0.3619 57.8 211.7 0.3612 0.358913293 1.016803365 0.801377 -21.2 0.759697365 67.8 0.360738944 1.316576229 4.35 0.3679 60.0 213.3 0.3672 0.36489332 1.03435605 0.794503 -21.1 0.766700268 70.3 0.366692241 1.337180865

10 4.29 0.3737 66.1 223.7 0.3730 0.370786675 1.036934184 0.811156 -21.1 0.784721572 72.9 0.372585067 1.33780132211 4.29 0.3796 68.7 225.2 0.3789 0.376672816 1.054593111 0.804289 -21.1 0.791328985 75.5 0.378444487 1.35665544312 4.29 0.3853 70.0 226.7 0.3846 0.382469122 1.069597815 0.797908 -21.1 0.796220474 78.1 0.384211364 1.37837657113 4.22 0.3909 72.7 228.0 0.3902 0.388171154 1.06921507 0.790688 -21 0.789263387 80.7 0.389859878 1.37217182414 4.22 0.3964 73.7 229.5 0.3957 0.393690657 1.083108154 0.784936 -21 0.793702615 83.3 0.395352427 1.394055915 4.22 0.4018 76.3 230.7 0.4011 0.399127597 1.099707946 0.777285 -21 0.798011937 85.9 0.40076313 1.40943442416 4.15 0.4071 77.3 232.0 0.4064 0.404473214 1.09467372 0.771144 -20.9 0.788609708 88.6 0.406056079 1.40665619517 4.15 0.4122 79.6 233.1 0.4115 0.409653249 1.10988596 0.764077 -20.9 0.792241207 91.2 0.411211519 1.4212687618 4.15 0.4173 80.7 234.4 0.4165 0.414745442 1.122745565 0.758018 -20.9 0.795065319 93.8 0.416278473 1.4400018619 4.09 0.4222 82.8 235.3 0.4214 0.419756451 1.120887813 0.751186 -20.8 0.787118763 96.4 0.421244828 1.43297076420 4.09 0.4270 83.8 236.4 0.4262 0.424617 1.132795848 0.745552 -20.8 0.7895147 99.0 0.426081873 1.45088210121 4.09 0.4318 85.9 237.3 0.4310 0.429402221 1.14700369 0.738827 -20.8 0.792206143 101.6 0.430844915 1.463936154

Data from CERN

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.26

0.28

0.3

0.32

0.34

0.36

Tank

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.4

0.5

0.6

0.7

Tank

Tank

BINP CERN CERN / BINP

1 4.21 4.40 1.052 4.21 4.40 1.053 4.21 4.40 1.05

4 4.15 4.42 1.075 4.15 4.42 1.076 4.15 4.42 1.07

7 4.05 4.35 1.078 4.05 4.35 1.079 4.05 4.35 1.07

10 3.90 4.29 1.1011 3.90 4.29 1.1012 3.90 4.29 1.10

13 3.80 4.22 1.1114 3.80 4.22 1.1115 3.80 4.22 1.11

16 3.70 4.15 1.1217 3.70 4.15 1.1218 3.70 4.15 1.12

19 3.60 4.09 1.1420 3.60 4.09 1.1421 3.60 4.09 1.14

E0MV/m

CERN set of E0

CERN set of E0

bavrl


1.5boutl


Probably the definition of “tank length” is different (?)

