A. Sukhanov

Fermilab, TD SRF T&D

HOMSC 2018, Cornell UniversityOctober 1-3, 2018

Update on HOM studies for PIP II SC Linac

PIP-II Project

•Mission: deliver intense beam of neutrinos to the international LBNF/DUNE project

•Goals:

‣ Deliver >1 MW proton beam power from the Fermilab Main Injector over the energy range 60 — 120 GeV, at the start of LBNF operation

‣ Support ongoing 8 GeV program at Fermilab, including upgrade path for Mu2e

‣ Possibility of extension of beam power to LBNF >2 MW

‣ Possibility of extension to high duty factor/higher beam power

2

PIP-II Project

• PIP-II Linac

3

8

Figure 1‐1: Site layout of PIP‐II (north is to the right). New construction includes the linac enclosure, transfer line enclosure (including the beam abort area and a stub to facilitate future connection to the Muon Campus), linac gallery, utility building, and cryo/compressor building. The blue areas denote identified wetland areas.   

PIP-II provides a variety of straightforward and cost effective upgrade paths. Delivery of more than 2 MW to the LBNF target will require replacement of the existing Booster. The most straightforward strategy would be to extend the 0.8 GeV linac to 1.5-2 GeV and to inject at this energy into a newly constructed 8-GeV rapid cycling synchrotron (RCS). Such a synchrotron could either be of a conventional sort, as currently deployed at the J-PARC facility in Japan, or could incorporate novel design features based on highly non-linear optical elements currently under study at Fermilab. In either case, the siting shown in Figure 1.1 is compatible with siting of such a RCS to the south of the linac, providing capabilities for injecting beam into the Main Injector.

Parameter

Particle species H-

Input beam energy 2.1 MeV

Output beam energy 800 MeV

Bunch repetition rate 162.5 MHz

RF pulse length pulsed-to-CW

Sequence of bunches Programmable

Average beam current 2 mA

Final rms norm trans. emittance

<= 0.3 mm-mrad

Final rms norm long. emittance

<= 0.35 mm-mrad

RMS bunch length < 4 ps

PIP-II Project

• PIP-II Linac

4

HWR SSR1 SSR2Elliptical 5-cell

Cavity Aperture, mm Eff. length, cm Eacc, MV/m Epeak, MV/m Bpeak, mT (R/Q), Ohm G, Ohm

LB650 88 70.3 16.9 40.3 74.6 341 193

HB650 118 106.1 18.8 38.9 73.1 610 260

CM #cav/CM #CM CM config CM length, m Q0 x1e10, @2K Rs, nOhm QL, x1e6

LB650 3 11 ccc 4.32 2.15 9.0 10.36

HB650 6 4 cccccc 9.92 3 8.7 9.92

LB650 HB650

HOM in PIP II (a.k.a. Project X)

• Presented at HOMSC 2012, published in Proceedings

5

Higher Order Modes in the Project-X Linac

V. Yakovlev, Fermilab

HOM in PIP II• Complex beam current spectrum• No HOM couplers and dumpers (QL up to 1e7)

• Investigation of HOM various effects in PIP II reported at HOMSC 12:‣ found no big issues

• Here we consider HOM effects in PIP II‣ new modes of linac operation (long trains of 162.5 MHz bunches, 10 mA)

- important for accelerator-driven sub-critical system demonstration‣ modifications to LB650 cavity design

- optimization of EM and mechanical parameters, production process

6

Frequency, MHz0 20 40 60 80 100 120 140 160 180 200

, mA

nI~

-210

-110

1

Frequency, GHz2.5 3 3.5 4 4.5 5 5.5

Ωm

ax

(R/Q

),

1

10

210

R0 31.89± 137.7

f0 0.1515± 1.425

R0 31.89± 137.7

f0 0.1515± 1.425

Beam Dynamics in PIP2 Linac with 10 mA

Motivation

• Transverse misalignment of SRF cavities and beam offset lead to excitation of dipole HOMs

‣ depends on bunch charge, mode (R/Q), Qext

‣ excited dipole HOMs introduce additional kick on beam particles

‣ increase of transverse beam emittance

‣ small effect in a steady state (CW beam, no variations in beam current and/or bunch timing pattern)

