1 Simulation of c onduction cooling of a 650 МHz 5-cell cavity

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Simulation of conduction cooling of a 650 МHz 5-cell

cavity

Roman Kostin

Euclid Techlabs, LLC., Bolingbrook, IL 60440

Abstract

The research note presents results of coupled RF and thermal simulation of a cryocooler

conduction cooled 650 MHz SRF cavity made of bulk niobium and coated with Nb3Sn on the RF

surface. The cavity is part of a particle accelerator design capable of producing 10 MeV,

1000 kW electron beam for application in wastewater treatment. More details of the accelerator

design are presented in R.C. Dhuley et al. (2022) Phys. Rev. Accel. Beams 25, 041601.

1. Introduction

Cryocooler conduction cooling of superconducting radiofrequency (SRF) Nb3Sn cavities [1] is a

dramatically simpler cooling scheme than the conventional liquid helium bath cooling. The

simpler and more reliable cryogenic scheme [2-7] can lead to wider adoption of the SRF

accelerator technology, particularly in the industrial area where high power electron beams are

required. Some examples are irradiation treatment of industrial and municipal wasterwater,

medical device sterilization, asphalt pavement curing, and scientific instruments such as UED

and UEM [8-10].

Due to limited cooling capacity of present day cryocoolers, it is imperative to properly design the

conduction cooling scheme than enhances the total thermal conductance of the cryocooler-cavity

system and also designing a cryostat enclosure that reduces the total heat leak into the system.

The cryostat design is presented in [8] while this research note focuses on thermal simulation

results of the conduction cooling system.

2. Simulation inputs

Thermal simulations of a 5-cell 650MHz Nb3Sn cavity is performed. The cavity provides

10 MeV beam that is accelerated from 300 keV by external injection. The 3D model of the cavity

is presented in Fig. 1. As one can see from this figure, six PT-420 are used for the cavity cells

cooling and two PT-425 are used for intercepting heat from RF fundamental power couplers. Fig.

2 shows cooling capacity of the two cryocoolers.

Fig. 1. 3D model of the 5cell 10MeV cavity

cooled by 6 PT-420 and 2 PT-425 cryocoolers.

Fig. 2. Capacity maps of PT-420 (2W at 4.2K)

and PT-425 (2.5W at 4.2K).

The heat sources to the cavity are presented in Table 1. These are conduction to the cavity

beampipes, thermal radiation, dynamic losses from RF and some heat dissipation due to the

beam loss. The total heat dissipation is around 20 W at 5 K for the cavity, scaled from a quality

factor of Q0=2e10 at 4.4 K.

0 2 4 6 8 10

P,W

Axis Title

Cap Map, Cryomech

PT-420

PT-425

Material properties required for the simulation are taken from the following sources: thermal

conductivity of bulk niobium from [11], BCS resistance of Nb3Sn from [12], thermal

conductivity of bulk aluminum from [13], thermal contact resistance from [14,15], and

cryocooler capacity from [16].

Table 1: Expected 5 K heat load on the 5-cell 650 MHz SRF cavity

Component

Heat load

[W]

Comment

Cavity body

Dynamic

11.7

RF dissipation at 5 K

Radiation

0.05

from thermal shield

Beam loss

1e-6 loss

Conduction

0.1

from supports

Total

12.9

Cavity injection side

Conduction

0.05

Beam pipe conduction

Radiation

0.24

Input port radiation

Total

0.29

Cavity body + injection

side

13.2

Cavity high-energy side

Coupler

two couplers, static + dynamic,

scaled from 100 kW

Conduction

0.05

Beam pipe conduction

Radiation

0.24

Input port radiation

Total

6.3

Cavity high-energy side

6.3

Cavity total

19.5

There are two different types of cavities: with internal and external injection. The cavity with

internal injection has lower energy beampipe opening of 35 mm and with external – 100 mm.

Both cavities’ electrodynamic paramters are presented in Table 2.

Table 2: “Preliminary” cavity parameters at 10 MV voltage gain.

It is worth to mention, that as was found later, surface electric field for 10 MeV energy gain

correpsonds to 36.5 mT and 17.5 MV/m [8]. The cavity under imvetigation is the cavity with

external injection. The provided information above is enough to proceed with thermal

simulations. We start with RF simulations to generate dynamic losses for the thermal module but

first field scaling to the required level is neededSimulations

3. 1st geometry case: Smaller OD beampipe

a. RF simulation and particle tracking

RF simulations were performed in order to provide a dynamic heat load for the cavity thermal

simulations. RF fields scaling to the required level is needed, i.e. when the cavity can provide an

energy gain of 10 MeV. The results obtained in Comsol were scaled by magnetic field to 36.5

mT which corresponds to 17.5 MV/m of electric field on surface and 18 MV/m electric field

amplitude on axis. One can find field distributions on axis and on the cavity surface on Fig.3.

Single particle tracking was done to find out if the obtained level of fields is enough to provide

10 MeV gain. The results of single particle tracking is presented on Fig. 4.

Electric field on the axis

Electric field on the surface

Magnetic field on the surface

Fig. 3. Electric field and Magnetic field in the 650 MHz 5-cell cavity with external injection to

provide 10 MeV gain to the beam.

Scale

0.7, Ø100

0.7, Ø35

R/Q, Ω

656.3

657.3

G, Ω

259.5

260.5

R/Q*G, 𝛀𝟐

170310

171230

𝑬𝒔, 𝒎𝒂𝒙, MV/m

21.2

21.

𝑯𝒔, 𝒎𝒂𝒙,mT

34.8

34.3

𝑷𝒍𝒐𝒔𝒔 , W

0.6∙𝑹𝒔

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摘要：

1Simulationofconductioncoolingofa650МHz5-cellcavityRomanKostinEuclidTechlabs,LLC.,Bolingbrook,IL60440AbstractTheresearchnotepresentsresultsofcoupledRFandthermalsimulationofacryocoolerconductioncooled650MHzSRFcavitymadeofbulkniobiumandcoatedwithNb3SnontheRFsurface.Thecavityispartofaparticleaccelerato...

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1 Simulation of c onduction cooling of a 650 МHz 5-cell cavity

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