/ 2

0

/ 2

1 T

T

L

mT L

E E z dzL

Ib=40 mATank E0 Pd W Pb Ptot Qext Coupling

MV/m kW MeV kW kW50.0

1 4.21 229 52.32 4.21 245 54.7 6 070 1.483 4.21 241 715 57.1 285 1 000

4 4.15 238 59.65 4.15 255 62.0 6 508 1.406 4.15 250 744 64.6 297 1 042

7 4.05 243 67.18 4.05 257 69.6 6 758 1.369 4.05 254 754 72.1 303 1 057

10 3.90 235 74.711 3.90 246 77.3 7 028 1.2912 3.90 244 725 79.9 312 1 037

13 3.80 237 82.514 3.80 247 85.1 7 321 1.2515 3.80 245 729 87.8 314 1 043

16 3.70 236 90.417 3.70 249 93.0 7 640 1.2018 3.70 245 729 95.6 313 1 042

19 3.60 235 98.220 3.60 247 100.8 8 000 1.1521 3.60 242 723 103.4 310 1 033

2 1

1

extrf

bd b ext d

d

P WPP P Q PP

b


Tank E0 Emax E/E2MV/m MV/m %

1 4.15 14.51 0.002 4.22 14.51 0.003 4.24 14.51 0.00

4 4.09 13.88 0.005 4.15 13.88 0.006 4.15 13.88 0.00

7 4.00 13.33 0.008 4.05 13.33 0.009 4.03 13.33 0.00

10 3.88 13.80 0.0011 3.95 13.80 0.0012 3.90 13.80 0.00

13 3.80 13.43 0.0014 3.80 13.43 0.0015 3.83 13.43 0.00

16 3.69 12.91 0.0017 3.70 12.91 0.0018 3.68 12.91 0.00

19 3.57 12.53 0.0020 3.60 12.53 0.0021 3.57 12.53 0.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 212.5

3

3.5

4

4.5

E0, MV/MV, MV

Tank

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2112.5

13

13.5

14

14.5

15

Tank

Em

ax, M

V/M

Another field distribution with equal Emax in the tanks of a module

/ 2

/ 2

VT

T

L

m

L

E z dz

Tank E0 Emax E/E2 W bout bavr l

MV/m MV/m % MeV mm50 0.314

1 4.15 14.51 0.00 52.3 0.320 270.02 4.22 14.51 0.00 54.7 0.327 275.63 4.24 14.51 0.00 57.1 0.334 281.2

4 4.09 13.88 0.00 59.5 0.340 286.75 4.15 13.88 0.00 62.0 0.346 292.16 4.15 13.88 0.00 64.5 0.353 297.5

7 4.00 13.33 0.00 67.0 0.359 302.88 4.05 13.33 0.00 69.5 0.365 307.99 4.03 13.33 0.00 72.0 0.371 313.0

10 3.88 13.80 0.00 74.6 0.376 318.011 3.95 13.80 0.00 77.2 0.382 323.012 3.90 13.80 0.00 79.9 0.388 327.9

13 3.80 13.43 0.00 82.5 0.394 332.714 3.80 13.43 0.00 85.1 0.399 337.315 3.83 13.43 0.00 87.7 0.404 341.9

16 3.69 12.91 0.00 90.3 0.410 346.417 3.70 12.91 0.00 92.9 0.415 350.818 3.68 12.91 0.00 95.5 0.420 355.1

19 3.57 12.53 0.00 98.1 0.424 359.220 3.60 12.53 0.00 100.6 0.429 363.321 3.57 12.53 0.00 103.2 0.434 367.3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.26

0.28

0.3

0.32

0.34

0.36

Tank

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210.4

0.5

0.6

0.7

Tank

bavrl


1.5boutl



Emax has to satisfy bavrl = gap-to-gap center distance



Ib=40 mATank E0 Emax E/E2 Pd W bout bavr l Pb Ptot 0.7 Q0 MWS Qext Coupling

MV/m MV/m % kW MeV mm kW kW50 0.314

1 4.15 14.51 0.00 222 52.3 0.320 270.0 37 9162 4.22 14.51 0.00 246 54.7 0.327 275.6 36 700 6 070 1.513 4.24 14.51 0.00 244 712 57.1 0.334 281.2 285 997 38 134

4 4.09 13.88 0.00 231 59.5 0.340 286.7 38 5485 4.15 13.88 0.00 255 62.0 0.346 292.1 37 217 6 508 1.416 4.15 13.88 0.00 250 737 64.5 0.353 297.5 296 1 032 38 700

7 4.00 13.33 0.00 237 67.0 0.359 302.8 38 9908 4.05 13.33 0.00 257 69.5 0.365 307.9 37 773 6 758 1.379 4.03 13.33 0.00 252 747 72.0 0.371 313.0 302 1 048 39 063

10 3.88 13.80 0.00 232 74.6 0.376 318.0 39 14011 3.95 13.80 0.00 252 77.2 0.382 323.0 38 351 7 028 1.3212 3.90 13.80 0.00 243 728 79.9 0.388 327.9 313 1 040 39 384

