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

Constant definition (Superfish style)

CERN geometry (as of August 4, 2008) Constant for all tanks Constant for tanks 1-9 and 10-21Variable Dependent variable

Constant definition (Superfish style) Constant for all tanks Constant for tanks 1-9 and Variable Dependent variable

CERN geometry

BINP geometry Design modifications: 1.Drift tube to stem connection 2.Gridded port for an ion pump 3.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  DN100CF (STDVFUHV0052) DN100CF Design modifications / Gridded port for an ion pump

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 # 3m  2 Tank # 3m  1 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 (1 st and 3 rd tanks in each module). Waveguide coupler port is accounted (2 nd tank in each module) 3D simulations m = 1…7 – module number

Constant definition (Superfish style)

Dependent variable BINP geometry Changes are highlighted  Constant for all tanks Constant for tanks 1-9 and Variable Dependent variable

CERN - BINP geometry Differences are within 1 mm

BINP geometry (hereinafter) Cavity parameters from 3D simulations

More realistic, but we better scale the values measured on the prototype …

ISTC prototype: Tank 1 Q 0 = Tank 2 Q 0 =

Tanks of a single module are highlighted

E z field on tank axis (z) from MWSNormalization E max = 1

E z field on tank axis (z) from MWS

L 21 = mm L 1 = mm Gap 1 = 71.5 mm Gap 21 = mm Drift tube 1 = mm Drift tube 21 = mm Nose cone 1 = 41.8 mm Nose cone 1 = 86.4 mm Tank #1 Tank #21 E z field on tank axis (z) from MWS

E0E0 E0LTE0LT Normalization E max = 1 Tanks of a single module are highlighted

 avr gap-to-gap center distance (within a single tank) 1.5  out gap-to-gap center distance (two adjacent tanks in a module) Equal E 0 in the tanks of a module E 0 has to satisfy  avr = gap-to-gap center distance (within a single tank) 1.5  out = gap-to-gap center distance (two adjacent tanks in a module) Tanks of a single module are highlighted

Equal E 0 in the tanks of a module E 0 has to satisfy  avr = gap-to-gap center distance (within a single tank) 1.5  out = gap-to-gap center distance (two adjacent tanks in a module)

Q 0 = 0.7 Q 0 MWS Equal E 0 in the tanks of a module

Data from CERN

CERN set of E 0  avr gap-to-gap center distance (within a single tank) 1.5  out gap-to-gap center distance (two adjacent tanks in a module) Probably the definition of “tank length” is different (?)

Equal E 0 in the tanks of a module

Another field distribution with equal E max in the tanks of a module

 avr gap-to-gap center distance (within a single tank) 1.5  out gap-to-gap center distance (two adjacent tanks in a module) Another field distribution with equal E max in the tanks of a module E max has to satisfy  avr = gap-to-gap center distance (within a single tank) 1.5  out = gap-to-gap center distance (two adjacent tanks in a module)

Another field distribution with equal E max in the tanks of a module

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

Tuning range of a single tuner  Tuners protrude into the cavity Tuners pulled out of the cavity  Each tuner position Total frequency shift by a single tuner Frequency shift  f 1 (x) by a single tuner (measured on the ISTC prototype tank 2) is plotted in magenta x  84 Tuner midposition kHz -100 kHz + 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.

Tank 2D simulations To be compensated by drift tube re-machining FLAT_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 ?

Tank 2D simulations To be compensated by drift tube re-machining FLAT_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

Drift tube 2D simulations To be compensated by tuners DT_FLAT_length manufacturing precision is considered as max error in R coordinate of DT nose cone (NC) machining starting point (MSP) which leads to an equal radial “displacement” of the entire drift tube nose cone ?

Tolerances accepted by BINP workshop

Drift tube 2D simulations To be compensated by tuners DT_FLAT_length manufacturing precision is considered as max error in R coordinate of DT nose cone (NC) machining starting point (MSP) which leads to an equal radial “displacement” of the entire drift tube nose cone Relaxed by a factor of 2 against the Workshop value

Tuning range of 2 equally positioned tuners  Tuners protrude into the cavity Tuners pulled out of the cavity  Each tuner position Total frequency shift by equally positioned 2 tuners Doubled frequency shift 2  f 1 (x) by a single tuner (measured on the ISTC prototype tank 2) is plotted in magenta x  84

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

by running medians over a window of 3 neighboor data points 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 Calculations (Linac4 tank 1, single tuner, without spring contact) Calculations (Linac4 tank 1, single tuner, with spring contact)

Coupling cell

 D cc  d cc L cc g cc R cc R cco R cci Coupling cell 2D simulations

 D cc  d cc L cc g cc R cc R cco R cci Coupling cell 2D simulations

Coupling cell tuning 3D simulations (MWS) Cutting plane Coupling cell Detuned cavities to account coupling cell field distortion due to the coupling slots

x  59 Coupling cell tuning 3D simulations (MWS)  D cc  d cc L cc g cc R cc R cco R cci Total frequency shift by equally positioned 2 tuners was calculated

Tuners midposition  Tuners protrude into the cavity Tuners pulled out of the cavity  Each tuner position Coupling cell tuning 3D simulations (MWS) + Total frequency shift by equally positioned 2 tuners Doubled frequency shift 2  f 1 (x) by a single tuner (measured on the ISTC prototype) is plotted in blue +783 kHz -783 kHz

Tuners midposition  Tuners protrude into the cavity Tuners pulled out of the cavity  Each tuner position Coupling cell tuning 3D simulations (MWS) + Total frequency shift by equally positioned 2 tuners Doubled frequency shift 2  f 1 (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

Tuners midposition + CC gap = mm Coupling cell tuning 3D simulations (MWS) Calculated coupling cell frequency with no tuners is MHz at CC gap of mm = f kHz f 0  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 L cc g cc R cc R cco R cci f 0 calc = (± 0.140) MHz 140 x 30 convergence accuracy Coupling cell Detuned cavities to account coupling cell field distortion due to the coupling slots f 0 meas = ? ?

 f vac | x=0 = MHz  D cc  d cc g cc R cc R cco R cci Could not compensate total frequency error by a single tuner, needed to use 0.2 mm shims in order to increase g cc (and L cc ) 20.9  59  f = +625 kHz  f vac | x=0 = MHz Measurements at BINP: f air = MHz  f vac = MHz L cc