A possible linearizer at 35.982 GHz · Wake fields studies on the 35.982 GHz structure 0 5 10 4 1 10 5 1,5 10 5 2 10 5 2,5 10 5 3 10 5 0 20 40 60 80 100 Transverse loss parameter

A possible linearizer at 35.982 GHz

on behalf of the SPARC - LAB collaboration

B. Spataro – M. Behtouei (phd) , L. Faillace- M. Migliorati - M.Sciscio’ and A. Variola

First XLS Annual Meeting ALBA, Barcelona, Spain 10-12 December 2018

Summary

Accelerating electric field estimations


Rounded cavity design (hard shape cavity already discussed in Trieste)

Longitudinal and transverse loss parameters estimations

Thermal stress studies

b = cavity radius

a = iris radius

h = iris thickness

TW cavity shape for the 2p/3 mode

𝑣𝑔𝑟

𝑐

1

𝑐

𝑑𝑑𝛷

𝛷 = 𝑝ℎ𝑎𝑠𝑒 𝑎𝑑𝑣𝑎𝑛𝑐𝑒

b

h

l = cell lenght l/3

I

a

Rounded shape


Shunt impedance and quality factor Q estimations of the roundedcavity as function of the iris radius at F = 35.982 GHz

100

120

140

160

180

200

220

240

0,6 0,8 1 1,2 1,4 1,6 1,8 2 2,2

Shunt impedance as function of

the iris radius at F = 35.982 GHz

iris radius (mm)

Y = M0 + M1*x + ... M8*x8 + M9*x

9

323,49M0

-151,26M1

20,423M2

0,99992R

F = 35.982 GHz iris radius a = 1.333 mm thickness iris h = 0.667 mm

Rsh / m = 158 M𝛀 /m (144 hard edge)


b = 3.657 mm

4000

4050

4100

4150

4200

4250

4300

0,6 0,8 1 1,2 1,4 1,6 1,8 2 2,2

Unloaded quality factor Q as functiom

of the iris radius at F = 35.982 GHz

iris radius (mm)

Y = M0 + M1*x + ... M8*x8 + M9*x

9

4012,7M0

-13,146M1

66,804M2

0,99889R

Q = 4110 ( Q = 3718 hard edge)

Dispersion relation of the rounded shape of the TW structure

K = 1.5 %

a = 1.333 mm, h = 0.667 mm mm, b = 3.657 mm

vgr /c = 0.04

35,5

35,6

35,7

35,8

35,9

36

36,1

36,2

-50 0 50 100 150 200

Frequency mode as function of the phase

advance of the TW structure (rounded shape)

Freq 35

phase advance per cell h


F = 35.982 GHz (2p/3 mode)

‘Rounded’ TW cavity fields estimations for the 2p/3 mode at F = 35.983 GHz

Magnetic field distribution of the TM010 mode Electric field distribution of the TM010 mode


a/𝞴 = 0.16

vgr/c = 0.04

Rsh/m = 158 M𝛀 /m

b = 3.657 mm (cavity radius)

h = 0.667 mm (iris thickness)

Q = 4110

a = 1.333 mm (iris radius)

Input RF power for different gradients of the rounded shape

Parameter Value

Filling Time, Tf 20 ns

L, length 25 cm

w, frequency 2pi*35.982 GHz

R/Q 38.4 kΩ/m

0.57

Assuming a structure length L = 25 cm ,Tf = 20 ns (filling time), R/Q = 38.4 KΩ/mand = 0.57 (attenuation)

For a CG structure: input group velocity vgr_in/c = 6.7%, output group velocity vgr_out/c = 2.2%,

For a CI structure : vgr = 0.04 c


𝑷𝒊𝒏 = 𝟏/𝑻𝒇𝟐𝝉

𝟏−𝒆−𝟐𝝉(𝑬𝒂𝒄𝒄∗𝑳)

𝟐

𝒘( ൗ𝑹 𝑸)𝑳, Wang

Max Esurface = 200 MV/mMax Hsurface = 0.26 MA/m

RF Pulsed HeatingΔT = 10.2 C

(below 50 C safety threshold)

• RF Breakdown rate statistics depends on numerous factors:RF pulsed heating, peak electric and magnetic field, Poynting vector S (modified)• Modified Poynting vector Sc=re(S)+im(S)/6 (A. Grudiev et. al.)• Safety threshold Sc < 6.3 MW/mm2 @50ns pulse

TRF = 50 ns, flat top

35.982 GHz cavity for the Compact light XLS project at Eacc=100MV/m caseRF Pulsed Heating and Modified Poynting Vector estimations

Main RF Parameters

Frequency 35.982 GHz

Accelerating Gradient 100 MV/m

Shunt Impedance 158 M/m

Quality Factor Q0 4110

E-field (V/m) H-field (A/m)

Sc ~ 5 MW/mm2

(below safety threshold)

Max Esurface = 250 MV/mMax Hsurface = 0.33 MA/m

RF Pulsed HeatingΔT = 16.5 C

(below 50 C safety threshold)