13 3.80 13.43 0.00 237 82.5 0.394 332.7 39 32314 3.80 13.43 0.00 247 85.1 0.399 337.3 38 427 7 321 1.2415 3.83 13.43 0.00 248 733 87.7 0.404 341.9 314 1 047 39 563

16 3.69 12.91 0.00 234 90.3 0.410 346.4 39 62417 3.70 12.91 0.00 249 92.9 0.415 350.8 38 406 7 640 1.2118 3.68 12.91 0.00 242 725 95.5 0.420 355.1 312 1 037 39 518

19 3.57 12.53 0.00 230 98.1 0.424 359.2 39 72920 3.60 12.53 0.00 247 100.6 0.429 363.3 38 513 8 000 1.1621 3.57 12.53 0.00 239 715 103.2 0.434 367.3 308 1 023 39 748


2 1

1

extrf

bd b ext d

d

P WPP P Q PP

b

Tan

k

Cav

ity le

ngth

EQ

UA

TO

R_f

lat

OU

TE

R_C

OR

Ner

_rad

ius

DIA

Met

er

INN

ER

_CO

RN

er_r

adiu

s

OU

TE

R_N

OS

E_r

adiu

s

INN

ER

_NO

SE

_rad

ius

FLA

T_l

engt

h

CO

NE

_ang

le

Nos

e le

ngth

Nos

e ba

se r

adiu

s

dt le

ngth

dt e

quat

or f

lat

DT

_DIA

Met

er

DT

_CO

RN

er_r

adiu

s

DT

_OU

TE

R_N

OS

E_r

adiu

s

DT

_IN

NE

R_N

OS

E_r

adiu

s

DT

_FLA

T_l

engt

h

DT

_OU

TE

R_F

AC

E_a

ngle

DT

_IN

NE

R_F

AC

E_a

ngle

dt n

ose

leng

th

dt s

pher

e ra

dius

BO

RE

_rad

ius

GA

P_L

engt

h

# LT Feq

Rco D Rci

Ro Ri F

alph

ac

H Rcb Ld F

deq

d Rc

Rdo Rdi Fd

alph

afo

alph

afi

Hd

Rs

Rb g

1 695.3 615.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 41.8 53.2 198.6 83.8 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 71.52 715.2 635.2 40.0 520.0 15.0 12.0 2.0 7.0 20.0 43.9 54.0 199.8 85.0 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 76.03 734.6 654.6 40.0 520.0 15.0 12.0 2.0 7.0 20.0 46.9 55.1 203.0 88.2 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 78.34 754.0 674.0 40.0 520.0 15.0 12.0 2.0 7.0 20.0 49.4 56.0 205.1 90.3 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 81.75 772.9 692.9 40.0 520.0 15.0 12.0 2.0 7.0 20.0 51.0 56.6 206.1 91.3 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 86.26 792.1 712.1 40.0 520.0 15.0 12.0 2.0 7.0 20.0 54.1 57.7 209.0 94.2 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 88.77 810.3 730.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 56.2 58.5 210.8 96.0 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 92.18 828.2 748.2 40.0 520.0 15.0 12.0 2.0 7.0 20.0 57.7 59.0 211.4 96.6 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 96.69 846.3 766.3 40.0 520.0 15.0 12.0 2.0 7.0 20.0 60.5 60.0 214.1 99.3 95.0 2.5 12.0 2.0 7.0 15.0 15.0 57.4 52.5 14.0 99.0