• Study transverse emittance variations due to transitions (beam turn on) and bunch charge variations in HB650 section of PIP2 linac

‣ (R/Q) of dipole modes in LB650 are much smaller compared to HB650

8

Dipole modes in HB650

• (R/Q) depends on beam velocity

•Mode 1376 MHz: (R/Q)=80kOhm/m2, Qext=1e7

9

Linac layout

•HB650 beta=0.92 section: 4 cryo-modules, 24 cavities (6 cavities per CM)

•Matrix tracking through linac elements

10

HB650 (6-cavity) Period

NC Doublet

CavityFieldMap

1.316m 1.525m

CavityFieldMap

CavityFieldMap

1.44m

SC Cryomodule

0.6m

0.2m

10.97m

CavityFieldMap

CavityFieldMap

CavityFieldMap

NC Doublet

1.429m

•  150mmspaceaddedforgatevalveflangeandmagnetflange.

HBSec9on

Cavity Gradient and Quadrupole Fields

•HB650 Vacc(beta_G) = 20 MV

•HB650 Quad gradient 12 T/m

11

0

5

10

15

20

25

0 20 40 60 80 100 120

Am

plitu

de (M

V)

Cavity #

MEBTHWRSSR1SSR2

LB650HB650

0

5

10

15

20

0 20 40 60 80 100 120 140 160G

radi

ent (

T/m

)

Position of the Center (m)

MEBTHWR

LB650HB650

Model• 60 pC bunches with 10% variation, 162.5 MHz bunch frequency

‣ train of 5e6 bunches

• Transverse misalignment of cavities R.M.S. = 0.5 mm

• Matrix tracking through linac

• Consider one dipole mode with highest (R/Q)

• Each bunch introduces voltage V[i] = jcq(R/Q)x

‣ bunch sees half of this kick voltage

• Total kick seen by bunch is sum of voltages from all previous bunches with proper time dependent factors: ~exp(jwTb)*exp(-wTb/2Q)

• Simulate 100 linac configurations (time consuming)

‣ random variations of transverse displacement of cavities and HOM frequency with 1 MHz RMS

•Calculate effective RMS emittance at the end of linac from variations of (x,x’) of bunches

‣ compare to nominal emittance 0.3 mm*mrad (relative emittance)

12

Tracking in linac

• bunch trajectories in linac

13

z , m0 5 10 15 20 25 30 35 40 45 50

x , u

m

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Effective emittance

• Effective emittance at the end of linac for single linac configuration as a function of bunch number

14

bunch

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000310×

rela

tive

emitt

ance

cha

nge

0

5

10

15

20

25

30

-610×

Maximum emittance growth

Initial emittance growth after turn on, scales ~ Qext

Emittance variations due to Qb variations

Maximum emittance growth

• 100 configurations of linac with random cavity misalignment of 0.5 mm

‣ Median value of relative emittance growth is 4e-5

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Relative emittance growth0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-310×0

2

4

6

8

10

Longitudinal emittance

• 10 mA (presented in LINAC’12, TUPB054)

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Relative emittance growth, !"z

Pro

babi

lity

Blue – old design Red – new design

10 mA

New Design of LB 650 MHz 5-cell Cavities

New Designs of LB650 5-cell Cavities

•New designs of LB650 5-cell cavities have been developed at FNAL, INFN and VECC

‣ Optimization of EM and mechanical properties, production process

• 3-D RF simulation of cavities of each design (A. Lunin)

‣ calculate frequency spectra, QL, (R/Q) of monopole, dipole and quadrupole modes

18

Monopole modes

•QL and (R/Q)

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Frequency, GHz0 0.5 1 1.5 2 2.5

LQ

310

410

510

610

710

810

910

1010FNALINFNVECC

Frequency, GHz0 0.5 1 1.5 2 2.5

, O

hmz

(R/Q

)

-210

-110

1

10

210

310FNALINFNVECC

Dangerous trapped mode in VECCdesign: f=1.663 GHz, (R/Q)=18 OhmThis mode is relatively far from mainbeam current harmonics of 162.5 MHz

Dipole modes

•QL and (R/Q)

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Frequency, GHz0 0.5 1 1.5 2 2.5

LQ

310

410

510

610

710

810

910

1010FNALINFNVECC

Frequency, GHz0 0.5 1 1.5 2 2.5

2 ,

Ohm

/mt

(R/Q

)