• RF Breakdown rate statistics depends on numerous factors:RF pulsed heating, peak electric and magnetic field, Poynting vector S (modified)• Modified Poynting vector Sc=re(S)+im(S)/6• Safety threshold Sc < 6.3 MW/mm2 @50ns pulse

TRF = 50 ns, flat top

35.982 GHz cavity for the Compact light XLS project at Eacc=125MV/m caseRF Pulsed Heating and Modified Poynting Vector estimations

Main RF Parameters

Frequency 35.982 GHz

Accelerating Gradient 125 MV/m

Shunt Impedance 158 M/m

Quality Factor Q0 4110

Sc ~ 8 MW/mm2

about 30% over safety threshold

• Hot spot = 40 C (standard operation). Possible to vary by adjusting water flux and temperature.• Stress Analysis shows yield strength (Von Mises) < 20 MPa (below safety threshold for copper ~ 70 MPa) • Maximum displacement ~ 1 m (frequency shift negligible)

• Cooling system will be optimized during final engineering (water jacket or brazed channels) in order to avoid water-to-vacuum leaks.

Thermal Simulation, single cell (35.982 GHz)

Pavg = 2 kW/mWater Flux=3 l/minHot spot ~ 40 C

*simplified cooling system for preliminary simulations

Yield strength < 20 MpaMax displacement~ 1 m

Stress Analysis (Von Mises), single cell (35.982 GHz)

CoolingChannels*

35.982 GHz cavity for the Compact light XLS projectThermal and Stress Analyses

2.800 mm

0.667 mm

7.320 mm2.660 mm

Wake fields studies on the 35.982 GHz structure (CST and ABCI software)

a/𝞴 = 0.16

vgr/c = 0.04

Rsh/m = 158 M𝛀 /m

Q = 4110


20 mm

252 mm

5 cells

90 cells

Wake fields studies on the 35.982 GHz structure (CST and ABCI software)


= 1 mm (bunch lenght)

= 0.5 mm (bunch lenght) [in order to confirm the K. Bane’s scaling scales for shortest bunches]

Longitudinal Loss factor[V/pC]

Transverse loss factor ( V/pC/m]

5 cells 18.2 16000

15 cells 54.3 46400

45 cells 161.5 136500

90 cells 319.4 268900

Bunch length (rms) : 1 mm

Wake fields studies on the 35.982 GHz structure

(CST and ABCI software)

252 mm90 cells


0

50

100

150

200

250

300

350

0 20 40 60 80 100

Longitudunal loss parameter as function of the

cells number of the structure at F = 35.982 GHz

Kl(V/pC)

y = 3,5585x

cells number

Wake fields studies on the 35.982 GHz structure

0

5 104

1 105

1,5 105

2 105

2,5 105

3 105

0 20 40 60 80 100

Transverse loss parameter as function of the

cells number of the structure at F = 35.982 GHz

Kt(V/pC/m)

y = 2999,5x

cells number

By assuming N = 90 cells (L= 252 mm), Kl 319.4 V/pC, Q = 100 pC

Elosses 32 KeV

Assuming N = 90 cells (L=252 mm), 𝑲𝒕 2.689 105V/pC/m, 𝒚(𝟎) = 10 10-6 m, Q = 100 pC ; E = 20 MeV

=𝒚(𝟎)

𝑬/𝒆Q 𝑲𝒕 13.45 10-6 rad


Longitudinal wakefields as function of the bunch head for a = 1 mm bunch lengthwith a = 1.333 mm, b = 3.657 mm, h = 0.667 mm (whole structure estimations)

KL = 319.35 V/pC



KT=268900 V/pC/m

Transverse wakefields as function of the bunch head for a = 1 mm bunch lengthwith a = 1.333 mm, b = 3.657 mm, h = 0.667 mm (whole structure estimations)

Longitudinal and transverse loss parameter as function of the bunch length (shorter bunches)

Y = 17.56 x-0.5 + 9.2

5 cells simulations

Y = 1.9 e4 x0.5 + 4 e3

(K. Bane-SLAC) (K. Bane-SLAC)

𝑲𝒕 ∝ 𝞈𝟐 𝞼1

𝒂𝟒

Longitudinal Transverse

Longitudinal and transverse loss parameter at F = 35.982 GHz as function of the iris aperture awith = 0.5 mm

5-cells structure

Y = 16.87 x-2 + 24.12

(K. Bane-SLAC) (K. Bane-SLAC)

Y = 1.6 e4 x-4 + 1.46 e4

𝑲𝒕 ∝ 𝞈𝟐 𝞼1

𝒂𝟒

Longitudinal Transverse

= 0.5 mm = 0.5 mm

Thank you very much for your attention

Documents

A possible linearizer at 35.982 GHz · Wake fields studies on the 35.982 GHz structure 0 5 10 4 1 10 5 1,5 10 5 2 10 5 2,5 10 5 3 10 5 0 20 40 60 80 100 Transverse loss parameter