10 862.9 782.9 40.0 520.0 15.0 7.0 2.0 3.0 20.0 66.6 58.2 224.6 79.9 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 93.511 881.5 801.5 40.0 520.0 15.0 7.0 2.0 3.0 20.0 68.6 58.9 225.2 80.5 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 97.912 897.3 817.3 40.0 520.0 15.0 7.0 2.0 3.0 20.0 70.5 59.6 227.7 83.0 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 100.313 915.7 835.7 40.0 520.0 15.0 7.0 2.0 3.0 20.0 73.2 60.6 229.0 84.3 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 103.814 930.1 850.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 73.7 60.8 229.5 84.8 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 107.915 948.1 868.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 76.8 61.9 231.6 86.9 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 110.416 962.2 882.2 40.0 520.0 15.0 7.0 2.0 3.0 20.0 77.8 62.2 233.0 88.3 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 113.517 978.7 898.7 40.0 520.0 15.0 7.0 2.0 3.0 20.0 79.7 63.0 233.3 88.6 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 117.618 992.5 912.5 40.0 520.0 15.0 7.0 2.0 3.0 20.0 81.1 63.5 235.3 90.6 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 119.919 1 008.4 928.4 40.0 520.0 15.0 7.0 2.0 3.0 20.0 83.3 64.3 236.2 91.5 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 123.120 1 021.4 941.4 40.0 520.0 15.0 7.0 2.0 3.0 20.0 83.9 64.5 236.7 92.0 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 126.821 1 037.1 957.1 40.0 520.0 15.0 7.0 2.0 3.0 20.0 86.4 65.4 238.2 93.5 95.0 2.5 12.0 2.0 3.0 15.0 15.0 72.3 52.5 14.0 129.3

3D simulationsof specified geometry (without tuners) lead to what frequency?

30 20 10 0 10 20 30 40 50

100

100

200

300

400

500

1 tuner (tank 1, calc)1 tuner (tank 21, calc)1 tuner (prototype, meas)

x, mm

df, k

Hz 200

29 37 .

Tank fMHz

1 352.1032 352.0773 352.1194 352.0995 352.1276 352.0997 352.0928 352.1089 352.08710 352.09911 352.09412 352.08013 352.11414 352.13315 352.11516 352.10117 352.13418 352.10819 352.10120 352.11521 352.111

Tuning range of a single tuner

Tuners protrude into the cavityTuners pulled out of the cavity

Each tuner position

Total frequency shift by a single

tuner

Frequency shift f1(x) by a single tuner (measured on the ISTC prototype tank 2)

is plotted in magenta

x

84

Tuner midposition

++100 kHz

-100 kHz

352.2MHz

+ tuner at its midposition

Tuning sequence

Tanks are made with certain accuracy leading to a frequency uncertainty (even if we assume that the drift tubes are machined precisely).

Tanks will be measured with installed aluminum dummy drift tubes with “precisely” known (measured after machining) dimensions similar (but not necessarily equal) to those of real drift tubes.

Dimensions of copper drift tubes required to bring the frequency of particular tank to the design value will be extrapolated from the measurements with aluminum dummy drift tubes.

Final frequency error of a tank with copper drift tubes depends on the precision of this extrapolation and on the drift tube final machining accuracy.

Could we relax the tolerances on the tanks manufacturing?No, because we do not want drift tubes to be substantially different from the design.No, because after few first tanks we might gain enough experience and eliminate “measure-extrapolate-machine” sequence, although unlikely.

Could we eliminate tuners as we adjust drift tube dimensions to a particular tank actual dimension?No, because even if we know exactly (with extrapolation precision) what ideal drift tube we need, we only can get it within manufacturing accuracy.

Ri

Rci F =

Fd

c

Ro

Rco

D /

2FEq

LT

Rb

Rcb c

Beam axis

Ver

tical

sym

met

ry p

lane

dF

NC MSP

Manufacturing precision

mm (deg)Tank # 1 21 1 21 1 21Cavity HALF length LT / 2 347.6 518.6 -104.9 -135.9EQUATOR_flat Feq 615.3 957.1OUTER_CORNer_radius Rco 40.0 40.0 35.5 18.0DIAMeter D 520.0 520.0 -440.7 -429.8INNER_CORNer_radius Rci 15.0 15.0 1.1 2.4OUTER_NOSE_radius Ro 12.0 7.0 45.2 28.4INNER_NOSE_radius Ri 2.0 2.0 10.2 9.4FLAT_length F 7.0 3.0 -218.0 -247.2CONE_angle alphac 20.0 20.0 -6.9 -19.7Nose length H 41.8 86.4

LT / 2 H 305.8 432.2 -360.5 -256.0Nose base radius Rcb 53.2 65.4BORE_radius Rb 14.0 14.0

Total frequency error

kHz

Frequency error

mm (deg) kHz/mm (deg)

Frequency sensitivityTank 2D simulations

To be compensated by drift tube re-machiningFLAT_length manufacturing precision is considered as max error in

R coordinate of nose cone (NC) machining starting point (MSP) which leads to an equal radial “displacement” of the entire nose

cone

?