-210

-110

1

10

210

310

410

510

610

710

810

Most possibly dangerous modes are:VECC: 0.974 GHz, (R/Q) = 38 hOhm/m**2df = 1 MHz FNAL: 0.973 GHz, (R/Q) = 35 kOhm/m**2df=2 MHz

Linac Layout

• LB650 beta=0.61 section: 11 cryo-modules, 33 cavities (3 cavities per CM)

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LB650 (3-cavity) Period

CavityFieldMap

0.6m

0.2m

NC Doublet

1.145m 1.184m

CavityFieldMap

CavityFieldMap

0.9m

SC Cryomodule

5.371m

NC Doublet

1.258m

•  150mmspaceaddedforgatevalveflangeandmagnetflange.

LBSec9on

Cavity Gradient and Quadrupole Fields

• LB650 Vacc(beta_G) = 12 MV

• LB650 Quad gradient 9 T/m

22

0

5

10

15

20

25

0 20 40 60 80 100 120

Am

plitu

de (M

V)

Cavity #

MEBTHWRSSR1SSR2

LB650HB650

0

5

10

15

20

0 20 40 60 80 100 120 140 160G

radi

ent (

T/m

)

Position of the Center (m)

MEBTHWR

LB650HB650

Model• 30 pC bunches with 10% variation, 162.5 MHz bunch frequency

‣ train of 1e5 bunches

‣ about 50% of bunches removed for injection at 44.705 MHz

• Transverse misalignment of cavities R.M.S. = 0.5 mm

• Matrix tracking through linac

• Consider one dipole mode with highest (R/Q)

• Each bunch introduces voltage V[i] = jcq(R/Q)x

‣ bunch sees half of this kick voltage

• Total kick seen by bunch is sum of voltages from all previous bunches with proper time dependent factors: ~exp(jwTb)*exp(-wTb/2Q)

• Simulate 100 linac configurations (time consuming)

‣ random variations of transverse displacement of cavities and HOM frequency with 1 MHz RMS

•Calculate effective RMS emittance at the end of linac from variations of (x,x’) of bunches

‣ compare to nominal emittance 0.3 mm*mrad (relative emittance)

23

bunch

0 10 20 30 40 50 60 70 80 90 100310×

rela

tive

emitt

ance

cha

nge

0

0.01

0.02

0.03

0.04

0.05

0.06-310×

Effective emittance

• Effective emittance at the end of linac for single linac configuration as a function of bunch number

24

Maximum emittance growth

Initial emittance growth after turn on, scales ~ Qext

Emittance variations due to Qb variations

Maximum emittance growth, VECC design

• 100 configurations of linac with random cavity misalignment of 0.5 mm

‣ Median value of relative emittance growth is 5e-5

‣ 95% of configurations have relative emittance growth less than 1e-3

25Relative emittance growth

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0010

5

10

15

20

25

30

35

40

45

Maximum emittance growth, FNAL design

• 100 configurations of linac with random cavity misalignment of 0.5 mm

‣ Median value of relative emittance growth is 2.5e-5

‣ 95% of configurations have relative emittance growth less than 1.5e-4

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Relative emittance growth0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0010

10

20

30

40

50

60

70

80

Conclusion

• Study effects of dipole HOM excitation on transverse beam dynamics in PIP2 linac with 10 mA peak current

‣ Considered mode with largest (R/Q)=80 kOhm/m2, f=1376 MHz, Qext=1e7

‣ 0.5 mm random cavity misalignment

‣ 10% bunch charge variations

• Relative emittance growth is 4e-5 - should not be a problem in PIP2 linac with 10 mA

• Study effects of dipole HOM excitation on transverse beam dynamics in LB650 section of PIP2 linac with different designs of LB650 cavities

‣ Considered modes with largest (R/Q)

- VECC design, mode 0.974 GHz, (R/Q)=38 Ohm/m**2, df=1MHz

- FNAL design, mode 0.973 GHz, (R/Q)=35 Ohm/m**2, df=2 Mhz

‣ 0.5 mm random cavity misalignment

‣ 10% bunch charge variations

• Relative emittance growth is 5e-5 for VECC design and 2.5e-5 for FNAL design

• No considerable effects are expected for INFN design

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