Ri

Rci F =

Fd

c

Ro

Rco

D /

2FEq

LT

Rb

Rcb c

Beam axis

Ver

tical

sym

met

ry p

lane

dF

NC MSP


mm (deg)Tank # 1 21 1 21 1 21Cavity HALF length LT / 2 347.6 518.6 0.30 -104.9 -135.9 31.5 40.8EQUATOR_flat Feq 615.3 957.1OUTER_CORNer_radius Rco 40.0 40.0 0.50 35.5 18.0 17.8 9.0DIAMeter D 520.0 520.0 0.13 -440.7 -429.8 57.3 55.9INNER_CORNer_radius Rci 15.0 15.0 0.50 1.1 2.4 0.6 1.2OUTER_NOSE_radius Ro 12.0 7.0 0.50 45.2 28.4 22.6 14.2INNER_NOSE_radius Ri 2.0 2.0 0.50 10.2 9.4 5.1 4.7FLAT_length F 7.0 3.0 0.20 -218.0 -247.2 43.6 49.4CONE_angle alphac 20.0 20.0 1/4 -6.9 -19.7 1.7 4.9Nose length H 41.8 86.4

LT / 2 H 305.8 432.2 0.05 -360.5 -256.0 18.0 12.8Nose base radius Rcb 53.2 65.4BORE_radius Rb 14.0 14.0 0.0 0.0

Total frequency error 198.1 192.9

kHz

Frequency error

mm (deg) kHz/mm (deg)

Frequency sensitivityTank 2D simulations

To be compensated by drift tube re-machiningFLAT_length manufacturing precision is considered as max error in

R coordinate of nose cone (NC) machining starting point (MSP) which leads to an equal radial “displacement” of the entire nose

cone

F =

Fd

LdRc

f=fo=fi

Rdo

Rdi

FdeqHdHd

d / 2Rs

f

Beam axis

Ver

tical

sym

met

ry p

lane

dFd

NC MSP


±mm (deg)Tank # 1 21 1 21 1 21dt length Ld 198.6 238.2 -913.5 -661.0dt equator flat Fdeq 83.8 93.5DT_DIAMeter d 95.0 95.0 47.5 63.3DT_CORNer_radius Rc 2.5 2.5DT_OUTER_NOSE_radius Rdo 12.0 12.0 295.8 224.6DT_INNER_NOSE_radius Rdi 2.0 2.0 44.4 35.8DT_FLAT_length Fd 7.0 3.0 -1 696.0 -1 515.0DT_OUTER_FACE_angle alphafo 15.0 15.0DT_INNER_FACE_angle alphafi 15.0 15.0dt nose length Hd 57.4 72.3dt sphere radius Rs 52.5 52.5 202.7 194.5BORE_radius Rb 14.0 14.0


mm (deg)

Frequency sensitivity

kHz/mm (deg)

Frequency error

±kHz

-193.6 -247.3

Drift tube 2D simulations

To be compensated by tuners

DT

_FLA

T_l

eng

th m

anuf

actu

ring

prec

isio

n is

co

nsid

ered

as

max

er

ror

in R

co

ordi

nate

of

DT

nos

e c

one

(N

C)

mac

hini

ng

star

ting

poin

t (M

SP

) w

hich

lead

s to

an

equ

al r

adia

l “di

spla

cem

ent”

of

the

entir

e dr

ift t

ube

nos

e co

ne

?

1

2 3

Tolerances accepted by BINP workshop

F =

Fd

LdRc

f=fo=fi

Rdo

Rdi

FdeqHdHd

d / 2Rs

f

Beam axis

Ver

tical

sym

met

ry p

lane

dFd

NC MSP


±mm (deg)Tank # 1 21 1 21 1 21dt length Ld 198.6 238.2 0.05 -913.5 -661.0 45.7 33.1dt equator flat Fdeq 83.8 93.5 0.0 0.0DT_DIAMeter d 95.0 95.0 0.05 47.5 63.3 2.4 3.2DT_CORNer_radius Rc 2.5 2.5 0.0 0.0DT_OUTER_NOSE_radius Rdo 12.0 12.0 0.10 295.8 224.6 29.6 22.5DT_INNER_NOSE_radius Rdi 2.0 2.0 0.10 44.4 35.8 4.4 3.6DT_FLAT_length Fd 7.0 3.0 0.05 -1 696.0 -1 515.0 84.8 75.8DT_OUTER_FACE_angle alphafo 15.0 15.0DT_INNER_FACE_angle alphafi 15.0 15.0dt nose length Hd 57.4 72.3 0.0 0.0dt sphere radius Rs 52.5 52.5 0.10 202.7 194.5 20.3 19.5BORE_radius Rb 14.0 14.0 0.0 0.0

Total frequency error 188.8 159.5

2.1

mm (deg)


kHz/mm (deg)

Frequency error

±kHz

1/120 -193.6 -247.3 1.6

Drift tube 2D simulations

To be compensated by tuners

DT

_FLA

T_l

eng

th m

anuf

actu

ring

prec

isio

n is

co

nsid

ered

as

max

er

ror

in R

co

ordi

nate

of

DT

nos

e c

one

(N

C)

mac

hini

ng

star

ting

poin

t (M

SP

) w

hich

lead

s to

an

equ

al r

adia

l “di

spla

cem

ent”

of

the

entir

e dr

ift t

ube

nos

e co

ne

Relaxed by a factor of 2 against the Workshop value

30 20 10 0 10 20 30 40 50

200

200

400

600

800

1000

2 tuners (tank 1, calc)2 tuners (tank 21, calc)2 x 1 tuner (prototype, meas)

x, mm

df, k

Hz

439

612

40 .

Tuning range of 2 equally positioned tuners


Each tuner position

Total frequency shift by equally

positioned 2 tuners

Doubled frequency shift 2f1(x) by a single tuner (measured on the ISTC

prototype tank 2) is plotted in magenta

x

84

130 120 110 100 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 1003.45 10

4

3.5 104

3.55 104

3.6 104

3.65 104

3.7 104

3.75 104

3.8 104

measurementsapproximation

x1 + x2, mm

Q0

35380

36770

0 80

.

No tuners – ports are blank terminated

At least 1 tuner is pulled out of the cavity and hidden inside the port

ISTC prototype tank 2

Measurements with various combinations of 2 fixed tuners of different lengths

130 120 110 100 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 1003.45 10

4

3.5 104

3.55 104

3.6 104

3.65 104

3.7 104

3.75 104

3.8 104

measurements (with smoothing)approximation

x1 + x2, mm

Q0

35380

36770

0 80

.

by running medians over a window of 3 neighboor data points

1 20 80mm

3.8%x x

Q

Q

10 40mm

2 3%x

Q

Q

Measurements(ISTC prototype tank 2, 2 tuners)

Calculations(Linac4 tank 1, single tuner)

ISTC prototype tank 2

No tuners – ports are blank terminated

At least 1 tuner is pulled out of the cavity and hidden inside the port

Same plot as the previous one, but with data points smoothing

Fixed tuner – CERN design (SPLACTUF0012)

BINP design is similar to CERN design, but without groove – no spring contact is foreseen

Accelerating cavity – DN100CF (STDVFUHV0094 )Coupling cavity – DN63CF (STDVFUHV0028 )

Copper piston

AC

85

CC

60

AC

84

CC

59

10 40mm

2 3%x

Q

Q

Calculations(Linac4 tank 1, single tuner,without spring contact)

10 40mm

2 1.5%x

Q

Q

Calculations(Linac4 tank 1, single tuner,with spring contact)

Coupling cell

D

cc



Frequency error

mm ±mm kHz/mm ±kHzcc length Lcc 230.0 -955.0cc diameter Dcc 214.0 -956.5cc corner radius Rcc 5.0 51.2cc nose diameter dcc 92.2 -599.6cc outer nose radius Rcco 5.0 112.0cc inner nose radius Rcci 5.0 1 576.4cc gap gcc 21.4 5 959.2


d cc

Lcc

gcc

Rcc

Rcco

Rcci

Coupling cell2D simulations

D

cc



Frequency error

mm ±mm kHz/mm ±kHzcc length Lcc 230.0 0.15 -955.0 143.3cc diameter Dcc 214.0 0.10 -956.5 95.7cc corner radius Rcc 5.0 0.20 51.2 10.2cc nose diameter dcc 92.2 0.10 -599.6 60.0cc outer nose radius Rcco 5.0 0.20 112.0 22.4cc inner nose radius Rcci 5.0 0.10 1 576.4 157.6cc gap gcc 21.4 0.05 5 959.2 298.0

Total frequency error 787.1

d cc

Lcc

gcc

Rcc

Rcco

Rcci

Coupling cell2D simulations

Coupling cell tuning3D simulations (MWS)

Cutting plane

Coupling cell

Detuned cavities to account coupling cell field distortion due to the coupling slots

x

59


D

cc

d cc

Lcc

gcc

Rcc

Rcco

Rcci

Total frequency shift by equally positioned 2 tuners was calculated

40 30 20 10 0 10 20 30 40 50

500

500

1000

1500

2000

2 tuners (calc)2 x 1 tuner (meas)

x, mm

df, k

Hz

156

1410

3 21.

Tuners midposition


Each tuner position


+

Total frequency shift by equally positioned 2 tuners

Doubled frequency shift 2f1(x) by a single tuner (measured on the ISTC prototype) is plotted in

blue

+783 kHz

-783 kHz

352.2MHz

40 30 20 10 0 10 20 30 40 50

500

500

1000

1500

2000

2 tuners (calc)2 x 1 tuner (meas)

x, mm

df, k

Hz

156

1410

3 21.

Tuners midposition


Each tuner position


+

Total frequency shift by equally positioned 2 tuners

Doubled frequency shift 2f1(x) by a single tuner (measured on the ISTC prototype) is plotted in

blue

Total frequency error due to manufacturing accuracy = 787 kHz

2 tuners + careful machining are

necessary

+783 kHz

-783 kHz

352.2MHz

Tuners midposition

+CC gap = 21.24 mm


Calculated coupling cell frequency with no tuners is 352.2 MHz at CC gap of 21.36 mm

352.2MHz = f0 + 733 kHz

f0 f (no tuners and no tuner ports)

… does not agree with the measurements on ISTC prototype, needs to be understood

CERN “Hot model” Coupling cell

3D simulations (MWS)

D

cc

d cc

Lcc

gcc

Rcc

Rcco

Rcci

mmcc length Lcc 240.0cc diameter Dcc 214.0cc corner radius Rcc 5.0cc nose diameter dcc 92.2cc outer nose radius Rcco 5.0cc inner nose radius Rcci 5.0cc gap gcc 22.8

f0 calc = 350.380 (± 0.140) MHz

140

x 30

convergence accuracy

Coupling cell

Detuned cavities to account coupling cell field distortion due to the coupling slots

f0 meas = ?

?

f vac|x=0= 350.130 MHz

D

cc

ISTC Prototype:Design value

Actual value

+ shims DeltaFrequency sensitivity

Frequency shift

mm mm mm mm kHz/mm kHzcc length Lcc 230.0 230.20 230.40 0.40 -955.0 -382.0cc diameter Dcc 214.0 214.06 214.06 0.06 -956.5 -57.4cc corner radius Rcc 5.0 5.00 5.00 0.00 51.2 0.0cc nose diameter dcc 92.2 92.10 92.10 -0.10 -599.6 60.0cc outer nose radius Rcco 5.0 5.00 5.00 0.00 112.0 0.0cc inner nose radius Rcci 5.0 5.40 5.40 0.40 1 576.4 630.6cc gap gcc 21.5 21.50 21.70 0.20 5 959.2 1 191.8

Total frequency shift 1 443.0

d cc

gcc

Rcc

Rcco

Rcci

Could not compensate total frequency error by a single tuner, needed to use 0.2 mm shims in order to increase gcc (and Lcc)

20.9

59

f = +625 kHz

f vac|x=0= 351.573 MHz Measurements at BINP:

f air = 352.078 MHz f vac = 352.198 MHz Lcc

BINP geometry (= cavity inner dimensions which define the boundary)

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Transcript of BINP geometry (= cavity inner dimensions which define the boundary)